Discussion Examples for Calcium Determination in Milk | Chelometric Titration and the Effects of Pretreatment

What Is the Determination of Calcium in Milk?

Determination of calcium in milk is an analysis in which the amount of calcium contained in milk is measured chemically.
Calcium is an important mineral involved in the formation of bones and teeth and is an important component when considering the nutritional value of milk.
In food labeling and nutritional evaluation, the calcium content of milk is often an important focus.

Calcium in milk exists in several states, including Ca2+ dissolved in the aqueous phase, calcium bound to casein micelles, and calcium associated with calcium phosphate.
Therefore, depending on the measurement method, the “state of calcium being measured” may differ.
In a report, it is important to discuss the fact that pretreatment converts calcium into a form that can be measured.

Main Items to Include in the Results

In the results of calcium determination in milk, organize the type of milk sample, sample amount, dilution factor, pretreatment method, pH conditions, concentration of the EDTA standard solution, titration volume, indicator, endpoint color change, calcium amount, and other information.
Because milk is a complex sample containing proteins and fats, it is important to clearly record the pretreatment conditions.

Main Items to Include in the Results

• Type of milk sample
• Amount of sample collected
• Dilution factor
• Pretreatment method
• Presence or absence of deproteinization
• Presence or absence of ashing or acid digestion
• Presence or absence of filtration or centrifugation
• pH adjustment conditions
• Type of buffer solution
• Concentration of the EDTA standard solution
• EDTA titration volume
• Type of indicator
• Color change at the endpoint
• Blank value
• Amount of calcium
• Converted value per 100 mL or per 100 g
• Comparison with the food-label value
• Causes of error and points for improvement

Reference Experimental Values and Calculation Examples for Calcium Determination in Milk

Here, for an experiment in which calcium in milk is determined by chelometric titration, pretreatment, EDTA titration volume, calcium concentration, content per 100 mL of milk, and recovery are organized using reference experimental values.

Because milk contains proteins and fats, titrating it directly may make the endpoint difficult to observe or may leave calcium bound to proteins and other substances.
Therefore, pretreatment such as acid digestion, deproteinization, and dilution is performed to convert calcium ions into a form that is easier to measure before titration.

Reference Experimental Conditions

Example Pretreatment Procedure

Because milk is turbid and contains proteins and fats, the calcium is converted into a state that is easier to measure before titration.
Here, an example is shown in which acid treatment and filtration are performed and the solution is diluted to a fixed volume.

EDTA Titration Results

An example is shown in which 10.00 mL of the pretreatment solution was aliquoted and titrated with a 0.0100 mol/L EDTA standard solution.
Here, three titrations are performed, and the average value is used to determine the amount of calcium.

Example Calculation of Average Titration Volume

The average value is calculated from the three titration volumes.

Average titration volume = (7.46 + 7.49 + 7.45) ÷ 3 = 7.47 mL

Therefore, in this reference example, an average of 7.47 mL of EDTA standard solution was required to titrate the calcium in 10.00 mL of the pretreatment solution.

Amount of Calcium in 10.00 mL of the Pretreatment Solution

EDTA reacts with calcium ions in a 1:1 ratio.
Therefore, the amount of EDTA consumed corresponds to the amount of Ca2+ in the titrated sample.

Amount of Ca2+ = EDTA concentration × EDTA titration volume

Because the EDTA concentration is 0.0100 mol/L and the average titration volume is 7.47 mL = 0.00747 L, the value can be calculated as follows.

Amount of Ca2+ = 0.0100 mol/L × 0.00747 L = 7.47 × 10−5 mol

Therefore, 10.00 mL of the pretreatment solution was considered to contain 7.47 × 10−5 mol of calcium ions.

Amount of Calcium in the Entire Pretreatment Solution

The pretreatment solution was diluted to 100.0 mL, and 10.00 mL of it was aliquoted and titrated.
Therefore, the amount of calcium contained in the entire pretreatment solution is 10 times the amount determined by titration.

Amount of Ca2+ in the entire pretreatment solution = 7.47 × 10−5 mol × 10 = 7.47 × 10−4 mol

The mass of calcium is determined by multiplying the amount of substance by the molar mass.

