When preparing a solution of concentrated sulfuric acid. Acid solutions

GAPOU LO "Kirishi Polytechnic College"

Methodical manual to study

MDK.02.01 Basics of preparing samples and solutions of various concentrations

240700.01 for the specialty chemical analysis laboratory assistant.

Developed

Teacher: Rasskazova V.V.

2016

Table of contents

Content

pages

Solutions

3-15

Calculations for preparing solutions of salts and acids

Recalculation of concentration from one type to another.

Mixing and diluting solutions.Law of mixing solutions

Technique for preparing solutions.

15-20

Preparation of salt solutions

Preparation of acid solutions

Preparation of base solutions

Technique for determining the concentration of solutions.

21-26

Determination of concentration by densimetry

Determination of concentration titrimetrically.

Six rules for titration.

Conditions for titrimetric determination of the concentration of a substance

Preparation of titrated

Setting the solution titer

Computations in volumetric analysis.

26-28

SOLUTIONS

The concept of solutions and solubility

Both in quality and in quantitative analysis The main work is carried out with solutions. Usually, when we use the name “solution,” we mean true solutions. In true solutions, the solute in the form of individual molecules or ions is distributed among the solvent molecules.Solution- a homogeneous (homogeneous) mixture consisting of particles of a dissolved substance, a solvent and the products of their interaction.When a solid substance is dissolved in water or another solvent, the molecules of the surface layer pass into the solvent and, as a result of diffusion, are distributed throughout the entire volume of the solvent, then a new layer of molecules passes into the solvent, etc. Simultaneously with the solvent, the reverse process also occurs - the release of molecules from the solution. The higher the concentration of the solution, the more to a greater extent this process will take place. By increasing the concentration of the solution without changing other conditions, we reach a state in which per unit time the same number of molecules of the dissolved substance will be released from the solution as they are dissolved. This solution is calledsaturated. If you add to it at least small quantity solute, it will remain undissolved.

Solubility- the ability of a substance to form homogeneous systems with other substances - solutions in which the substance is in the form of individual atoms, ions, molecules or particles.The amount of substance in a saturated solution determinessolubility substances under given conditions. Solubility various substances in certain solvents is different. No more than a certain amount of a given substance can be dissolved in a certain amount of each solvent.Solubility expressed by the number of grams of a substance in 100 g of solvent in a saturated solution, at a given temperature. Based on their ability to dissolve in water, substances are divided into: 1) highly soluble (caustic soda, sugar); 2) sparingly soluble (gypsum, Berthollet salt); 3) practically insoluble (copper sulfite). Practically insoluble substances are often called insoluble, although there are no absolutely insoluble substances. “Insoluble substances are usually called those substances whose solubility is extremely low (1 part by weight of a substance dissolves in 10,000 parts of solvent).

Generally, the solubility of solids increases with increasing temperature. If you prepare a solution that is close to saturated by heating, and then quickly but carefully cool it, the so-calledsupersaturated solution. If you drop a crystal of a dissolved substance into such a solution or mix it, then crystals will begin to fall out of the solution. Consequently, a cooled solution contains more substance than is possible for a saturated solution at a given temperature. Therefore, when a crystal of a solute is added, all excess substance crystallizes out.

The properties of solutions always differ from the properties of the solvent. The solution boils at more than high temperature than pure solvent. On the contrary, the freezing point of the solution is lower than that of the solvent.

Based on the nature of the solvent, solutions are divided intoaquatic and non-aquatic. The latter include solutions of substances in organic solvents such as alcohol, acetone, benzene, chloroform, etc.

Solutions of most salts, acids, and alkalis are prepared in aqueous solutions.

Methods of expressing the concentration of solutions. The concept of gram equivalent.

Each solution is characterized by solute concentration: the amount of substance contained in a certain amount of solution. The concentration of solutions can be expressed as a percentage, in moles per 1 liter of solution, in equivalents per 1 liter of solution and by titre.

The concentration of substances in solutions can be expressed in different ways:

The mass fraction of the dissolved substance w(B) is a dimensionless quantity equal to the ratio of the mass of the dissolved substance to total mass solution m

w(B)= m(B) / m

or otherwise called:percentage concentration solution - determined by the number of grams of substance in 100 g of solution. For example, a 5% solution contains 5 g of substance in 100 g of solution, i.e. 5 g of substance and 100-5 = 95 g of solvent.

Molar concentration C(B) shows how many moles of solute are contained in 1 liter of solution.

C(B) = n(B) / V = m(B) / (M(B) V),

where M(B) - molar mass solute g/mol.

Molar concentration is measured in mol/L and is designated "M". For example, 2 M NaOH is a two-molar solution of sodium hydroxide;monomolar (1 M) solutions contain 1 mole of substance per 1 liter of solution, bimolar (2 M) solutions contain 2 moles per 1 liter, etc.

In order to establish how many grams of a given substance are in 1 liter of a solution of a given molar concentration, you need to know itmolar mass, i.e., the mass of 1 mole. The molar mass of a substance, expressed in grams, is numerically equal to the molecular mass of the substance. For example, the molecular weight of NaCl is 58.45, therefore, the molar mass is also 58.45 g. Thus, a 1 M NaCl solution contains 58.45 g of sodium chloride in 1 liter of solution.

The normality of a solution indicates the number of gram equivalents of a given substance in one liter of solution or the number of milligram equivalents in one milliliter of solution.
Gram equivalent of a substance is the number of grams of a substance that is numerically equal to its equivalent.

Compound Equivalent - they call the amount of it that corresponds (equivalent) to 1 mole of hydrogen in a given reaction.

The equivalence factor is determined by:

1) the nature of the substance,

2) a specific chemical reaction.

a) in metabolic reactions;

ACIDS

The equivalent value of acids is determined by the number of hydrogen atoms that can be replaced by metal atoms in the acid molecule.

Example 1. Determine the equivalent for acids: a) HCl, b) H 2 SO 4 , c) N 3 RO 4 ; d) N 4 .

Solution.

a) E= M.M/1

b) E= M.M/2

c) E= M.M/3

d) E= M.M/4

In the case of polybasic acids, the equivalent depends on the specific reaction:

A) H 2 SO 4 +2KOH→ K 2 SO 4 + 2H 2 O.

in this reaction, two hydrogen atoms are replaced in the sulfuric acid molecule, therefore, E = M.M/2

b) H 2 SO 4 + KOH→ KHSO 4 +H 2 O.

In this case, one hydrogen atom is replaced in the sulfuric acid molecule E = M.M/1

For phosphoric acid, depending on the reaction, the values are a) E = M.M/1

b) E= M.M/2 c) E= M.M/3

BASES

The base equivalent is determined by the number of hydroxyl groups that can be replaced by the acid residue.

Example 2. Determine the equivalent of the bases: a) KOH; b)Cu( OH) 2 ;

V)La( OH) 3 .

Solution.

a) E= M.M/1

b) E= M.M/2

c) E= M.M/3

SALT

Salt equivalent values are determined by cation.

The value by which M.M should be divided in the case of salts it is equalq·n , Whereq – charge of the metal cation,n – the number of cations in the salt formula.

Example 3. Determine the equivalent of salts: a) KNO 3 ; b)Na 3 P.O. 4 ; V)Cr 2 ( SO 4 ) 3;

G)Al( NO 3 ) 3.

Solution.

A)q·n = 1 b)1 3 = 3 V)z = 3 2 = 6, G)z = 3 1 = 3

The value of equivalence factors for salts also depends on

reaction, similar to its dependence for acids and bases.

b) in redox reactions to determine

equivalent use an electronic balance scheme.

The value by which the M.M for a substance must be divided in this case is equal to the number of electrons accepted or given up by a molecule of the substance.

TO 2 Cr 2 O 7 + HCl → CrCl 3 + Cl 2 + KCl + H 2 O

for straight 2Сr +6 +2·3e →2Cr 3+

2Cl reactions - - 2 1e →Cl 2

for reverse 2Cr+3-2 3e →Cr +6

Cl2-2 reactionse →2Cl

(K 2 Cr 2 O 7 )=1/6

(Cr)=1/3 (HCl)=1 (Cl)=1) (Cl2)=1/2 (Cl)=1

The normal concentration is indicated by the letterN (in calculation formulas) or the letter “n” - when indicating concentration of this solution. If 1 liter of solution contains 0.1 equivalent of a substance, it is called decinormal and is designated 0.1 N. A solution containing 0.01 equivalent of a substance in 1 liter of solution is called centinormal and is designated 0.01 N. Since the equivalent is the amount of any substance that is in a given reaction. corresponds to 1 mole of hydrogen, obviously, the equivalent of any substance in this reaction must correspond to the equivalent of any other substance. And this means thatIn any reaction, substances react in equivalent quantities.

Titrated are called solutions whose concentration is expressedcaption, i.e., the number of grams of a substance dissolved in 1 ml of solution. Very often in analytical laboratories, solution titers are recalculated directly to the substance being determined. TogYes The titer of a solution shows how many grams of the substance being determined corresponds to 1 ml of this solution.

To prepare solutions of molar and normal concentrations, a sample of the substance is weighed on an analytical balance, and the solutions are prepared in a volumetric flask. When preparing acid solutions, the required volume of concentrated acid solution is measured with a burette with a glass stopcock.

The weight of the solute is calculated to the fourth decimal place, and the molecular weights are taken with the accuracy with which they are given in the reference tables. The volume of concentrated acid is calculated to the second decimal place.

