Installing the titer is one of the most important operations of laboratory equipment. From the correct preparation of the titrated solution will depend on the result of the analysis. It should not be forgotten that, for example, at a plant, based on the analysis data, the process flow is monitored and incorrect analysis can lead to certain complications. Since each analysis is almost always accompanied by a titration, each laboratory worker must master the technique of this operation well.

There are a few rules to remember about titrations.

1. Titrated solutions should be as fresh as possible. Long-term storage should not be allowed. Each solution has its own shelf life.

2. Titrated solutions change their titer upon standing, so they should be checked occasionally. If a particularly responsible analysis is done, checking the titer of the solution is mandatory.

3. Titrated solutions that are affected by light (solutions of AgNO3, etc.) should be stored in yellow bottles or in those that would protect the solution from light.

4. When preparing solutions of potassium permanganate, their titer should be set no earlier than 3-4 days after preparation. The same applies to all other solutions capable of changing with time or in contact with air, glass, etc.

5. It is better to store titrated solutions of alkalis in bottles coated with paraffin inside, and also protect them from the action of carbon dioxide in the air (calcium chloride tube with soda lime or ascarite),

6. All bottles of titrated solutions must be clearly labeled with the substance, normality, correction, time of preparation of the solution and the date the titer was checked.

7. When titrating acidic or alkaline solutions, it is useful to use the so-called witness solution.

During the titration, the flask must be held with the left hand, and right hand operate the burette stopcock, allowing the liquid to drain evenly. When titrated very great importance has the speed of it. Therefore, during repeated titration of the same solution, it is necessary that the rate of adding the solution from the burette be as similar as possible, i.e., a certain amount of liquid would flow out at the same time. The position of the hands during titration is shown in fig. 352.

It is very convenient to use magnetic stirrers to stir the titratable solution. In this case, the titration can be carried out both in an ordinary conical flask and in special titration-adapted tem-colored liquids.

In analytical work, much attention should be paid to calculations. They will not seem difficult if, from the very beginning of the work, one learns the concepts that underlie all calculations, that is, the concepts of titer, normality and gram equivalent and the relationship between them.

For example, if some sample of the desired substance is taken, then the titer T of the prepared solution will be equal to the sample A divided by the volume (V) of the solution:

Rice. 352. The position of the hands during titration.

a= T*1000 g

Normality can be calculated if the sample is known A and gram equivalent E of the solute

If the solution is prepared in a different volume, less or more than 1000 ml, the sample is calculated per 1 liter, and then the formula for calculating the normality will take the form

This formula allows you to calculate the normality of the solution from the sample taken, regardless of its volume. There is a simple relationship between titer, gram equivalent and normality:

Sometimes in the calculations they use a correction for normality or the coefficient of normality K. This correction is the ratio of the practical titer T to the theoretical titer (To):

This correction shows how many milliliters of exactly normal solution corresponds to 1 ml of this solution. When multiplying the results of the titration (ml) by this amendment, the resulting volume is brought to a certain concentration, for example, 0.1 N. solution.

However, the expediency of using the normality correction is very doubtful, since all calculations can be successfully done without this correction, which only complicates the calculation.

When working with normal solutions, the problem is always reduced first to determining the normality of an unknown solution, and then to determining the amount of an unknown substance contained in the solution. Thus, the main calculation and analytical formula for all volumetric definitions will be

i.e., the product of the normality of the known solution and the volume of the known solution when the end of the reaction is reached is always equal to the product of the normality of the unknown solution and the volume of the latter. This product shows the number of equivalents of reactants. From here we can determine the normality of the unknown solution A2, which will be equal to

(2)

When the value of N2 is known, apply the general formula for determining the normality of the sample (a);

(3)

Since the task of the analyst is to determine the value of a, from this formula one finds;

(4)

Or, substituting the value of N2 from formula (2), we obtain:

The above formulas allow all calculations to be carried out without corrections for normality, since it is assumed that it can be expressed by any integer or fractional number. The main thing in any calculation is to find the number of equivalents, when multiplied by the value of the gram equivalent, the amount of the desired substance will always be obtained.

Example. Let a sample of 0.5000 g of ore containing iron be taken. After its dissolution and dilution of the resulting solution Up to 100 ml in a volumetric flask for titration by permangapatometry, each time take 10 ml of the analyzed solution.

KMnO4-0.0495 N solution Went for titration: 11.2; 11.1; 11.0; 11.1 ml KMnO4 solution. We take an average of 11.1 ml. The normality of the solution is 11.1 0.0495 = 10 * N2, whence

The amount of Fe in 100 ml of solution (the gram equivalent of Fe in this case is 55.85):

To express the iron content in the ore as a percentage, the right side of the equation is multiplied by JOO and divided by the sample of ore taken, i.e.

Titrimetric Analysis Technique

Measuring utensils.Measuring cylinders used for approximate, with an accuracy of 1-2 ml, measurement of liquids.

Volumetric flasks used to prepare solutions with precisely known concentrations. Usually, a sample of a substance is quantitatively transferred to a volumetric flask, dissolved and diluted with water to a certain volume (for example, 100 ml), limited by a circular mark (line) on the neck (until the lower edge of the meniscus of the liquid will not touch the line).