Mass of Ca = 7.47 × 10−4 mol × 40.1 g/mol = 0.0299 g

0.0299 g is 29.9 mg.
Therefore, approximately 29.9 mg of calcium was calculated to be contained in the collected 10.00 mL of milk.

Amount of Calcium per 100 mL of Milk

Because 10.00 mL of milk was collected for this measurement, the value is multiplied by 10 to convert it to the content per 100 mL.

Amount of Ca per 100 mL of milk = 29.9 mg × 10 = 299 mg/100 mL

Therefore, in this reference example, the amount of calcium in milk was determined to be 299 mg/100 mL.

Example Comparison Among Samples

The following shows reference examples in which different types of milk and dairy products were measured using the same method.
The conditions are those in which 10.00 mL of a 100.0 mL pretreatment solution was aliquoted and titrated with 0.0100 mol/L EDTA.

Comparison With and Without Pretreatment

If pretreatment of milk is insufficient, calcium may not be completely measured or the endpoint may become unclear.
Here, reference examples are shown for different pretreatment conditions.

In this reference example, the endpoint was easiest to observe and the measured values were most stable under the condition involving acid treatment and filtration.
If pretreatment is insufficient, the calcium amount may be underestimated, while turbidity may cause overestimation.

Example of Checking Recovery by Standard Addition

For a complex sample such as milk, a known amount of calcium may be added and the recovery calculated in order to examine the effects of pretreatment and coexisting components.

Example Calculation of Recovery

Recovery indicates how much of the added standard component was recovered as a measured value.

Recovery (%) = (Measured value after addition − Measured value before addition) ÷ Added amount × 100

When 5.0 mg of calcium was added, if the measured value before addition was 29.9 mg and the measured value after addition was 34.7 mg, the recovery is calculated as follows.

Recovery = (34.7 − 29.9) ÷ 5.0 × 100 = 96.0%

The closer the recovery is to 100%, the smaller the major losses caused by pretreatment and titration procedures are considered to be.

Effect of Magnesium

Milk contains magnesium in addition to calcium.
Because EDTA reacts not only with Ca2+ but also with Mg2+, it may affect the measured value depending on the conditions.

When calcium alone is to be determined, the pH conditions must be appropriately adjusted to minimize the effect of Mg2+ as much as possible.

Example of How to Write the Results

After 10.00 mL of milk was acid-treated and filtered, the solution was diluted to 100.0 mL, and 10.00 mL of this solution was aliquoted for EDTA titration.
The titration volumes with 0.0100 mol/L EDTA standard solution were 7.46 mL, 7.49 mL, and 7.45 mL, and the average titration volume was 7.47 mL.

Because EDTA and Ca2+ react in a 1:1 ratio, the amount of Ca2+ in 10.00 mL of the pretreatment solution was determined to be 7.47 × 10−5 mol.
In the entire 100.0 mL of pretreatment solution, the amount was 7.47 × 10−4 mol, and the mass of calcium was 29.9 mg.
Because this corresponds to the amount in 10.00 mL of milk, the value per 100 mL of milk was 299 mg/100 mL.

In addition, when 5.0 mg of calcium standard solution was added, the measured calcium amount was 34.7 mg and the recovery was 96.0%.
From this, major losses of calcium due to pretreatment and titration procedures were considered to be small.

Points for Connecting the Results to the Discussion

In chelometric titration of calcium in milk, it is important to discuss not only the titration calculation but also the meaning of pretreatment and the effects of coexisting components.

• Has the 1:1 reaction between EDTA and Ca2+ been correctly reflected in the calculation?
• Have the dilution factor of the pretreatment solution and the aliquot volume been considered when converting to the amount in milk?
• Has the value been converted to the amount of calcium per 100 mL of milk?
• Can the reason for pretreatment be explained in relation to proteins, fats, and turbidity?
• If the endpoint color change was unclear, can its effect on the titration value be explained?
• Has the possibility that coexisting ions such as Mg2+ affect the EDTA titration been considered?
• Can the appropriateness of the pretreatment and measurement procedures be evaluated from the recovery?