When preparing solutions of percentage concentration, the substance is weighed on a technical-chemical balance, and liquids are measured with a measuring cylinder. Therefore, the weight of a substance is calculated with an accuracy of 0.1 g, and the volume of 1 liquid with an accuracy of 1 ml.

Before starting to prepare the solution, it is necessary to make a calculation, i.e., calculate the amount of solute and solvent to prepare a certain amount of a solution of a given concentration.

Calculations for preparing salt solutions

Example 1. It is necessary to prepare 500 g of a 5% solution of potassium nitrate. 100 g of such a solution contains 5 g KN0 3 ; Let's make a proportion:

100 g solution - 5 g KN0 3

500" -X » KN0 3

5*500/100 = 25 g.

You need to take 500-25 = 475 ml of water.

Example 2. It is necessary to prepare 500 g of 5% CaC solutionIfrom salt CaCl 2 .6N 2 0. First, we perform the calculation for anhydrous salt.

100 g solution - 5 g CaCl 2

500 "" -x g CaC1 2

5*500/ 100 = 25 g

Molar mass of CaCl 2 = 111, molar mass of CaCl 2 6H 2 0 = 219. Therefore,

219 g CaCl 2 *6H 2 0 contain 111 g CaCl 2 . Let's make a proportion:

219 g CaCl 2 *6H 2 0 -- 111 g CaCl 2

X » CaС1 2 -6H 2 0- 25 "CaCI 2 ,

219*25/ 111= 49.3 g.

The amount of water is 500-49.3=450.7 g, or 450.7 ml. Since water is measured using a measuring cylinder, tenths of a milliliter are not taken into account. Therefore, you need to measure 451 ml of water.

4. Calculations for preparing acid solutions

When preparing acid solutions, it is necessary to take into account that concentrated acid solutions are not 100% and contain water. In addition, the required amount of acid is not weighed out, but measured using a measuring cylinder.

Example 1. You need to prepare 500 g of a 10% solution hydrochloric acid, based on the available 58% acid, the density of which is d=l.19.

1. Find the amount of pure hydrogen chloride that should be in the prepared acid solution:

100 g solution -10 g HC1

500 "" -X » NS1

500*10/100= 50 g

To calculate solutions of percentage concentration, molar mass is rounded to whole numbers.

2. Find the number of grams of concentrated acid that will contain 50 g of HC1:

100 g acid - 38 g HC1

X » » - 50 » NS1

100 50/38 = 131.6 g.

3. Find the volume occupied by this amount of acid:

V= 131,6 / 1,19= 110, 6 ml. (round to 111)

4. The amount of solvent (water) is 500-131.6 = 368.4 g, or 368.4 ml. Since the required amount of water and acid is measured with a measuring cylinder, tenths of a milliliter are not taken into account. Therefore, to prepare 500 g of a 10% hydrochloric acid solution, you need to take 111 ml of hydrochloric acid and 368 ml of water.

Example 2. Usually, when making calculations for the preparation of acids, standard tables are used, which indicate the percentage of the acid solution, the density of this solution at a certain temperature and the number of grams of this acid contained in 1 liter of a solution of this concentration. In this case, the calculation is simplified. The amount of acid solution prepared can be calculated for a certain volume.

For example, you need to prepare 500 ml of a 10% hydrochloric acid solution based on a concentrated 38% solution. According to the tables, we find that a 10% solution of hydrochloric acid contains 104.7 g of HC1 in 1 liter of solution. We need to prepare 500 ml, therefore, the solution should contain 104.7:2 = 52.35 g of HCl.

Let's calculate how much concentrated acid you need to take. According to the table, 1 liter of concentrated HC1 contains 451.6 g of HC1. Let's make a proportion:

1000 ml-451.6 g HC1

X ml - 52.35 "NS1

1000*52.35/ 451.6 =115.9 ml.

The amount of water is 500-116 = 384 ml.

Therefore, to prepare 500 ml of a 10% solution of hydrochloric acid, you need to take 116 ml of a concentrated solution of HC1 and 384 ml of water.

Example 1. How many grams of barium chloride are needed to prepare 2 liters of 0.2 M solution?

Solution. The molecular weight of barium chloride is 208.27. Hence. 1 liter of 0.2 M solution should contain 208.27 * 0.2 = = 41.654 g of BaCI 2 . To prepare 2 liters you will need 41.654*2 = 83.308 g of VaCI 2 .

Example 2. How many grams of anhydrous soda Na 2 C0 3 you will need to prepare 500 ml of 0.1 N. solution?

Solution. The molecular weight of soda is 106.004; equivalent mass of Na 2 C0 3 =M: 2 = 53.002; 0.1 eq. = 5.3002 g

1000 ml 0.1 n. solution contain 5.3002 g Na 2 C0 3
500 »» » » »X » Na 2 C0 3

x= 2.6501 g Na 2 C0 3 .

Example 3. How much concentrated sulfuric acid (96%: d=l.84) is required to prepare 2 liters of 0.05 N. sulfuric acid solution?

Solution. The molecular weight of sulfuric acid is 98.08. Equivalent mass of sulfuric acid H 2 so 4 =M: 2 = 98.08: 2 = 49.04 g. Mass 0.05 eq. = 49.04*0.05 = 2.452 g.

Let's find how many H 2 S0 4 should contain 0.05 N in 2 liters. solution:

1 l-2.452 g H 2 S0 4

2"-X » H 2 S0 4

X = 2.452*2 = 4.904 g H 2 S0 4 .

To determine how much 96.% H solution should be taken for this 2 S0 4 , let's make a proportion:

in 100 g conc. H 2 S0 4 -96 g H 2 S0 4

U » » H 2 S0 4 -4.904 g H 2 S0 4

Y = 5.11 g H 2 S0 4 .

We recalculate this amount to volume: 5,11:1.84=2.77

Thus, to prepare 2 liters of 0.05 N. solution you need to take 2.77 ml of concentrated sulfuric acid.

Example 4. Calculate the titer of a NaOH solution if it is known that its exact concentration is 0.0520 N.

Solution. Let us recall that the titer is the content in 1 ml of a solution of a substance in grams. Equivalent mass of NaOH=40. 01 g Let's find how many grams of NaOH are contained in 1 liter of this solution:

40.01*0.0520 = 2.0805 g.

1 liter of solution contains 1000 ml.

T=0.00208 g/ml. You can also use the formula:

T=E N/1000 g/l

WhereT - titer, g/ml;E - equivalent mass;N- normality of the solution.

Then the titer of this solution is: 40.01 0.0520/1000=0.00208 g/ml.

Example 5 Calculate the normal concentration of a solution HN0 3 , if it is known that the titer of this solution is 0.0065 To calculate, we use the formula:

T=E N/1000 g/l, from here:

N=T1000/E 0,0065.1000/ 63.05= 0.1030 n.

Example 6. What is the normal concentration of a solution if it is known that 200 ml of this solution contains 2.6501 g of Na 2 C0 3

Solution. As calculated in example 2: ENA 2 with 3 =53,002.
Let's find how many equivalents are 2.6501 g of Na 2 C0 3 :
2.6501: 53.002 = 0.05 eq.

In order to calculate the normal concentration of a solution, we create a proportion:

200 ml contain 0.05 eq.

1000 ""X "

X=0.25 eq.

1 liter of this solution will contain 0.25 equivalents, i.e. the solution will be 0.25 N.

For this calculation you can use the formula:

N =P 1000/E V

WhereR - amount of substance in grams;E - equivalent mass of the substance;V - volume of solution in milliliters.

ENA 2 with 3 =53.002, then the normal concentration of this solution is

2,6501* 1000 / 53,002*200=0,25

5. Recalculation of concentration from one type to another .

In laboratory practice, it is often necessary to recalculate the concentration of available solutions from one unit to another. When converting percentage concentration to molar concentration and vice versa, it is necessary to remember that the percentage concentration is calculated for a certain mass of the solution, and the molar and normal concentration is calculated for the volume, therefore, for conversion, you need to know the density of the solution.

The density of the solution is given in reference books in the corresponding tables or measured with a hydrometer. If we denote:WITH - percentage concentration;M - molar concentration;N- normal concentration;d - solution density;E - equivalent mass;m - molar mass, then the formulas for converting from percentage concentration to molar and normal concentration will be as follows:

Example 1. What is the molar and normal concentration of a 12% sulfuric solutionacid whose densityd=l.08g/cm??

Solution. The molar mass of sulfuric acid is98. InvestigatorBut,

E n 2 so 4 =98:2=49.

Substituting the required valuesVformulas, we get:

1) molar concentration12% sulfuric acid solution is equal to

M=12*1.08 *10/98=1.32 M;

2) normal concentration12% sulfuric acid solutionequal to

N= 12*1.08*10/49= 2.64 n.

Example 2. What is the percentage concentration of 1 N. hydrochloric acid solution, the density of which is1,013?

Solution. MolnayaweightNSIequal to 36.5,therefore Ens1=36,5. From the above formula(2) we get:

C= N*E/10d

therefore the percentage concentration1 n. hydrochloric acid solution is equal to

36,5*1/ 1,013*10 =3,6%

Sometimes in laboratory practice it is necessary to recalculate the molar concentration to normal and vice versa. If the equivalent mass of a substance is equal to the molar mass (for example, KOH), then the normal concentration is equal to the molar concentration. So, 1 n. a solution of hydrochloric acid will simultaneously be a 1 M solution. However, for most compounds the equivalent mass is not equal to the molar mass and, therefore, the normal concentration of solutions of these substances is not equal to the molar concentration. To convert from one concentration to another, we can use the formulas:

M = (NE)/m; N=M(m/E)

Example 3. Normal concentration of 1M sulfuric acid solution Answer-2M

Example 4, Molar concentration 0.5 N. Na solution 2 CO 3 The answer is 0.25N

When converting percentage concentration to molar concentration and vice versa, it is necessary to remember that percentage concentration is calculated for a certain mass of the solution, and molar and normal concentration is calculated for volume, so for conversion you need to know the density of the solution. If we denote: c - percentage concentration; M - molar concentration; N - normal concentration; e - equivalent mass, r - solution density; m is molar mass, then the formulas for conversion from percentage concentration will be as follows:

M = (s p 10)/m
N = (c p 10)/e

The same formulas can be used if you need to convert normal or molar concentration to percentage.