Pipettes used to withdraw and transfer a precise volume of solution from one vessel to another. Before use, the pipette is washed, washed with distilled water and be sure to rinse with the same solution that will be measured. Otherwise, the water remaining in the pipette will dilute the solution measured for analysis and its concentration will change. Rules for working with pipettes: The lower end of the pipette is immersed in the solution and the solution is sucked with a rubber bulb through the upper hole. When the liquid level rises above the line, quickly close the top hole with the index finger of the right hand and remove the pipette from the solution. Next, the excess solution is carefully released until the lower edge of the meniscus does not coincide with the line applied to the pipette. At the moment when the meniscus touches the line, the finger is pressed firmly against the upper hole of the pipette and the liquid stops flowing. The filled pipette is transferred to the titration flask. To do this, the flask is held in an inclined position, the pipette is placed with its lower end against the wall of the flask, holding the pipette vertically. Slightly releasing the index finger, allow the solution to drain, wait another 15 seconds or so, and remove the last drop by touching the pipette tip to the side of the flask. Do not blow or shake out the last drops of liquid from the pipette., since when calibrating the pipette, the mark is applied taking into account the fact that with the free flow of liquid, a little of it remains on the walls.

Burettes are cylindrical graduated vessels with a tap or rubber stopper. Large divisions are applied every milliliter, and small divisions - every 0.1 ml. Burettes are used to measure the volume of solution used for titration. Before use, the burette is washed, then rinsed with the solution that will be titrated. Then, placing the clamp on the rubber part of the burette, fill it with titration solution above the ʼʼ0ʼʼ division, fill the withdrawn tube, making sure that there is no air left in it. After that, the lower meniscus is set at ʼʼ0ʼʼ division, releasing excess solution from the burette. Burette readings are made to the nearest 0.05 ml. Reading is hampered by the fact that the liquid in the burette has a concave meniscus. For this reason the eye should be kept exactly at the level of the liquid during the reading. Otherwise, the reading will be incorrect. Each titration starts with a ʼʼ0ʼʼ division, as this is the best way to compensate for burette calibration errors. The solution is not released from the burette very quickly (no faster than 3-4 drops per second), otherwise it will not drain from the walls in time and the reading will be incorrect.

Preparation of standard solutions:

1. Write an equation for the reaction between the standard substance and the substance whose concentration is to be determined. Using the reaction equation, calculate the molar mass of the equivalent (E) of the standard substance. Next, calculate the mass of the standard substance required to prepare a given volume of a solution of a given concentration using the formula:

where C is the molar concentration of the equivalent (normality) of the solution; V is the required volume of solution in ml.

2. Weigh an empty bottle on the technochemical scales.

3. Weigh a weighing bottle with a sample on a technochemical balance.

4. Weigh the weighing bottle with sample on an analytical balance.

5. Quantitatively, without loss, transfer the sample from the weighing bottle to the volumetric flask through a dry funnel (after transferring the substance, do not remove the funnel from the flask!). Weigh an empty bottle on an analytical balance.

6. Prepare the solution.
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To do this, first wash off the remnants of the substance from the funnel into the flask, first slightly raise the funnel so that there is a gap between it and the walls of the flask. Add distilled water to the flask for 1/3 - 1/2 of its volume and thoroughly mix the contents of the flask with rotational movements until the sample is completely dissolved. Bring the volume of the solution to the calibration mark (along the lower meniscus), close the flask with a stopper and, holding it with your index finger, mix thoroughly, turning the flask upside down at least 8 times.

Sampling and titration:

1. Prepare the burette for work. To do this, rinse the burette with a small amount of titrant solution and discard the used solution. After that, fill the buret with the titrant solution almost to the top; then, substituting a glass under it and opening the clamp, fill the ʼʼ spoutʼʼ of the burette (pulled out tube of the burette) so that no air bubbles remain in it. Set the titrant level to ʼʼ0ʼʼ division along the lower meniscus of the solution.

2. Take a separate portion of the titrated solution (an aliquot) into the titration flask using a volumetric pipette, after rinsing the pipette with the sampled solution to remove the remaining water from it. Add reagents necessary for titration, indicator to the flask.

3. Titrate. To do this, the flask with the solution to be titrated is placed on a tripod under the burette so that the ʼʼ spoutʼʼ of the burette is in the flask. With the left hand they hold the clamp, with the right hand - the flask by its upper part, so as not to close the solution in the flask. Squeezing the clamp and in a circular motion constantly stirring the contents of the flask, carry out the titration. In this case, the titrant is released from the burette no faster than 3-4 drops per second, otherwise it will not drain from the walls in time and the reading will be incorrect. Upon reaching the equivalence point (outwardly, this is manifested in a change in the color of the solution), the titration is stopped. Take readings of the titration on the burette with an accuracy of 0.05 ml and record the volume of the titrant in the laboratory journal. Titration is carried out at least three times. In this case, the results of the titration should be converging, ᴛ.ᴇ. the discrepancy should not exceed 0.1 ml. When three converging results are obtained, the average value is found and the concentration of the analyzed solution is calculated. If, as a result of three titrations, converging results are not obtained, the 4th, 5th titration is carried out until three converging results.

Calculations of titration results:

Calculation of the average titrant volume carried out according to the formula:

Calculation of the molar concentration of the equivalent (normality) of the titrant from a solution of a standard substance. According to the law of equivalents:

where C st.r-ra is the normality of the standard solution; C t is the normality of the titrant; V st.r-ra - the volume of the standard solution, equal to the volume of the pipette; V t is the volume of the titrant, equal to the average value of readings over the buret (V cf).

From formula (31) we express the molar concentration of the titrant equivalent:

Calculation of the mass of the analyte in a certain volume of solution carried out according to the formula:

where C is the normality of the titrant; E is the molar mass of the equivalent of the analyte; V cf is the average volume of three converging titration results.

Titrimetric analysis technique - concept and types. Classification and features of the category "Technique for performing titrimetric analysis" 2017, 2018.

titrimetric analysis

Titrimetric (volume) analysis combines a group of quantitative chemical analysis methods based on the titration process. It consists in measuring the volume of the reagent solution consumed for equivalent interaction with the analyte. The content of the analyte is calculated from the concentration and volume of the reagent solution. The titrimetric method of analysis is applicable for the determination of medium and high contents of substances (over 1%).