Sometimes in laboratory practice it is necessary to recalculate the molar concentration to normal and vice versa. If the equivalent mass of a substance is equal to the molar mass (For example, for HCl, KCl, KOH), then the normal concentration is equal to the molar concentration. So, 1 n. a solution of hydrochloric acid will simultaneously be a 1 M solution. However, for most compounds the equivalent mass is not equal to the molar mass and, therefore, the normal concentration of solutions of these substances is not equal to the molar concentration.
To convert from one concentration to another, you can use the following formulas:

M = (N E)/m
N = (M m)/E

6. Mixing and diluting solutions.

If a solution is diluted with water, its concentration will change in inverse proportion to the change in volume. If the volume of a solution doubles due to dilution, then its concentration will also decrease by half. When mixing several solutions, the concentrations of all mixed solutions decrease.

When two solutions of the same substance but different concentrations are mixed, a solution of a new concentration is obtained.

If you mix a% and b% solutions, you will get a solution with % concentration, and if a>b, then a>c>b. The new concentration is closer to the concentration of the solution of which a larger amount was taken during mixing.

7. Law of mixing solutions

The quantities of mixed solutions are inversely proportional to the absolute differences between their concentrations and the concentration of the resulting solution.

The law of mixing can be expressed by a mathematical formula:

mA/ mB=S-b/a-s,

WheremA, mB– quantities of solutions A and B taken for mixing;

a, b, c-respectively, the concentrations of solutions A and B and the solution obtained as a result of mixing. If the concentration is expressed in %, then the quantities of mixed solutions must be taken in weight units; if concentrations are taken in moles or normals, then the quantities of mixed solutions must be expressed only in liters.

For ease of usemixing rules applyrule of the cross:

m1 / m2 = (w3 – w2) / (w1 – w3)

To do this, diagonally from greater value concentrations subtract the smaller one, get (w 1 – w 3 ), w 1 >w 3 and (w 3 – w 2 ), w 3 >w 2 . Then the ratio of the masses of the initial solutions m is calculated 1 /m 2 and calculate.

Example
Determine the masses of the initial solutions with mass fractions of sodium hydroxide 5% and 40%, if mixing them resulted in a solution weighing 210 g with mass fraction sodium hydroxide 10%.

5 / 30 = m 1 / (210 - m 1 )
1/6 = m 1 / (210 – m 1 )
210 – m 1 = 6m 1
7m 1 = 210
m 1 =30 g; m 2 = 210 – m 1 = 210 – 30 = 180 g

TECHNIQUES FOR PREPARING SOLUTIONS.

If the solvent is water, then only distilled or demineralized water should be used.

Pre-prepare the appropriate container in which the resulting solution will be prepared and stored. The dishes must be clean. If there is concern that the aqueous solution may interact with the material of the dishes, then the inside of the dishes should be coated with paraffin or other chemically resistant substances.

Before preparing solutions, you need to prepare, if possible, 2 identical vessels: one for dissolving, and the other for storing the solution. Pre-calibrate the washed vessel.

Pure substances should be used for dissolution. Prepared solutions must be checked for the content of the required substance and, if necessary, the solution is corrected. It is necessary to take measures to protect the prepared solutions from dust or gases with which some solutions may react.

During preparation and during storage of solutions, bottles or other containers must be capped.

For particularly precise analyses, the possibility of glass leaching should be taken into account and, if possible, quartz glassware should be used.

In this case, it is better to leave solutions in porcelain dishes rather than in glass.

1. Technique for preparing salt solutions.

Approximate solutions.

The finished solution is either filtered or allowed to settle from water-insoluble impurities, after which a clear solution is separated using a siphon. It is useful to check the concentration of each prepared solution. The easiest way to do this is to measure the density with a hydrometer and compare the resulting value with tabular data. If the solution has a concentration less than a given one, the required amount of dissolved solid is added to it. If the solution has a concentration greater than the specified one, add it to water and adjust the concentration to the required one.

Precise solutions.

Accurate solutions of salts are most often prepared for analytical purposes, and usually of normal concentration. Some of the precise solutions are not stable enough during storage and may change under the influence of light or oxygen, or other organic impurities contained in the air. Such precise solutions are checked periodically. In an accurate solution of sodium sulphate, when standing, sulfur flakes often appear. This is the result of the vital activity of a particular type of bacteria. Solutions of potassium permanganate change when exposed to light, dust and impurities of organic origin. Solutions of silver nitrate are destroyed when exposed to light. Therefore, you should not have large reserves of precise salt solutions that are unstable for storage. Solutions of such salts are stored in compliance with known precautions. Solutions change under the influence of light:AgNO 3, KSCN, N.H. 4 SCN, KI, I 2, K 2 Cr 2 O 7.

2. Technique for preparing acid solutions.

In most cases, solutions of hydrochloric, sulfuric and nitric acids are used in the laboratory. Concentrated acids are supplied to laboratories; The percentage of acids is determined by density.

To prepare a solution, fill a 1-liter flask with distilled water (halfway), add the required amount of a substance with a certain density, stir, and then add up to a liter of volume. During dilution, the flasks become very hot.

Exact solutions are prepared in the same way, using chemically pure preparations. Solutions are prepared at a higher concentration, which is further diluted with water. Solutions of exact concentration are checked by titration with sodium carbonate (Na 2 CO 3 ) or acid potassium carbonate (KHCO 3 ) and “correct”.

3. Technique for preparing alkali solutions.

The most commonly used solution is caustic soda (NaOHInitially, a concentrated solution (approximately 30-40%) is prepared from the solid substance. During dissolution, the solution is strongly heated. As a rule, lye is dissolved in porcelain dishes. The next step is settling the solution.

Then the transparent part is poured into another container. Such a container is equipped with a calcium chloride tube to absorb carbon dioxide. To prepare a solution of approximate concentration, the density is determined using a hydrometer. Storing concentrated solutions in glass containers is permitted if the surface of the glass is covered with paraffin, because otherwise the glass will leach.
To prepare precise solutions, chemically pure alkali is used. The prepared solution is checked by titration with oxalic acid and corrected.

4. Preparation of a working solution from fixanal.

Fixanaly- these are precisely weighed quantities of solid chemically pure substances or precisely measured volumes of their solutions, placed in sealed glass ampoules.

Fixanals are prepared at chemical plants or in special laboratories. Most often, the ampoule contains 0.1 or 0.01g-eq substances. Most fixanals are well preserved, but some of them change over time. Thus, solutions of caustic alkalis become cloudy after 2-3 months due to the interaction of the alkali with the glass of the ampoule.

To prepare a solution from fixanal, the contents of the ampoule are transferred quantitatively into a volumetric flask, the solution is diluted with distilled water, bringing its volume to the mark.

This is done as follows: the strikers in the box with the fixanal are washed first with tap water and then with distilled water. One striker is inserted into a clean chemical funnel 3 so that the long end of the striker enters the funnel tube, and its short (sharp) end is directed upward; the cross-shaped thickening of the striker rests on the lower part of the funnel body. The funnel along with the striker is inserted into a clean volumetric flask.

The ampoule is washed first with warm and then with cold distilled water to wash off the label and dirt. The bottom of a well-washed ampoule is hit (where there is a depression) against the striker in the funnel and the bottom of the ampoule is broken. Without changing the position of the ampoule above the funnel, the second striker pierce the upper recess on it.

The contents of the ampoule are poured (or poured) into a volumetric flask. Without changing the position of the ampoule, insert the end of the washing tube drawn into the capillary into the formed upper hole and wash the ampoule from the inside with a strong stream. Then, with a stream of water from the washer, thoroughly wash the outer surface of the ampoule and the funnel with the striker. After removing the ampoule from the funnel, bring the liquid level in the flask to the mark. The flask is tightly capped and the solution is thoroughly mixed.

TECHNIQUE FOR DETERMINING THE CONCENTRATION OF SOLUTIONS.

The concentration of a substance in a solution is determined by densimetry and titrimetric methods.

1. Densimetry measures the density of the solution, knowing which the weight % concentration is determined from the tables.

2. Titrimetric analysis is a quantitative analysis method in which the amount of reagent consumed during chemical reaction.

1. Determination of concentration by densimetry. Density concept

Density - physical quantity, determined for a homogeneous substance by the mass of its unit volume. For an inhomogeneous substance, the density at a certain point is calculated as the limit of the ratio of the mass of the body (m) to its volume (V), when the volume contracts to this point. The average density of a heterogeneous substance is the ratio m/V.

The density of a substance depends on its mass , of which it consists, and on the packing densityatomsand molecules in matter. The greater the massatoms, the greater the density.

Types of density and units of measurement

Density is measured in kg/m³ in the SI system and in g/cm³ in the GHS system, the rest (g/ml, kg/l, 1 t/ ) – derivatives.

For granular and porous bodies there are:

- true density, determined without taking into account voids

-apparent density, calculated as the ratio of the mass of a substance to the entire volume it occupies.

Dependence of density on temperature

As a rule, as the temperature decreases, the density increases, although there are substances whose density behaves differently, for example, water, bronze andcast iron.

Thus, the density of water has a maximum value at 4 °C and decreases with both increasing and decreasing temperature.

2. Determination of concentration titrimetric analysis

In titrimetric analysis, two solutions are forced to react and the end of the reaction is determined as accurately as possible. Knowing the concentration of one solution, you can determine the exact concentration of another.

Each method uses its own working solutions and indicators, and solves the corresponding typical problems.

Depending on the type of reaction that occurs during titration, several methods of volumetric analysis are distinguished.

Of these, the most commonly used are:

1. Neutralization method. The main reaction is the neutralization reaction: the interaction of an acid with a base.
2.Method of oxidimetry, including methods of permanganatometry and iodometry. It is based on oxidation-reduction reactions.
3.Deposition method. It is based on the formation of poorly soluble compounds.
4. Complexometry method - for the formation of low-dissociating complex ions and molecules.

Basic concepts and terms of titrimetric analysis.

Titrant - a reagent solution of known concentration (standard solution).

Standard solution – Primary secondary standard solutions are distinguished according to the method of preparation. Primary is prepared by dissolving an exact amount of pure chemical substance in a certain amount of solvent. The secondary is prepared at an approximate concentration and its concentration is determined using the primary standard.

Equivalence point – the moment when the added volume of the working solution contains an amount of substance equivalent to the amount of the substance being determined.

Purpose of titration - precise measurement volumes of two solutions containing an equivalent amount of substance

Direct titration – this is the titration of a certain substance “A” directly with titrant “B”. It is used if the reaction between “A” and “B” proceeds quickly.

Scheme of titrimetric determination.

To carry out titrimetric determination, standard (working) solutions are required, that is, solutions with exact normality or titer.
Such solutions are prepared by exact or approximate weighing, but then the exact concentration is determined by titration using solutions of setting substances.

For acids, the installation solutions are: sodium tetraborate (borax), sodium oxalate, ammonium oxalate.
For alkalis: oxalic acid, succinic acid

Preparation of the solution includes three stages:
Weight calculation
Taking a hitch
Dissolution of the sample
If the concentration is determined using an accurate sample, it is weighed on an analytical balance.

If the concentration cannot be determined from an accurate sample, then it is taken on a technochemical balance, and in the case of liquid substances, the calculated volume is measured.

To determine the exact concentration, titration is carried out, which consists in the fact that two solutions react with each other and the equivalence point is fixed using an indicator.

The concentration of one of the solutions (working) is precisely known. Typically, it is placed in a burette. The second solution with an unknown concentration is pipetted into conical flasks in strictly defined volumes (pipetting method), or an exact sample is dissolved in an arbitrary amount of solvent (separate sample method). An indicator is added to each flask. Titration is carried out at least 3 times until the results converge; the difference between the results should not exceed 0.1 ml. The definition ends with the calculation of the analysis results. The most important point is to fix the equivalence point.

Six rules for titration .

1. Titration is carried out in conical glass flasks;

2. The contents of the flask are mixed with rotational movements without removing the flask from under the burette.

3. The extended end of the burette should be 1 cm below the top edge of the flask. The liquid level in the burette is set to zero before each titration.

4. Titrate in small portions - drop by drop.

5. Titration is repeated at least 3 times until consistent results are obtained with a difference of no more than 0.1 ml.

6. After the end of the titration, the divisions are counted after 20-30 seconds to allow the liquid remaining on the walls of the burette to drain.

Conditions for titrimetric determination of the concentration of a substance.

In volumetric analysis, the main operation is to measure the volume of two interacting solutions, one of which contains the analyte, and the concentration of the second is known in advance. The unknown concentration of the analyzed solution is determined by knowing the ratio of the volumes of the reacting solutions and the concentration of one of them.

To successfully carry out volumetric analysis, the following conditions must be met:

The reaction between the reacting substances must go to completion and proceed quickly and quantitatively.

Since during titration it is necessary to accurately establish the moment of equivalence or fix the equivalence point, the end of the reaction between solutions should be clearly visible by a change in the color of the solution or by the appearance of a colored precipitate.

Indicators are often used to establish the equivalence point in volumetric analysis

The concentration of the solution of one of the solutions (working solution) must be precisely known. Other substances in the solution should not interfere with the main reaction.

Preparation of standard solutions.

1. Preparation of titrated solution according to an exact weighing of the starting substance

The main solution in volumetric analysis is titrated, orstandard- a solution of the initial reagent, during titration of which the content of the substance in the analyzed solution is determined.

The most in a simple way preparing a solution of precisely known concentration, i.e. characterized by a certain titer, is to dissolve an accurate weighed portion of the original chemically pure substance in water or another solvent and dilute the resulting solution to the required volume. Knowing the mass (A ) of a chemically pure compound dissolved in water and the volume (V) of the resulting solution, it is easy to calculate the titer (T) of the prepared reagent:

T = a/V (g/ml)

This method prepares titrated solutions of substances that can be easily obtained in pure form and the composition of which corresponds to a precisely defined formula and does not change during storage. The direct method of preparing titrated solutions is used only in certain cases. In this way, it is impossible to prepare titrated solutions of substances that are highly hygroscopic, easily lose water of crystallization, are exposed to atmospheric carbon dioxide, etc.

2. Setting the solution titer using setting agent

This method of setting titers is based on preparing a reagent solution of approximately the required normality and then precise definition concentrations obtained.Titerornormalitythe prepared solution is determined by titrating solutions of the so-calledinstallation substances.

A setting substance is a chemically pure compound of precisely known composition, used to set the titer of a solution of another substance.

Based on the titration data of the setting substance, the exact titer or normality of the prepared solution is calculated.

A solution of a chemically pure setting substance is prepared by dissolving its calculated amount (weighed on an analytical balance) in water and then bringing the volume of the solution to a certain value in a volumetric flask. Separate (aliquot) parts of the solution prepared in this way are pipetted from a volumetric flask into conical flasks and titrated with a solution whose titer is established. Titration is carried out several times and the average result is taken.

COMPUTATIONS IN VOLUMETRIC ANALYSIS.

1. Calculation of the normality of the analyzed solution based on the normality of the working solution

When two substances interact, a gram equivalent of one reacts with a gram equivalent of the other. Solutions of different substances of the same normality contain equal volumes the same number of gram equivalents of the solute. Consequently, equal volumes of such solutions contain equivalent amounts of the substance. Therefore, for example, to neutralize 10 ml of 1N. HCI requires exactly 10 ml of 1N. NaOH solution.Solutions of the same normality react in equal volumes.

Knowing the normality of one of the two reacting solutions and their volumes spent on titrating each other, it is easy to determine the unknown normality of the second solution. Let us denote the normality of the first solution by N 2 and its volume through V 2 . Then, based on what has been said, we can create the equality

V 1 N 1 =V 2 N 2

2. Calculation titer for the working substance.

This is the mass of solute expressed in grams contained in one milliliter of solution. The titer is calculated as the ratio of the mass of the dissolved substance to the volume of the solution (g/ml).

T= m/ V

where: m - mass of dissolved substance, g; V -- total volume of solution, ml;

T=E*N/1000.(g/ml)

Sometimes, to indicate the exact concentration of titrated solutions, the so-calledcorrection factororamendment K.

K = actual weight taken/calculated weight.

The correction shows by what number the volume of a given solution must be multiplied in order to bring it to the volume of a solution of a certain normality.

Obviously, if the correction for a given solution is greater than unity, then its actual normality is greater than the normality taken as the standard; if the correction is less than unity, then the actual normality of the solution is less than the reference normality.

Example: From 1.3400G X. h.NaClcooked 200ml solution. Calculate the correction to bring the concentration of the prepared solution to exactly 0.1 N.

Solution. At 200ml O,1n. solutionNaClmust contain

58.44*0.1*200/1000 =1.1688g

Hence: K=1.3400/1.1688=1.146

The correction can be calculated as the ratio of the titer of the prepared solution to the titer of a solution of a certain normality:

K = Titer of the prepared solution/ solution titer of a certain normality

In our example, the titer of the prepared solution is 1.340/200= 0.00670g/ml

Tetr 0.1 N solutionNaClequal to 0.005844g/ml

Hence K= 0.00670/0.005844=1.146

Conclusion: If the correction for a given solution is greater than one, then its actual normality is greater than the normality taken as the standard; If the correction is less than one, then its actual normality is less than the reference one.

3. Calculation of the amount of the analyte from the titer of the working solution, expressed in grams of the analyte.

Titer of the working solution in grams of the substance being determined equal to the number grams of the substance being determined, which is equivalent to the amount of substance contained in 1 ml of the working solution. Knowing the titer of the working solution for the analyte T and the volume of the working solution used for titration, you can calculate the number of grams (mass) of the analyte.

Example. Calculate the percentage of Na 2 CO 3 in the sample, if the sample for titration is 0.100 g. 15.00 ml of 0.1 N was consumed.HCI.

Solution .

M(Na 2 CO 3 ) =106,00 gr. E(Na 2 CO 3 ) =53,00 gr.

T(HCI/Na 2 CO 3 )= E(Na 2 CO 3 )*N HCI./1000 G/ ml

m(Na 2 CO 3 ) = T(HCI/Na 2 CO 3 ) V HCI=0,0053*15,00=0,0795 G.

Na percentage 2 CO 3 equals 79.5%

4. Calculation of the number of milligram equivalents of the test substance.

By multiplying the normality of the working solution by its volume spent on titrating the test substance, we obtain the number of milligram equivalents of the dissolved substance in the titrated part of the test substance.