Reactions used in titrimetry must meet the following basic requirements:

- the reaction must proceed quantitatively, i.e., the equilibrium constant of the reaction must be sufficiently large;

- the reaction should be fast;

- the reaction should not be complicated by the occurrence of side reactions;

– there must be a way to determine the end of the reaction.

If a reaction does not satisfy at least one of these requirements, it cannot be used in titrimetric analysis.

Depending on the type of reaction that underlies the determination, the following methods of titrimetric analysis are distinguished: acid-base, redox, precipitation and compleximetric.

According to the method of indicating the end point, they distinguish visual, potentiometric, photometric, conductometric, amperometric titration and etc.

Depending on the method of titration, titration is direct, reverse, indirect (by substituent).

Titration can be done from individual weighings and pipetting. In the first case, the entire amount of the analyte is titrated. When pipetting, the test solution (or weighed portion of the substance) is quantitatively transferred into a volumetric flask, diluted with water to the mark and mixed thoroughly. Next, several samples of the solution (aliquots) are taken from the volumetric flask with a pipette for parallel titrations.

Basic terms used in titrimetric analysis

Titration- the process of gradual controlled addition of a solution with a precisely known concentration to a certain volume of another solution.

Titrant (titrated, working solution)- the solution that is poured has a precisely known concentration.

titratable solution A solution to which a titrant is added.

Titrimetric system- a mixture of substances formed during the interaction of a titrant and a titrated substance.

Equivalence point (i.e.) is the moment of titration when the number of equivalents of the titrant is equal to the number of equivalents of the analyte.

Indicator- the substance or device used to establish the end point of a titration, which usually differs little from the equivalence point.

Titration degree ( f) is the ratio of the number of equivalents of the titrant used for titration at any moment of the titration to the initial number of equivalents of the analyte:

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The burette is graduated in cm3 with divisions through one or two tenths of cm3. According to the SI system, it is recommended to express volumes in dm3 and cm3, however, old units are also allowed: liters and milliliters. 1 liter occupies a volume of 1 dm3, 1 milliliter - 1 cm3. Conventional burettes have a capacity of 10, 25 and 50 cm3 (ml), and the reading of the volume of the solution in them gives three digital signs - tens, units and tenths of a milliliter. Hundredths of a milliliter are determined approximately.

Volumetric flasks usually have a capacity of 25, 50, 100, 200, 250, 500 and 1000 cm3 (mL). Pipettes are usually made in volumes of 5, 10, 15, 20, 25, 50 cm3 (ml).

When using measuring utensils, it should be remembered that its capacity often does not exactly match the indicated one. Class 1 glassware with a capacity of more than 10 ml is suitable for work with an accuracy of 0.1%, for class 2 glassware the tolerances are twice as large.

Filling burettes with solution

A clean burette is filled 1/3 with titrant, make sure that the shutter is in good condition and that there is no air bubble in it. To do this, lift the tip of the burette and slightly open the clamp. If the liquid flows evenly, without air bubbles, the burette is filled correctly. By tilting and turning the burette, the walls are wetted with a solution, after which almost all the solution is drained through the spout. Before starting the titration, the burette is set strictly vertically and filled with titrant to zero. In this case, the level of the meniscus of the liquid with the concave part must coincide with the zero division of the scale (zero division should be at eye level) for colorless solutions. For colored solutions, zero is set at the upper edge of the meniscus.

Measuring solutions with a pipette

Fill a clean pipette with a rubber bulb with the titrated solution until expansion begins. Having closed the upper end with the index finger, turn the pipette several times, trying to moisten the entire inner surface slightly above the mark with the solution. Drain off the solution.

Now fill the pipette with a rubber bulb just above the mark. The pear is removed, the hole is slightly closed with a finger, “holding” the pipette mark at eye level, the excess solution is carefully drained so that the meniscus of the liquid with the concave part coincides with the mark. After that, the pipette hole is clamped and transferred to another vessel. The top of the pipette is opened and the liquid is allowed to flow out quietly. After the liquid drains from the pipette, the last drops are drained, touching the wall of the vessel into which the liquid is poured. Then the pipette is removed, ignoring the liquid that remains in it. Do not blow liquid out of the pipette.

Titration Rules

The place where the titration is carried out should be well prepared and lit. Place a sheet of white paper on the base of the tripod with a burette. The burette is fixed parallel to the rod of the tripod.

Titrated in small portions - drop by drop. Open the clamp of the burette with the left hand, and hold the titration flask with the right, constantly mixing its contents with rotational movements. After the solution has flowed out, the divisions on the burette are counted after 20-30 s to allow the liquid remaining on the walls of the burette to drain.

The reading is taken along the lower (colorless solutions) or upper (colored solutions) edge of the meniscus. The meniscus should be at eye level. To obtain reliable results, repeat the titration at least three times. Each repeat titration starts with the burette zero.

Titration errors

During titration, random and systematic errors are possible. Random errors are associated with the measurement of the volume and weight of the sample, systematic (indicator) errors appear when the end point of the titration does not correspond to the equivalence point.

Measurement errorssolutions arise due to inaccurate measurement of solutions of the substance and titrant. They consist of the volume of one drop (V ~ 0.05 ml), which is usually used to retitrate the solution, and the calibration errors of meters (burettes, pipettes, volumetric flasks), which have deviations of ± (0.01 - 0.02) ml. The relative error of titration depends on the volume of the spent titrant or titrated solution and is equal to:

where v is the sum of the drop volume (~ 0.05 ml) and deviations in volume

burettes (~0.02 ml) and pipettes (~0.02 ml);

V is the volume of the titrated solution or titrant, ml.