List of used literature

Alekseev V. N. “Quantitative analysis”

Zolotov Yu. A. “Fundamentals of analytical chemistry”

Kreshkov A.P., Yaroslavtsev A.A. “Course of analytical chemistry. Quantitative Analysis"

Piskareva S.K., Barashkov K.M. “Analytical chemistry”

Shapiro S.A., Gurvich Ya.A. "Analytical Chemistry"

In neutralization assays, 0.1 N is used. and 0.5 n. accurate solutions of sulfuric and hydrochloric acids, and in other methods of analysis, for example, redox, 2 N is often used. approximate solutions of these acids.

For instant cooking For accurate solutions, it is convenient to use fixatives, which are weighed portions (0.1 g-eq or 0.01 g-eq) of chemically pure substances, weighed with an accuracy of four to five significant figures, located in sealed glass ampoules. When preparing 1 l. solution from fixanal is obtained 0.1 N. or 0.01 n. solutions. Small amounts of solutions of hydrochloric and sulfuric acids 0.1 N. concentrations can be prepared from fixanals. Standard solutions prepared from fixanals are usually used to establish or check the concentration of other solutions. Fixanal acids can be stored for a long time.

To prepare an accurate solution from fixanal, the ampoule is washed warm water, washing off the inscription or label from it, and wipe it well. If the inscription is made with paint, then it is removed with a cloth moistened with alcohol. In a 1 liter volumetric flask. insert a glass funnel, and into it a glass striker, the sharp end of which should be directed upward. After this, the ampoule with fixanal is lightly struck with its thin bottom against the tip of the striker or allowed to fall freely so that the bottom breaks when it hits the tip. Then, using a glass pin with a pointed end, they break the thin wall of the recess in the upper part of the ampoule and allow the liquid contained in the ampoule to flow out. Then the ampoule located in the funnel is thoroughly washed with distilled water from the wash, after which it is removed from the funnel, the funnel is washed and removed from the flask, and the solution in the flask is added to the mark with distilled water, capped and mixed.

When preparing solutions from dry fixinals (for example, from oxalic acid fixanal), take a dry funnel so that the contents of the ampoule can be poured into the flask with gentle shaking. After the substance is transferred to the flask, wash the ampoule and funnel, dissolve the substance in the water in the flask, and bring the volume of the solution to the mark with distilled water.

Large quantities 0.1 n. and 0.5 n. solutions of hydrochloric and sulfuric acids, as well as approximate solutions of these acids (2 N, etc.) are prepared from concentrated chemically pure acids. First, the density of the concentrated acid is determined using a hydrometer or densimeter.

Based on the density in the reference tables, the concentration of the acid is found (the content of hydrogen chloride in hydrochloric acid or monohydrate in sulfuric acid), expressed in grams per 1 liter. The formulas are used to calculate the volume of concentrated acid required to prepare a given volume of acid of the appropriate concentration. The calculation is carried out with an accuracy of two or three significant figures. The amount of water for preparing the solution is determined by the difference in the volumes of the solution and concentrated acid.

A solution of hydrochloric acid is prepared by pouring half the required amount of distilled water into a vessel for preparing the solution, and then concentrated acid; After mixing, the solution is added to the full volume with the remaining amount of water. Use part of the second portion of water to rinse the beaker used to measure the acid.

A solution of sulfuric acid is prepared by slowly pouring concentrated acid with constant stirring (to prevent heating) to water poured into a heat-resistant glass vessel. In this case, a small amount of water is left to rinse the beaker with which the acid was measured, pouring this residue into the solution after it has cooled.

Sometimes solutions of solid acids (oxalic, tartaric, etc.) are used for chemical analysis. These solutions are prepared by dissolving a sample of chemically pure acid in distilled water.

The mass of a sample of acid is calculated using the formula. The volume of water for dissolution is taken approximately equal to the volume of the solution (if the dissolution is not carried out in a volumetric flask). To dissolve these acids, water that does not contain carbon dioxide is used.

In the table by density we find the content of hydrogen chloride HCl in concentrated acid: Гк = 315 g/l.

We calculate the volume of a concentrated hydrochloric acid solution:

V k = 36.5N V / T k = 36.5 0.1 10000 / 315 = 315 ml.

Amount of water required to prepare the solution:

V H 2 O = 10000 - 115 = 9885 ml.

Weight of a sample of oxalic acid H2C2O4 2H2O:

63.03N V / 1000 = 63.03 0.1 3000 / 1000 = 12.6 g.

Establishing the concentration of working acid solutions can be carried out with sodium carbonate, borax, precise alkali solution (titrated or prepared from fixanal). When establishing the concentration of solutions of hydrochloric or sulfuric acids using sodium carbonate or borax, they use the titration method of weighed portions or (less often) the pipetting method. When using the titration method, burettes with a capacity of 50 or 25 ml are used.

When establishing the concentration of acids great value has a choice of indicator. Titration is performed in the presence of an indicator in which the color transition occurs in the pH range corresponding to the equivalence point for the chemical reaction occurring during titration. When a strong acid interacts with a strong base, methyl orange, methyl red, phenolphthalein and others, in which the color transition occurs at pH = 4?10, can be used as indicators.

When a strong acid interacts with a weak base or with salts of weak acids and strong bases, those in which the color transition occurs in an acidic environment, for example methyl orange, are used as indicators. When weak acids interact with strong alkalis, indicators are used in which the color transition occurs in an alkaline environment, for example phenolphthalein. The concentration of a solution cannot be determined by titration if a weak acid reacts with a weak base during titration.

When establishing the concentration of hydrochloric or sulfuric acids based on sodium carbonate On an analytical balance in separate bottles, take three or four weighed portions of anhydrous chemically pure sodium carbonate with an accuracy of 0.0002 g. To establish a concentration of 0.1 N. solution by titration from a burette with a capacity of 50 ml, the mass of the sample should be about 0.15 g. By drying in an oven at 150 ° C, the samples are brought to constant weight, and then transferred to conical flasks with a capacity of 200-250 ml and dissolved in 25 ml of distilled water . The bottles with carbonate residues are weighed and the exact mass of each sample is determined from the difference in mass.

Titration of a solution of sodium carbonate with an acid is carried out in the presence of 1-2 drops of a 0.1% solution of methyl orange (titration ends in an acidic medium) until the yellow color of the solution changes to orange-yellow. When titrating, it is useful to use a “witness” solution, for the preparation of which one drop of acid from a burette and as many drops of indicator as it is added to the titrated solution are added to distilled water poured into the same flask as the flask in which the titration is performed.

The volume of distilled water for preparing the “witness” solution should be approximately equal to the volume of the solution in the flask at the end of the titration.

The normal acid concentration is calculated from the titration results:

N = 1000m N/E Na 2 CO 3 V = 1000m N/52.99V

where m n is the mass of a sample of soda, g;

V is the volume of acid solution (ml) consumed for titration.

The average convergent concentration value is taken from several experiments.

We expect to use about 20 ml of acid for titration.

Weight of soda sample:

52.99 0.1 20 / 1000 = 0.1 g.

Example 4. A 0.1482 g sample of sodium carbonate was titrated with 28.20 ml of hydrochloric acid solution. Determine the acid concentration.

Normal concentration of hydrochloric acid:

1000 0.1482 / 52.99 28.2 = 0.1012 n.

When determining the concentration of an acid solution with respect to sodium carbonate by pipetting, a sample of chemically pure sodium carbonate, previously brought to a constant mass by drying in an oven and weighed with an accuracy of 0.0002 g, is dissolved in distilled water in a calibrated volumetric flask with a capacity of 100 ml.

The sample size when setting the concentration to 0.1 N. the acid solution should be about 0.5 g (to obtain approximately 0.1 N solution when dissolved). For titration, pipet 10-25 ml of sodium carbonate solution (depending on the capacity of the burette) and 1-2 drops of 0.1% methyl orange solution.

The pipetting method is often used to determine the concentration of solutions using 10 ml semi-microburettes with 0.02 ml divisions.

The normal concentration of an acid solution when established by pipetting using sodium carbonate is calculated using the formula:

N = 1000m n V 1 / 52.99V to V 2,

where m n is the mass of a sample of sodium carbonate, g;

V 1 - volume of carbonate solution taken for titration, ml;

V k is the volume of the volumetric flask in which the carbonate sample was dissolved;

V 2 is the volume of acid solution consumed for titration.

Example 5. Determine the concentration of a sulfuric acid solution if, to establish it, 0.5122 g of sodium carbonate was dissolved in a 100.00 ml volumetric flask and 14.70 ml of an acid solution was used to titrate 15.00 ml of a carbonate solution (using a burette with a capacity of 25 ml) .

Normal concentration of sulfuric acid solution:

1000 0.5122 15 / 52.99 100 14.7 = 0.09860 n.

When establishing the concentration of sulfuric or hydrochloric acids using sodium tetraborate (borax) Usually the titration method is used. Borax crystalline hydrate Na 2 B 4 O 7 10H 2 O must be chemically pure and before determining the acid concentration, it is subjected to recrystallization. For recrystallization, 50 g of borax are dissolved in 275 ml of water at 50-60°C; the solution is filtered and cooled to 25-30°C. Stirring the solution vigorously causes crystallization. The crystals are filtered on a Buchner funnel, dissolved again and recrystallized. After filtering, the crystals are dried between sheets of filter paper at an air temperature of 20°C and relative humidity air 70%; drying is carried out in air or in a desiccator over a saturated sodium chloride solution. The dried crystals should not stick to the glass rod.