Titrimetric or volumetric analysis- a method of quantitative analysis based on measuring the volume (or mass) of the reagent T spent on the reaction with the analyte X. In other words, titrimetric analysis is an analysis based on titration.

The purpose of laboratory classes on titrimetric methods of analysis is to develop practical skills in the technique of performing titrimetric analysis and master the methods of statistical processing of analysis results using the example of specific quantitative determinations, as well as to consolidate theoretical knowledge by solving typical calculation problems for each topic.

Knowledge of the theory and practice of titrimetric analysis methods is necessary for the subsequent study of instrumental methods of analysis, other chemical and special pharmaceutical disciplines (pharmaceutical, toxicological chemistry, pharmacognosy, pharmaceutical technology). The studied methods of titrimetric analysis are pharmacopoeial and are widely used in the practice of a pharmacist to control the quality of drugs.

Conventions

A, X, T - any substance, analyte and titrant, respectively;

m(A), m(X), t(T)- mass of any substance, analyte and titrant, respectively, g;

M(A), M(X), M(T)- molar mass of any substance, analyte and titrant, respectively, g/mol;

n(A), n(X), n(T) - the amount of any substance, analyte and titrant, respectively, mol;

The amount of the substance of the equivalent of any substance, the substance to be determined and the titrant, respectively, mol;

- the volume of a solution of any substance, analyte and titrant, respectively, l;

- the volume of an aliquot of the analyte, equal to the capacity of the pipette, l;

- the volume of the analyzed solution of the analyte, equal to the capacity of the flask, l.

1. Basic concepts of titrimetric

analysis

1.1. Titration- the process of determining substance X by the gradual addition of small amounts of substance T, in which, in some way, the detection of the point (moment) when all substance X has reacted is provided. Titration allows you to find the amount of substance X from a known amount of substance T added up to this point (moment), taking into account the fact that the ratio in which X and T react is known from stoichiometry or otherwise.

1.2. titrant- a solution containing active reagent T, with which the titration is carried out. Titration is usually carried out by adding titrant from a calibrated burette to the titration flask containing the solution to be analyzed. Into this flask before titration add aliquot analyzed solution.

1.3. Aliquot share (aliquot)- precisely known part of the analyzed solution, taken for analysis. It is often taken with a calibrated pipette and its volume is usually indicated by the symbol V ss .

1.4. Equivalence point (TE)- such a point (moment) of titration at which the amount of added titrant T is equivalent to the amount of titrated substance X. Synonyms for TE: stoichiometric point, theoretical end point.

1.5. End point titration (KTT) - the point (moment) of the titration, at which some property of the solution (for example, its color) shows a noticeable (sharp) change. LTT corresponds more or less to TE, but most often does not coincide with it.

1.6. Indicator- a substance that exhibits a visible change in the TE or near it. Ideally, the indicator is present at a concentration low enough to transition interval not cost-

a significant amount of titrant T was used. A sharp visible change in the indicator (for example, its color) corresponds to CTT.

1.7. Indicator transition interval- the area of ​​concentration of hydrogen, metal or other ions within which the eye is able to detect a change in hue, color intensity, fluorescence or other property of a visual indicator caused by a change in the ratio of two corresponding forms of the indicator. This area is usually expressed as the negative logarithm of the concentration, for example: For a redox indicator, the transition range is the corresponding region of the redox potential.

1.8. Degree of titration - volume ratio V (T) of the added titrant to the volume V (TE) of the titrant corresponding to the TE. In other words, the degree of titration of a solution is the ratio of the amount of the titrated substance to its initial amount in the analyzed solution:

1.9. Titration level- order the concentration of the titrant solution used, for example, 10 -1 , 10 -2 , 10 -3 , etc.

1.10. Titration curve - graphic representation of the dependence of the change in concentration c (X) of the analyte X or some related property of the system (solution) on the volume V (T) added titrant T. The value of c (X) during the titration changes by several orders of magnitude, so the titration curve is often plotted in the coordinates: The abscissa shows the volume of added titrant V (T) or degree of titration / . If the equilibrium concentration c (X) or the intensity of a property proportional to it is plotted along the y-axis, then we get linear titration curve. If on the y-axis we set aside or the logarithm of the intensity of a property proportional to c(X), then one gets logarithmic (or monologarithmic) titration curve. To more clearly identify the features of the titration process and for applied purposes, sometimes they build differential titration curves, plotting along the abscissa axis the volume of the added titrant V (T), and along the y-axis - the first derivative of the logarithm of the concentration (or the intensity of a property proportional to it) with respect to the volume of the added titrant: Such titration curves are usually used in physicochemical methods of analysis, for example, in potentiometric titrations.

1.11. Standard solution- a solution having a known concentration of the active substance.

1.12. Standardization- the process of finding the concentration of an active reagent in a solution (most often by titrating it with a standard solution of the corresponding substance).

1.13. Titration jump- the interval of a sharp change in any physical or physico-chemical property of the solution near the equivalence point, usually observed when 99.9-100.1% of the titrant is added compared to its stoichiometric amount.

1.14. Blank titration- titration of a solution that is identical to the analyzed solution in terms of volume, acidity, amount of indicator, etc., but does not contain the analyte.

2. Basic operations of titrimetric analysis

2.1. Cleaning, washing, storage of measuring utensils.

2.2. Checking the capacity of measuring utensils.

2.3. Taking a sample with a precisely known mass by the difference between the results of two weighings (usually on an analytical balance).

2.4. Quantitative transfer of a sample of a substance into a volumetric flask and dissolution of the substance.

2.5. Filling volumetric utensils (flasks, burettes, pipettes) with a solution.

2.6. Emptying pipettes, burettes.

2.7. Selection of an aliquot of the analyzed solution.

2.8. Titration and calculations based on titration results.

3. Calibration of measuring instruments

In titrimetric analysis, the exact volumes of the solution are measured using measuring utensils, which are volumetric flasks with a capacity of 1000, 500, 250, 100, 50 and 25 ml, pipettes and graduated pipettes with a capacity of 10, 5, 3, 2 and 1 ml. The capacity of the flask and pipette at 20 °C is engraved on the neck of the flask or on the side of the pipette (nominal volume). In the mass production of volumetric utensils, the actual (true) capacity of volumetric flasks, burettes, pipettes may differ from the nominal values ​​indicated on the utensils. To achieve the required accuracy of the obtained results of titrimetric analysis

Calibration of volumetric glassware is based on determining the exact mass of distilled water poured in or poured out, which is determined by the results of weighing the glassware before and after pouring in or pouring out water. The volume of water in the calibrated vessel (its capacity) and the mass of water are related by the ratio:

Where - density of water at the temperature of the experiment, g/ml.

The density of water depends on temperature, so when making calculations, you should use the data in Table. 2-1.

Table 2-1. Density values ​​of water at the corresponding temperature

Volumetric flasks are calibrated for infusion, and burettes and pipettes are calibrated for pouring, since small amounts of liquid always remain on the walls of the dish during pouring.

3.1. Volumetric flask capacity check

The flask is thoroughly washed, dried and weighed on an analytical balance with an accuracy of ± 0.002 g. Then it is filled with water (hereinafter - distilled) along the lower meniscus, the drops of water in the upper part of the neck of the flask are removed with filter paper and weighed again. Each weighing of an empty flask and a flask with water is carried out at least twice, while the difference between two weighings should not exceed ± 0.005 g. The difference between the mass of the flask with water and the mass of the empty flask is equal to the mass of water contained by the flask at a given temperature. The true capacity of the flask is calculated by dividing the average mass of water by its density at the test temperature (see Table 2-1).

For example, if a volumetric flask with a nominal volume of 100 ml is calibrated, the average mass of water at 18 °C is 99.0350 g. Then the true capacity of the volumetric flask is:

3.2. Burette capacity check

The burette is a glass cylinder, the inner diameter of which can vary slightly along the length of the burette. Equal divisions on the burette in its various parts correspond to unequal volumes of the solution. That is why burette calibration calculates the true volumes for each selected buret site.

A clean and dried burette is filled with water to the zero mark along the lower meniscus and water drops are removed from the inner surface of the upper part of the burette with filter paper. Then, under the burette substitute a bottle, previously weighed with a lid on an analytical balance. A certain volume of water (for example, 5 ml) is slowly poured into the bottle from the burette. After that, the bottle is closed with a lid and weighed again. The difference between the mass of the weighing bottle with water and the empty weighing bottle is equal to the mass of water contained in the burette between divisions of 0 and 5 ml at the temperature of the experiment. Then the burette is again filled with water to the zero mark along the lower meniscus, 10 ml of water is slowly poured into an empty bottle and the mass of water contained in the burette between divisions 0 and 10 ml is determined in a similar way. When calibrating the burette, for example, for 25 ml, this operation is carried out 5 times and the mass of water corresponding to the nominal volumes indicated on the burette of 5, 10, 15, 20 and 25 ml is calculated. Each weighing of an empty bottle and a bottle of water is repeated at least twice, while the difference between two weighings should not exceed ± 0.005 g.

Then according to the table. 2-1 determine the density of water at the temperature of the experiment and calculate the true capacity of the burette for each value of the nominal volume indicated on it.

Based on the data obtained, the correction value is calculated equal to the difference between the calculated value of the true capacity and the corresponding value of the nominal volume of the burette:

and then draw a curve of burette capacity errors in coordinates (Figure 2-1).

For example, let the following experimental data be obtained when calibrating a burette with a capacity of 25 ml at a temperature of 20 °C, which, together with the results of the corresponding calculations, are presented in Table. 2-2.

Based on the obtained tabular data, a capacity correction curve for a given buret is plotted, using which it is possible to refine the results of reading by buret.

Table 2-2. Calibration results for a 25 ml burette

Rice. 2-1. Burette capacity adjustment curve

For example, let 7.50 ml of titrant be used for titration of an aliquot of the analyte according to the results of counting on a burette. According to the graph (see Fig. 2-1), the correction value corresponding to this nominal volume is 0.025 ml, the true volume of titrant used is: 7.50 - 0.025 = 7.475 ml.

3.3. Checking pipette capacity

A pipette, clean and weighed on an analytical balance, is filled with water to the zero mark along the lower meniscus and then the water is slowly filled.

poured along the wall into a pre-weighed bottle. The bottle is covered with a lid and weighed with water. Each weighing of an empty bottle and a bottle with water is repeated at least two times, while the difference between two weighings should not exceed ± 0.005 g. The difference between the mass of a bottle with water and an empty bottle is equal to the mass of water contained by a pipette. The true capacity of the pipette is calculated by dividing the average mass of water by the density of the water at the test temperature (see Table 2-1).

4. Typical calculations in titrimetric analysis

4.1. Ways of expressing concentrations used for calculations in titrimetric analysis

4.1.1. Molar concentration of substance c (A), mol / l - the amount of substance A in mol contained in 1 liter of solution:

(2.1)

Where - the amount of substance A in mol, dissolved in V (A) l

solution.