For titration, 3-4 samples of borax are taken alternately into a bottle with an accuracy of 0.0002 g and transferred to conical flasks for titration, dissolving each sample in 40-50 ml warm water with vigorous shaking. After transferring each sample from the bottle to the flask, the bottle is weighed. Based on the difference in mass during weighing, the size of each sample is determined. The size of a separate sample of borax to establish a concentration of 0.1 N. the acid solution when using a burette with a capacity of 50 ml should be about 0.5 g.

Titration of borax solutions with acid is carried out in the presence of 1-2 drops of a 0.1% solution of methyl red until the yellow color of the solution changes to orange-red or in the presence of a solution of a mixed indicator consisting of methyl red and methylene blue.

The normal concentration of an acid solution is calculated using the formula:

N = 1000m n / 190.69V,

where m n is the mass of the borax sample, g;

V is the volume of acid solution consumed for titration, ml.

It is assumed that 15 ml of acid solution will be used for titration.

Weight of borax sample:

190.69 0.1 15 / 1000 = 0.3 g.

Example 7. Find the concentration of the hydrochloric acid solution if 24.38 ml of hydrochloric acid was consumed to titrate a 0.4952 g sample of borax.

1000 0,4952 / 190,624,38 = 0,1068

Determination of acid concentration using sodium hydroxide solution or caustic potassium is carried out by titrating an alkali solution with an acid solution in the presence of 1-2 drops of a 0.1% solution of methyl orange. However, this method of determining the acid concentration is less accurate than the above. It is usually used in control tests of acid concentrations. An alkali solution prepared from fixanal is often used as a starting solution.

The normal concentration of acid solution N2 is calculated using the formula:

N 2 = N 1 V 1 / V 2,

where N 1 is the normal concentration of the alkali solution;

V 1 - volume of alkali solution taken for titration;

V 2 - volume of acid solution consumed for titration ( average value convergent titration results).

Example 8. Determine the concentration of the sulfuric acid solution if the titration is 25.00 ml of 0.1000 N. sodium hydroxide solution, 25.43 ml of sulfuric acid solution was consumed.

Acid solution concentration.

The gram equivalent of sulfuric acid is 49.04 (98.08:2), hydrochloric acid is 36.465. Therefore, to prepare normal solutions it is necessary to take sulfuric or hydrochloric acid in quantities corresponding to these values.

Sulfuric and hydrochloric acids are prepared from chemically pure concentrated solutions of these acids. The required amount of acids is calculated as follows. Suppose there is sulfuric acid relative density 1.84 (95.6%), it is necessary to prepare 1 liter of 1 n. acid solution, for this you should take concentrated acid:

The required amount of hydrochloric acid is calculated in the same way. If the relative density of the concentrated acid is 1.185 (37.3%), then to prepare 1 liter of 1 N. you need to take the solution:

The required amount of acid is measured by volume, poured into water, cooled, then transferred to a 1-liter volumetric flask and adjusted to the mark.

The titer of acids is determined using chemically pure reagents: sodium carbonate, borax, or a titrated solution of sodium hydroxide.

Setting the sodium carbonate titer

Three portions of sodium carbonate of 0.15-0.20 g each (for a 0.1 N solution) are taken into separate bottles with an accuracy of 0.0001 g and dried at 150 ° C to constant mass (weight). After this, the samples are transferred into 250 ml conical flasks and dissolved in 25 ml of distilled water. The bottle is weighed again and the mass (weight) of a sample of the dried reagent is determined by the difference. An indicator - 1-2 drops of methyl orange - is added to the solution in the flask and titrated with the prepared acid solution until the color changes from yellow to orange-yellow. The correction factor is calculated using the formula (for 0.1 N solution)

where g is the weight of salt, g; V is the amount of acid consumed for titration, ml; 0.0053 - the amount of sodium carbonate corresponding to 1 ml of exactly 0.1 N. acid solution, g.

Setting the acid titer for borax

The borax is pre-dried between sheets of filter paper until individual crystals no longer stick to the glass rod. It is best to dry borax in a desiccator filled with a saturated solution of sodium chloride and sugar or a saturated solution of sodium bromide.

Take, with an accuracy of 0.0001 g, three samples of borax into bottles in the amount of 0.5 g (for a 0.1 N solution) and transfer them to conical flasks with a capacity of 250 ml, the bottles are weighed and the exact mass (weight) of the sample is determined by difference. Then add 30-60 ml of warm water to the samples, shaking vigorously. Then, adding 1-2 drops of methyl red solution, titrate the borax solution with the prepared acid solution until the color changes from yellow to red. The correction factor is calculated using the following formula:

where the meaning of the letters is the same as in the previous formula; 0.019072 - the amount of borax corresponding to 1 ml exactly 0.1 n. acid solution, g.

Solutions

Preparation of salt solutions

Technique for determining the concentration of solutions.

Determination of concentration by densimetry

Determination of concentration titrimetrically.

Basic concepts and terms of titrimetric analysis.

Scheme of titrimetric determination.

Six rules for titration.

Conditions for titrimetric determination of the concentration of a substance

Preparation of a titrated solution using an accurate weighing of the starting substance

Setting the solution titer using an adjusting agent

Computations in volumetric analysis.

List of used literature

SOLUTIONS

1. The concept of solutions and solubility

In both qualitative and quantitative analysis, the main work is done with solutions. Usually, when we use the name “solution,” we mean true solutions. In true solutions, the solute in the form of individual molecules or ions is distributed among the solvent molecules.

Solution- a homogeneous (homogeneous) mixture consisting of particles of a dissolved substance, a solvent and the products of their interaction. When a solid substance is dissolved in water or another solvent, the molecules of the surface layer pass into the solvent and, as a result of diffusion, are distributed throughout the entire volume of the solvent, then a new layer of molecules passes into the solvent, etc. Simultaneously with the solvent, the reverse process also occurs - the release of molecules from the solution. The higher the concentration of the solution, the more this process will occur. By increasing the concentration of the solution without changing other conditions, we reach a state in which per unit time the same number of molecules of the dissolved substance will be released from the solution as they are dissolved. This solution is called saturated. If you add even a small amount of solute to it, it will remain undissolved.

Solubility- the ability of a substance to form homogeneous systems with other substances - solutions in which the substance is in the form of individual atoms, ions, molecules or particles. The amount of substance in a saturated solution determines solubility substances under given conditions. The solubility of various substances in certain solvents is different. No more than a certain amount of a given substance can be dissolved in a certain amount of each solvent. Solubility expressed by the number of grams of a substance per 100 g of solvent in a saturated solution at a given temperature . Based on their ability to dissolve in water, substances are divided into: 1) highly soluble (caustic soda, sugar); 2) sparingly soluble (gypsum, Berthollet salt); 3) practically insoluble (copper sulfite). Practically insoluble substances are often called insoluble, although there are no absolutely insoluble substances. “Insoluble substances are usually called those substances whose solubility is extremely low (1 part by weight of a substance dissolves in 10,000 parts of solvent).

Generally, the solubility of solids increases with increasing temperature. If you prepare a solution that is close to saturated by heating, and then quickly but carefully cool it, the so-called supersaturated solution. If you drop a crystal of a dissolved substance into such a solution or mix it, then crystals will begin to fall out of the solution. Consequently, a cooled solution contains more substance than is possible for a saturated solution at a given temperature. Therefore, when a crystal of a solute is added, all excess substance crystallizes out.

The properties of solutions always differ from the properties of the solvent. The solution boils at a higher temperature than the pure solvent. On the contrary, the freezing point of the solution is lower than that of the solvent.

Based on the nature of the solvent, solutions are divided into aquatic and non-aquatic. The latter include solutions of substances in organic solvents such as alcohol, acetone, benzene, chloroform, etc.

Solutions of most salts, acids, and alkalis are prepared in aqueous solutions.

2. Methods of expressing the concentration of solutions. The concept of gram equivalent.

The concentration of substances in solutions can be expressed in different ways:

The mass fraction of the dissolved substance w(B) is a dimensionless quantity equal to the ratio of the mass of the dissolved substance to the total mass of the solution m

or otherwise called: percentage concentration solution - determined by the number of grams of substance in 100 g of solution. For example, a 5% solution contains 5 g of substance in 100 g of solution, i.e. 5 g of substance and 100-5 = 95 g of solvent.

Molar concentration C(B) shows how many moles of solute are contained in 1 liter of solution.

C(B) = n(B) / V = m(B) / (M(B) V),

where M(B) is the molar mass of the dissolved substance g/mol.

Molar concentration is measured in mol/L and is designated "M". For example, 2 M NaOH is a two-molar solution of sodium hydroxide; monomolar (1 M) solutions contain 1 mole of substance per 1 liter of solution, bimolar (2 M) solutions contain 2 moles per 1 liter, etc.

In order to establish how many grams of a given substance are in 1 liter of a solution of a given molar concentration, you need to know it molar mass, i.e., the mass of 1 mole. The molar mass of a substance, expressed in grams, is numerically equal to the molecular mass of the substance. For example, the molecular weight of NaCl is 58.45, therefore, the molar mass is also 58.45 g. Thus, a 1 M NaCl solution contains 58.45 g of sodium chloride in 1 liter of solution.

Compound Equivalent- they call the amount of it that corresponds (equivalent) to 1 mole of hydrogen in a given reaction.

The equivalence factor is determined by:

1) the nature of the substance,

2) a specific chemical reaction.

a) in metabolic reactions;

The equivalent value of acids is determined by the number of hydrogen atoms that can be replaced by metal atoms in the acid molecule.