4.1.2. Molar concentration equivalent of a substance , mol / l - the amount of substance A equivalent in mol contained in 1 liter of solution (the former name is the “normality” of the solution):

(2.2)

Where
- the amount of substance equivalent to A in mol,

dissolved in V (A) l of solution; - molar mass of the equivalent of ve-

substances A, g / mol; - the equivalence factor of the substance.

4.1.3. Substance titer T(A), g / ml - the mass of solute A in grams, contained in 1 ml of solution:

4.1.4. Titrimetric conversion factor I, g / ml - mass of the analyte in grams, interacting with 1 ml of titrant:

(2.4)

4.1.5. Correction factor F- a value showing how many times the practical concentrations of the titrant differ from the corresponding theoretical values ​​specified in the method:

(2.5)

4.2. Calculation of the molar mass equivalent of substances in reactions used in titrimetric analysis

An equivalent is a real or conditional particle that can add or donate one hydrogen ion H + (or be otherwise equivalent to it in acid-base reactions) or add or donate one electron in redox reactions.

Equivalence factor - a number indicating which

the equivalent fraction is from a real particle of substance A. The equivalence factor is calculated based on the stoichiometry of this reaction:

Where Z- the number of protons donated or added by one reacting particle (molecule or ion) in an acid-base reaction, or the number of electrons donated or accepted by one reacting particle (molecule or ion) in an oxidation or reduction half-reaction.

The molar mass of the equivalent of a substance is the mass of one mole of the equivalent of a substance, equal to the product of the equivalence factor by the molar mass of the substance, g / mol. It can be calculated using the formula:

(2.6)

4.3. Preparation of a solution by diluting a more concentrated solution with a known concentration

When carrying out titrimetric analysis, in some cases it is required to prepare a solution of substance A with a volume approximately known concentration by diluting a more concentrated solution.

When the solution is diluted with water, the amount of substance A or the amount of substance A does not change, therefore, in accordance with expressions (2.1) and (2.2), we can write:

(2.7)
(2.8)

where indices 1 and 2 refer to solutions before and after dilution, respectively.

From the ratios obtained, the volume of a more concentrated solution is calculated , which must be measured to prepare a given solution.

4.4. Preparation of a predetermined volume of solution by weighing a precisely known mass

4.4.1. Sample Weight Calculation

The theoretical mass of a sample of a standard substance A, necessary to prepare a given volume of a solution with a known concentration, is calculated from expressions (2.1) and (2.2). It is equal to:

(2.9)

if the molar concentration of a substance in solution is used, and:

(2.10)

if the molar concentration of the equivalent of the substance in solution is used.

4.4.2. Calculation of the exact concentration of the prepared solution

The concentration of a solution of substance A, prepared by an accurate sample of mass m (A), is calculated from the relationships (2.1-2.3), where t(A)- the practical mass of substance A, taken from the difference between two weighings on an analytical balance.

4.5. Calculation of titrant concentration during its standardization

Known volume of standard solution with concentration titrated with a titrant solution of volume V (T)(or vice versa). In this case, for the reaction taking place in the solution during the titration process , the law of equivalents has the form:

And

From here, an expression is obtained for calculating the molar concentration of the titrant equivalent from the results of titration:

(2.12)

4.6. Calculation of the mass of the analyte in the analyzed solution4.6.1. direct titration

The substance to be determined in the analyzed solution is titrated directly with a titrant.

4.6.1.1. Calculation using titrant equivalent molar concentration

An aliquot of the analyte solution titrated

titrant solution with volume V(T). In this case, for the reaction occurring in the solution during the titration process:

the law of equivalents has the form: And

(2.13)

Hence, the molar concentration of the equivalent of the analyte, calculated from the results of titration, is equal to:

(2.14)

The resulting expression is substituted into equation (2.2) and a formula is obtained for calculating the mass of the analyte in a flask with a volume according to the results of direct titration:

(2.15)

If, during titration, part of the titrant is consumed by the reaction with the indicator, a "blank experiment" is carried out and the volume of titrant V "(T) is determined,

used for indicator titration. In calculations, this volume is subtracted from the volume of the titrant, which was used to titrate the solution of the analyte. Such an amendment is made during the "blank experiment" in all calculation formulas used in titrimetric analysis. For example, formula (2.15) for calculating the mass of the analyte, taking into account the “blank experiment”, will look like:

(2.16)

4.6.1.2. Calculation using titrimetric conversion factor

We have an analyzed solution with a volume For titration of alik-

mil's share solution of analyte used volume of titrant V (T) with theoretical titrimetric conversion factor and correction factor F. Then the mass of the analyte in an aliquot is equal to:

(2.17)

and throughout the analyzed volume

(2.18)

4.6.2. substitution titration

a known excess of reagent A is added and substituent B is isolated in an amount equivalent to the analyte:

Substituent B is titrated with a suitable titrant:

The law of equivalents for substitution titration:

using relation (2.8) can be written in the form:

From here, a formula is obtained for calculating the molar concentration of the equivalent of the analyte in solution according to the results of substitution titration:

which has the same form as in direct titration (2.14). That is why all calculations of the mass of the analyte in the analyzed problem during substitution titration are carried out according to formulas (2.15-2.18) for direct titration. 4.6.3. Back titration

To an aliquot of the analyte add famous excess of the first titrant :

Then the excess of the unreacted first titrant is titrated with the second titrant, which consumes the volume :

The law of equivalents in this case can be written as:

From here, the molar concentration of the equivalent of substance X in solution is calculated:

(2.19)

Substitute the resulting expression into equation (2.2) and obtain a formula for calculating the mass of the analyte in the analyzed solution, equal to the volume of the flask, based on the results of back titration:

5. Implementation and provision of practical work on titrimetric analysis

5.1. General provisions

When studying the section "Titrimetric analysis", it is planned to carry out work on the following topics.

Theme I Methods of acid-base titration.

Theme II. Methods of redox titration.

Topic III. Methods of precipitation titration.

Topic IV. Methods of complexometric titration.

Lesson 1. Preparation of hydrochloric acid solution and its standardization.

Lesson 2. Determination of the mass of alkali in solution. Determination of the mass of carbonates in solution. Determination of the mass of alkali and carbonate in solution in the joint presence.

Lesson 3. Determination of the mass of ammonia in solutions of ammonium salts.

a) Test control 1.

b) Determination of the mass of ammonia in solutions of ammonium salts. Lesson 4. Permanganometric titration.

a) Written test 1.

b) Determination of the mass of hydrogen peroxide in solution.

c) Determination of the mass of iron(II) in a salt solution. Determination of the mass fraction of iron(II) in a salt sample.

Lesson 5. Iodometric titration.

a) Determination of the mass of hydrogen peroxide in solution.

b) Determination of the mass of copper(II) in solution. Lesson 6. iodimetric titration.

Lesson 7. Bromatometric titration. Determination of the mass of arsenic (III) in solution.

Lesson 8. bromometric titration. Determination of the mass fraction of sodium salicylate in the preparation.

Lesson 9. Nitritometric titration.

a) Test control 2.

b) Determination of the mass fraction of novocaine in the preparation. Lesson 10. Argentometric titration and hexacyanoferratom-

tric titration.

a) Written test 2.

b) Determination of the mass of potassium bromide and potassium iodide in solution by argentometric titration.

c) Determination of the mass of zinc in solution by hexacyanoferratometric titration.

Lesson 11. Complexometric determination of the mass of zinc and lead in solution.

a) Test control 3.

b) Determination of the mass of zinc and lead in solution.

Lesson 12. Complexometric determination of iron(III) and calcium in solution.

a) Written test 3.

b) Determination of the mass of iron(III) and calcium in solution.

Depending on the specific situation, it is allowed to carry out some work during not one, but two lessons. It is also possible to shift the timing of test controls and written tests.

At the end of each topic, examples of test items for intermediate control of students' knowledge, the content of the final written test, an example of a ticket for a written test are given.

At the end of each lesson, the student draws up a protocol that includes the date and name of the work performed, the essence of the methodology, the order of work, the experimental data obtained, calculations, tables, conclusions. All calculations of the results of the analysis (concentration of the solution, mass of the analyte) are performed by students with an accuracy of the fourth significant figure, except for cases specifically specified in the text.

Intermediate control of practical skills and theoretical knowledge is carried out with the help of test control and written tests.

5.2. Material support for classes in titrimetric analysis

Glassware: burettes with a capacity of 5 ml, volumetric pipettes with a capacity of 2 and 5 ml, volumetric flasks with a capacity of 25, 50, 100 and 250 ml, conical flasks with a capacity of 10-25 ml, glass bottles, glass funnels with a diameter of 20-30 mm, bottles of ordinary or dark glass with a capacity of 100, 200 and 500 ml, measuring cylinders with a capacity of 10, 100 ml.

Reagents: Reagents of "chemically pure" qualification are used in the work and "ch.d.a.", indicator paper.

Devices: analytical balances with weights, technical balances with weights, oven, laboratory thermometer with a scale of 20-100 °C, tripods with burette clamps and rings for asbestos nets, gas burners, water baths.

Auxiliary materials and accessories: detergents (soda, washing powders, chromium mixture), dishwashing brushes, rubber bulbs, asbestos nets, stationery glue, glass pencils, filter paper.

Bibliography

1. Lectures for students on the section "Titrimetric analysis".

2.Kharitonov Yu.Ya. Analytical chemistry (analytics): In 2 volumes - ed. 5th - M.: graduate School, 2010 (hereinafter referred to as the "Textbook").

3.Lurie Yu.Yu. Handbook of Analytical Chemistry.- M.: Chemistry, 1989 (hereinafter referred to as the "Handbook").

4.Dzhabarov D.N. Collection of exercises and tasks in analytical chemistry.- M.: Russian doctor, 2007.

Section III

CALCULATIONS IN TITRIMETRIC ANALYSIS

1. CALCULATION OF THE MOLAR MASS OF THE EQUIVALENT OF A SUBSTANCE

Equivalent called a real or conditional particle of a substance, which in a given acid-base reaction is equivalent to one hydrogen ion or in a given oxidation-reduction reaction - to one electron.

Equivalence factor feq. (А)=1/z – a number showing what fraction the equivalent is of a real particle of matter A, calculated from the stoichiometry of the given reaction.

Molar mass equivalent substances A, M(1/zA) – mass of one mole equivalent of a substance A

M(1/zA) = 1/zM(A).

IN acid-base reactions for one HCl molecule, one hydrogen atom participates in the reaction, so the equivalent of HCl is equal to the HCl molecule, and feq.(HCl) = 1; for one NaOH molecule, one OH- ion participates in the reaction, therefore the NaOH equivalent is equal to the NaOH molecule, and feq.(NaOH) = 1.

In the reaction H3PO4 + 2NaOH → Na2HPO4 + 2H2O

one H3PO4 molecule reacts with two molecules, or two equivalents, of NaOH, so feq.(H3PO4) \u003d ½ and M (½H3PO4) \u003d ½ M (H3PO4) \u003d 49.00 g / mol.

In the reaction NH4Cl + NaOH → NH3 + NaCl + H2O

one molecule of ammonium chloride reacts with one molecule, or one equivalent, of NaOH, so feq.(NH4Cl) = 1 and the molar mass of the NH4Cl equivalent is equal to its molar mass of 53.49 g/mol.