Example 1. Determine the equivalent for acids: a) HCl, b) H 2 SO 4, c) H 3 PO 4; d) H 4.

Solution.

In the case of polybasic acids, the equivalent depends on the specific reaction:

a) H 2 SO 4 + 2KOH → K 2 SO 4 + 2H 2 O.

in this reaction, two hydrogen atoms are replaced in the sulfuric acid molecule, therefore, E = M.M/2

b) H 2 SO 4 + KOH → KHSO 4 + H 2 O.

In this case, one hydrogen atom is replaced in the sulfuric acid molecule E = M.M/1

For phosphoric acid, depending on the reaction, the values are a) E = M.M/1

b) E= M.M/2 c) E= M.M/3

BASES

The base equivalent is determined by the number of hydroxyl groups that can be replaced by the acid residue.

Example 2. Determine the equivalent of the bases: a) KOH; b) Cu(OH) 2;

Solution.

Salt equivalent values are determined by cation.

The value by which M must be divided. In the case of salts is equal to q·n, Where q– charge of the metal cation, n– the number of cations in the salt formula.

Example 3. Determine the equivalent of salts: a) KNO 3 ; b) Na 3 PO 4; c) Cr 2 (SO 4) 3;

Solution.

A) q·n = 1 b) 1 3 = 3 V) z = 3 2 = 6, G) z = 3 1 = 3

The value of equivalence factors for salts also depends on

reaction, similar to its dependence for acids and bases.

b) in redox reactions to determine

equivalent use an electronic balance scheme.

The value by which the M.M for a substance must be divided in this case is equal to the number of electrons accepted or given up by a molecule of the substance.

K 2 Cr 2 O 7 + HCl → CrCl 3 + Cl 2 + KCl + H 2 O

for straight line 2Сr +6 +2 3 e→2Cr 3+

reactions 2Cl - - 2 1 e→Cl 2

for reverse 2Cr+3-2 3 e→Cr +6

Cl2-2 reactions e→2Cl

(K 2 Cr 2 O 7) = 1/6

(Cr)=1/3 (HCl)=1 (Cl)=1) (Cl2)=1/2 (Cl)=1

The normal concentration is indicated by the letter N (in calculation formulas) or the letter “n” - when indicating the concentration of a given solution. If 1 liter of solution contains 0.1 equivalent of a substance, it is called decinormal and is designated 0.1 N. A solution containing 0.01 equivalent of a substance in 1 liter of solution is called centinormal and is designated 0.01 N. Since the equivalent is the amount of any substance that is in a given reaction. corresponds to 1 mole of hydrogen, obviously, the equivalent of any substance in this reaction must correspond to the equivalent of any other substance. This means that in any reaction, substances react in equivalent quantities.

Titrated are called solutions whose concentration is expressed caption, i.e., the number of grams of a substance dissolved in 1 ml of solution. Very often in analytical laboratories, solution titers are recalculated directly to the substance being determined. Tog Yes The titer of a solution shows how many grams of the substance being determined corresponds to 1 ml of this solution.

The weight of the solute is calculated accurate to the fourth decimal place, and molecular weights are taken with the accuracy with which they are given in the reference tables. The volume of concentrated acid is calculated to the second decimal place.

Before starting to prepare the solution, it is necessary to make a calculation, i.e., calculate the amount of solute and solvent to prepare a certain amount of a solution of a given concentration.

3. Calculations when preparing salt solutions

Example 1. It is necessary to prepare 500 g of a 5% solution of potassium nitrate. 100 g of such a solution contains 5 g of KN0 3; Let's make a proportion:

100 g solution - 5 g KN0 3

500" - X» KN0 3

5*500/100 = 25 g.

You need to take 500-25 = 475 ml of water.

Example 2. It is necessary to prepare 500 g of a 5% CaCI solution from the salt CaCl 2 .6H 2 0. First, we perform the calculation for the anhydrous salt.

100 g solution - 5 g CaCl 2

500 "" - x g CaC1 2

5*500/ 100 = 25 g

Molar mass of CaCl 2 = 111, molar mass of CaCl 2 6H 2 0 = 219. Therefore,

219 g of CaC1 2 *6H 2 0 contain 111 g of CaC1 2. Let's make a proportion:

219 g CaC1 2 *6H 2 0 -- 111 g CaC1 2

X» CaС1 2 -6Н 2 0- 25 » CaCI 2 ,

219*25/ 111= 49.3 g.

4. Calculations for preparing acid solutions

Example 1. It is necessary to prepare 500 g of a 10% solution of hydrochloric acid, based on the available 58% acid, the density of which is d = l.19.

1. Find the amount of pure hydrogen chloride that should be in the prepared acid solution:

100 g solution -10 g HC1

500 "" - X» NS1

500*10/100= 50 g

To calculate solutions of percentage concentration, molar mass is rounded to whole numbers.

2. Find the number of grams of concentrated acid that will contain 50 g of HC1:

100 g acid - 38 g HC1

X» » - 50 » NS1

100 50/38 = 131.6 g.

3. Find the volume occupied by this amount of acid:

V= 131,6/ 1.19= 110.6 ml. (round to 111)

Let's calculate how much concentrated acid you need to take. According to the table, 1 liter of concentrated HC1 contains 451.6 g of HC1. Let's make a proportion:

1000 ml-451.6 g HC1

X ml- 52.35 "NS1

1000*52.35/ 451.6 =115.9 ml.

The amount of water is 500-116 = 384 ml.

Therefore, to prepare 500 ml of a 10% solution of hydrochloric acid, you need to take 116 ml of a concentrated solution of HC1 and 384 ml of water.

Example 1. How many grams of barium chloride are needed to prepare 2 liters of 0.2 M solution?

Solution. The molecular weight of barium chloride is 208.27. Hence. 1 liter of 0.2 M solution should contain 208.27 * 0.2 = 41.654 g BaCI 2 . To prepare 2 liters you will need 41.654 * 2 = 83.308 g BaCI 2.

Example 2. How many grams of anhydrous soda Na 2 C0 3 are required to prepare 500 ml of 0.1 N. solution?

Solution. The molecular weight of soda is 106.004; equivalent mass of Na 2 C0 3 =M: 2 = 53.002; 0.1 eq. = 5.3002 g

1000 ml 0.1 n. solution contain 5.3002 g Na 2 C0 3
500 »» » » » X » Na 2 C0 3

x = 2.6501 g Na 2 C0 3.

Example 3. How much concentrated sulfuric acid (96%: d=l.84) is required to prepare 2 liters of 0.05 N. sulfuric acid solution?

Solution. The molecular weight of sulfuric acid is 98.08. Equivalent mass of sulfuric acid H 2 so 4 = M: 2 = 98.08: 2 = 49.04 g. Mass 0.05 eq. = 49.04*0.05 = 2.452 g.

Let's find how much H 2 S0 4 should be contained in 2 liters of 0.05 n. solution:

1 l-2.452 g H 2 S0 4

2"- X » H 2 S0 4

X= 2.452*2 = 4.904 g H 2 S0 4.

To determine how much 96.% H 2 S0 4 solution needs to be taken for this, let’s make a proportion:

in 100 g conc. H 2 S0 4 -96 g H 2 S0 4

U» » H 2 S0 4 -4.904 g H 2 S0 4

Y = 5.11 g H 2 S0 4.

We recalculate this amount to volume: 5.11: 1.84 = 2.77

Thus, to prepare 2 liters of 0.05 N. solution you need to take 2.77 ml of concentrated sulfuric acid.

Example 4. Calculate the titer of a NaOH solution if it is known that its exact concentration is 0.0520 N.

40.01*0.0520 = 2.0805 g.

1 liter of solution contains 1000 ml.

T=0.00208 g/ml. You can also use the formula:

T=E N/1000 g/l

Where T- titer, g/ml; E- equivalent mass; N- normality of the solution.

Then the titer of this solution is: 40.01 0.0520/1000 = 0.00208 g/ml.

Example 5 Calculate the normal concentration of a solution HN0 3 if it is known that the titer of this solution is 0.0065 To calculate, we use the formula:

T=E N/1000 g/l, from here:

N=T1000/E0,0065.1000/ 63.05= 0.1030 n.

Example 6. What is the normal concentration of a solution if it is known that 200 ml of this solution contains 2.6501 g of Na 2 C0 3

Solution. As was calculated in example 2: ENа 2 с 3 =53.002.
Let's find how many equivalents are 2.6501 g of Na 2 C0 3:
2.6501: 53.002 = 0.05 eq.

In order to calculate the normal concentration of a solution, we create a proportion:

1000 "" X "

1 liter of this solution will contain 0.25 equivalents, i.e. the solution will be 0.25 N.

For this calculation you can use the formula:

N =P 1000/E V

Where R - amount of substance in grams; E - equivalent mass of the substance; V - volume of solution in milliliters.

ENа 2 с 3 =53.002, then the normal concentration of this solution is

2,6501* 1000 / 53,002*200=0,25

5.Recalculation of concentration from one type to another.

The density of the solution is given in reference books in the corresponding tables or measured with a hydrometer. If we denote: WITH- percentage concentration; M- molar concentration; N - normal concentration; d- solution density; E- equivalent mass; m- molar mass, then the formulas for converting from percentage concentration to molar and normal concentration will be as follows:

Example 1. What is the molar and normal concentration of a 12% sulfuric acid solution, the density of which is d = l.08 g/cm??

Solution. The molar mass of sulfuric acid is 98. Therefore,

E n 2 so 4 =98:2=49.

Substituting the necessary values into the formulas, we get:

1) the molar concentration of a 12% sulfuric acid solution is equal to

M=12*1.08 *10/98=1.32 M;

2) the normal concentration of a 12% sulfuric acid solution is

N= 12*1.08*10/49= 2.64 n.

Example 2. What is the percentage concentration of 1 N. hydrochloric acid solution, the density of which is 1.013?

Solution. The molar mass of HCI is 36.5, therefore Ens1 = 36.5. From the above formula (2) we get:

therefore, the percentage concentration is 1 N. hydrochloric acid solution is equal to

36,5*1/ 1,013*10 =3,6%

M = (NE)/m; N=M(m/E)

Example 3. Normal concentration of 1M sulfuric acid solution Answer-2M

Example 4, Molar concentration 0.5 N. Na 2 CO 3 solution Answer - 0.25H

M = (s p 10)/m
N = (c p 10)/e

The same formulas can be used if you need to convert normal or molar concentration to percentage.

Sometimes in laboratory practice it is necessary to recalculate the molar concentration to normal and vice versa. If the equivalent mass of a substance is equal to the molar mass (For example, for HCl, KCl, KOH), then the normal concentration is equal to the molar concentration. So, 1 n. a solution of hydrochloric acid will simultaneously be a 1 M solution. However, for most compounds the equivalent mass is not equal to the molar mass and, therefore, the normal concentration of solutions of these substances is not equal to the molar concentration.
To convert from one concentration to another, you can use the following formulas:

M = (N E)/m
N = (M m)/E

Law of mixing solutions

The quantities of mixed solutions are inversely proportional to the absolute differences between their concentrations and the concentration of the resulting solution.

The law of mixing can be expressed by a mathematical formula:

mA/mB =С-b/а-с,

where mA, mB are the quantities of solutions A and B taken for mixing;

a, b, c - respectively, the concentrations of solutions A and B and the solution obtained as a result of mixing. If the concentration is expressed in %, then the quantities of mixed solutions must be taken in weight units; if concentrations are taken in moles or normals, then the quantities of mixed solutions must be expressed only in liters.

For ease of use mixing rules apply rule of the cross:

m1 / m2 = (w3 – w2) / (w1 – w3)

To do this, subtract the smaller one diagonally from the larger concentration value, obtaining (w 1 – w 3), w 1 > w 3 and (w 3 – w 2), w 3 > w 2. Then the mass ratio of the initial solutions m 1 / m 2 is compiled and calculated.

Example
Determine the masses of the initial solutions with mass fractions of sodium hydroxide of 5% and 40%, if mixing them resulted in a solution weighing 210 g with a mass fraction of sodium hydroxide of 10%.

5 / 30 = m 1 / (210 - m 1)
1/6 = m 1 / (210 – m 1)
210 – m 1 = 6m 1
7m 1 = 210
m 1 =30 g; m 2 = 210 – m 1 = 210 – 30 = 180 g

Basic concepts and terms of titrimetric analysis.

Titrant - a reagent solution of known concentration (standard solution).

Standard solution– Primary secondary standard solutions are distinguished according to the method of preparation. Primary is prepared by dissolving a precise amount of pure chemical in a specific amount of solvent. The secondary is prepared at an approximate concentration and its concentration is determined using the primary standard.

Equivalence point– the moment when the added volume of the working solution contains an amount of substance equivalent to the amount of the substance being determined.

Purpose of titration- accurate measurement of the volumes of two solutions containing an equivalent amount of a substance

Direct titration– this is the titration of a certain substance “A” directly with titrant “B”. It is used if the reaction between “A” and “B” proceeds quickly.

Solutions

The concept of solutions and solubility

Methods of expressing the concentration of solutions. The concept of gram equivalent.

Calculations for preparing solutions of salts and acids

Recalculation of concentration from one type to another.

Mixing and diluting solutions. The law of mixing solutions

Technique for preparing solutions.

Preparation of salt solutions

Preparation of acid solutions

Preparation of base solutions

Preparation of a working solution from fixanal.

Approximate solutions. In most cases, the laboratory has to use hydrochloric, sulfuric and nitric acids. Acids are commercially available in the form of concentrated solutions, the percentage of which is determined by their density.

Acids used in the laboratory are technical and pure. Technical acids contain impurities and therefore are not used in analytical work.

Concentrated hydrochloric acid smokes in air, so you need to work with it in a fume hood. The most concentrated hydrochloric acid has a density of 1.2 g/cm3 and contains 39.11% hydrogen chloride.

The dilution of the acid is carried out according to the calculation described above.

Example. You need to prepare 1 liter of a 5% solution of hydrochloric acid, using a solution with a density of 1.19 g/cm3. From the reference book we find out that a 5% solution has a density of 1.024 g/cm3; therefore, 1 liter of it will weigh 1.024 * 1000 = 1024 g. This amount should contain pure hydrogen chloride:

An acid with a density of 1.19 g/cm3 contains 37.23% HCl (we also find it from the reference book). To find out how much of this acid should be taken, make up the proportion:

or 137.5/1.19 = 115.5 acid with a density of 1.19 g/cm3. Having measured out 116 ml of acid solution, bring its volume to 1 liter.

Sulfuric acid is also diluted. When diluting it, remember that you need to add acid to the water, and not vice versa. When diluted, strong heating occurs, and if you add water to the acid, it may splash, which is dangerous, since sulfuric acid causes severe burns. If acid gets on your clothes or shoes, you should quickly wash the spilled area. a large number water, and then neutralize the acid with sodium carbonate or ammonia solution. In case of contact with the skin of your hands or face, immediately wash the area with plenty of water.

Particular care is required when handling oleum, which is a sulfuric acid monohydrate saturated with sulfuric anhydride SO3. According to the content of the latter, oleum comes in several concentrations.

It should be remembered that with slight cooling, oleum crystallizes and is in a liquid state only when room temperature. In air it smokes, releasing SO3, which forms sulfuric acid vapor when interacting with air moisture.

It is very difficult to transfer oleum from large to small containers. This operation should be carried out either under draft or in air, but where the resulting sulfuric acid and SO3 cannot have any harmful effect on people and surrounding objects.

If the oleum has hardened, it should first be heated by placing the container with it in a warm room. When the oleum melts and turns into an oily liquid, it must be taken out into the air and there poured into a smaller container, using the method of squeezing with air (dry) or an inert gas (nitrogen).

When mixed with water nitric acid heating also occurs (not as strong, however, as in the case of sulfuric acid), and therefore precautions must be taken when working with it.

Solid organic acids are used in laboratory practice. Handling them is much simpler and more convenient than liquid ones. In this case, care should only be taken to ensure that the acids are not contaminated with anything foreign. If necessary, solid organic acids are purified by recrystallization (see Chapter 15 “Crystallization”),

Precise solutions. Precise acid solutions They are prepared in the same way as approximate ones, with the only difference that at first they strive to obtain a solution of a slightly higher concentration, so that later it can be diluted precisely, according to calculations. For precise solutions, use only chemically pure preparations.

The required amount of concentrated acids is usually taken by volume calculated based on density.

Example. You need to prepare 0.1 and. H2SO4 solution. This means that 1 liter of solution should contain:

An acid with a density of 1.84 g/cmg contains 95.6% H2SO4 n to prepare 1 liter of 0.1 n. of the solution you need to take the following amount (x) of it (in g):

The corresponding volume of acid will be:

Having measured exactly 2.8 ml of acid from the burette, dilute it to 1 liter in a volumetric flask and then titrate with an alkali solution to establish the normality of the resulting solution. If the solution turns out to be more concentrated), the calculated amount of water is added to it from a burette. For example, during titration it was found that 1 ml of 6.1 N. H2SO4 solution contains not 0.0049 g of H2SO4, but 0.0051 g. To calculate the amount of water needed to prepare exactly 0.1 N. solution, make up the proportion:

Calculation shows that this volume is 1041 ml; the solution needs to be added 1041 - 1000 = 41 ml of water. You should also take into account the amount of solution taken for titration. Let 20 ml be taken, which is 20/1000 = 0.02 of the available volume. Therefore, you need to add not 41 ml of water, but less: 41 - (41*0.02) = = 41 -0.8 = 40.2 ml.

* To measure the acid, use a thoroughly dried burette with a ground stopcock. .

The corrected solution should be checked again for the content of the substance taken for dissolution. Accurate solutions of hydrochloric acid are also prepared using the ion exchange method, based on an accurately calculated sample of sodium chloride. The sample calculated and weighed on an analytical balance is dissolved in distilled or demineralized water, and the resulting solution is passed through a chromatographic column filled with a cation exchanger in the H-form. The solution flowing from the column will contain an equivalent amount of HCl.

As a rule, accurate (or titrated) solutions should be stored in tightly closed flasks. A calcium chloride tube must be inserted into the stopper of the vessel, filled with soda lime or ascarite in the case of an alkali solution, and with calcium chloride or simply cotton wool in the case of an acid.

To check the normality of acids, calcined sodium carbonate Na2COs is often used. However, it is hygroscopic and therefore does not fully satisfy the requirements of analysts. It is much more convenient to use acidic potassium carbonate KHCO3 for these purposes, dried in a desiccator over CaCl2.

When titrating, it is useful to use a “witness”, for the preparation of which one drop of acid (if an alkali is being titrated) or alkali (if an acid is being titrated) and as many drops of an indicator solution as added to the titrated solution are added to distilled or demineralized water.

The preparation of empirical, according to the substance being determined, and standard solutions of acids is carried out by calculation using the formulas given for these and the cases described above.