IN redox reaction:

K2Cr2O7 + 3K2SO3 + 4H2SO4 → 4K2SO4 + Cr2(SO4)3 + 4H2O

according to the reduction half-reaction equation:

Cr2O72– + 14H+ + 6ē → 2Cr3+ + 7H2O

one Cr2O72– ion accepts 6 electrons, therefore feq.(K2Cr2O7) = feq.(Cr2O72–) = 1/6 and М(1/6К2Сr2О7) = 1/6 М(К2Сr2О7) = 49.03 g/mol.

According to the oxidation half-reaction equation:

SO32– + H2O – 2ē → SO42– + 2H+

one SO32– ion donates two electrons, therefore feq.(Na2SO3) = feq.(SO32–) \u003d ½ and M (½Na2SO3) \u003d ½M (Na2SO3) \u003d 63.02 g / mol.

2. CHARACTERISTICS OF SOLUTIONS USED IN CALCULATIONS IN TITRIMETRY

Molar concentration substances A in solution C(A), mol/dm3 (mol/l) shows the number of moles of a substance A, contained in 1 dm3 (l) solution:

https://pandia.ru/text/80/149/images/image002_91.gif" width="235" height="43 src="> (3.2)

where n(1/z A) is the amount of substance equivalent to A, mol, dissolved in V dm3 (l) of the solution;

M(1/z A) is the molar mass of the equivalent of substance A, g/mol;

1/z is the equivalence factor.

Titer substances T(A), g / cm3 (g / ml) - mass concentration, showing how many grams of a solute A contained in 1 cm3 (ml) of solution:

https://pandia.ru/text/80/149/images/image004_74.gif" width="253" height="41 src=">, (3.4)

where T(T) is the titer of the titrant, g/cm3 (g/mL);

M(1/z X) is the molar mass of the analyte equivalent, g/mol;

М(1/zТ) is the molar mass of the titrant equivalent, g/mol;

С(1/z Т) is the molar concentration of the titrant equivalent, mol/dm3 (mol/l).

Correction factor F- value showing how many times the practical molar concentration of the titrant equivalentС(1/zТ)pr., his caption T(T)pr . or titrimetric conversion factor t(T/X)pr. differ from the corresponding "theoretical" values C(1/zT)theor., T(T)theor. And t(T/X)theor., given in the methodology.

DIV_ADBLOCK324">

if the molar concentration of the substance is used;

if the molar concentration of the substance equivalent is used;

m(A) = T(A) V(A) 103,

if the titer of the substance is used, and

if a titrimetric conversion factor is used (titre for the analyte).

3.2. Calculation of the concentration of the prepared solution

The concentration values ​​of the solutions prepared from weighed portions are calculated using formulas (3.1 - 3.3).

3.3. Preparation of solutions by diluting more concentrated solutions

When a solution is diluted with water (or another solvent), the amount of substance A and the amount of substance A do not change, therefore

n1(А) = n2(А), and

n1(1/zА) = n2(1/zА),

therefore, one can write:

C1(A) V1(A) = C2(A) V2(A)

C1(1/zA) V1(A) = C2(1/zA) V2(A),

where indices 1 and 2 refer to solutions before and after dilution, respectively.

4. STANDARDIZATION OF THE TITRANT

4.1. Calculation of the molar concentration of the titrant equivalent

4.1.1. Single weight method

A sample of a standard substance with a mass m(A) is dissolved in water and the resulting solution is titrated with a titrant solution with a volume V(T). In this case, the law of equivalents has the form:

n(1/z A) = n(1/z T)

https://pandia.ru/text/80/149/images/image010_50.gif" width="154" height="39 src=">.

4.1.2. Pipetting method (aliquot)

A known volume of a standard solution V(A) with a concentration of C(1/z A) is titrated with a titrant solution of volume V(T). In this case, the law of equivalents has the form:

https://pandia.ru/text/80/149/images/image012_43.gif" width="145" height="39 src=">

4.2. Calculation of titrimetric conversion factor, titer and titrant correction factor

The titer of titrant T(T) (g/ml) is calculated by the formula

https://pandia.ru/text/80/149/images/image014_22.gif" width="154" height="64 src=">

where m(X) is the mass of the analyte X in the sample.

Hence, the mass of the analyte X in the sample is equal to:

m(X) = C(1/zT)∙V(T)∙M(1/zX).

When performing mass analyzes, it is convenient to calculate the mass of the analyte using titrimetric conversion factor (titre by analyte) t(T/X).

If during the titration of a weighed portion of the analyzed sample, the volume of titrant V(T), l with a titer for the analyte t(T/X) was consumed, then the mass of the analyte is equal to:

m(X) = t(T/X)∙V(T)∙103.

Titration aliquot share solution of the analyte with a volume V (X), the law of equivalents has the form:

https://pandia.ru/text/80/149/images/image016_19.gif" width="165" height="39 src=">

and the mass of the analyte in the flask with volume Vk:

https://pandia.ru/text/80/149/images/image018_17.gif" width="184" height="41 src=">.

5.1.2. substitution titration

A known excess of reagent A is added to the analyte X, and substituent B is isolated in an amount equivalent to the analyte:

X + A → B + ...

Substituent B is titrated with titrant T:

B + T → C + ...

The law of equivalents for substitution titration is:

https://pandia.ru/text/80/149/images/image027_11.gif" width="120" height="91">

where w(X) is the mass fraction of substance X in the sample,

w%(X) – mass fraction of substance X in the sample, %,

m(X) is the mass of substance X in the sample.