Example Discussion

In this experiment, calcium in milk was determined by EDTA chelometric titration.
After 10.00 mL of milk was pretreated and diluted to 100.0 mL, 10.00 mL of the solution was titrated.
The average titration volume of the 0.0100 mol/L EDTA standard solution was 7.47 mL.
Because EDTA and Ca2+ react in a 1:1 ratio, the amount of calcium in 10.00 mL of milk was determined to be 29.9 mg.
When converted to the amount per 100 mL, the value was 299 mg/100 mL.

Milk contains proteins and fats, and if it is titrated directly, turbidity makes the endpoint difficult to observe.
In addition, some calcium exists in association with proteins, phosphates, and other components, so the measured value may be low if pretreatment is not performed.
In this reference example, the endpoint was easier to observe and the titration values were stable under conditions involving acid treatment and filtration, so pretreatment was considered effective for calcium determination.

When the presence or absence of pretreatment was compared, the calculated calcium amount under the dilution-only condition was 273 mg/100 mL, which was lower than the 299 mg/100 mL obtained with acid treatment and filtration.
This suggests that calcium in bound states may not have been sufficiently measured.
On the other hand, without filtration, the endpoint became unclear and turbidity may have caused the titration value to shift.

The recovery determined by standard addition was 96.0%, indicating that most of the added calcium was recovered as the measured value.
From this, major losses due to pretreatment and titration procedures were considered to be small.
However, because EDTA reacts not only with Ca2+ but also with Mg2+, the measured value may become high if the pH conditions are inappropriate.
Therefore, accurate determination of calcium requires appropriate pH adjustment, pretreatment, and endpoint judgment.

Summary

In the determination of calcium in milk, the 1:1 reaction between EDTA and Ca2+ is used to determine the amount of calcium from the titration volume.
By considering the dilution factor of the pretreatment solution and the aliquot volume, the result can be converted to the calcium content per 100 mL of milk.

In this reference example, the amount of calcium in milk was 299 mg/100 mL.
In a report, it is useful to discuss not only the titration calculation but also the necessity of pretreatment, endpoint judgment, coexisting ions, and recovery in relation to one another.

What Is EDTA Chelometric Titration?

EDTA chelometric titration is a titration method for determining the concentration of metal ions by utilizing the property of EDTA to form stable complexes with metal ions.
EDTA reacts with many metal ions such as Ca2+ and Mg2+.
In calcium determination, the fact that Ca2+ and EDTA form a complex in a 1:1 ratio is used.

In EDTA titration, a metal indicator is used to determine the endpoint.
The indicator shows different colors when it is bound to a metal ion and when the metal ion has been removed from it by EDTA.
This color change is used to determine the point at which the metal ions have completely reacted with EDTA.

Ca2+ + EDTA4- → CaEDTA2-

The 1:1 Reaction Between Calcium and EDTA

EDTA forms a complex with calcium ions in a 1:1 molar ratio.
In other words, 1 mol of EDTA reacts with 1 mol of Ca2+.
This simple quantitative relationship is the basis of calcium determination by EDTA titration.

The larger the EDTA titration volume, the greater the amount of Ca2+ considered to be contained in the sample.
However, if the sample contains other metal ions such as Mg2+ that also react with EDTA, the titration volume may not reflect only calcium.
Therefore, it is necessary to consider the effects of pH conditions, masking, and pretreatment.

Forms of Calcium Present in Milk

Calcium in milk exists in several states, unlike Ca2+ in a simple aqueous solution.
Some exists as ions dissolved in the aqueous phase, while some exists in forms associated with casein micelles and calcium phosphate.
Therefore, milk can be considered a complex dispersion system containing calcium.

In EDTA titration, it is important to use pretreatment to convert calcium into a state in which it can readily react with EDTA in solution.
If pretreatment is insufficient, calcium remaining in casein micelles or precipitates may not be reflected in the titration, resulting in underestimation of the calcium amount.

Why Pretreatment Is Necessary

Milk is a complex food containing water, fats, proteins, sugars, inorganic salts, and other components.
If it is titrated directly, turbidity caused by fats and proteins, difficulty observing the indicator color change, and the binding state of calcium may affect the measurement.
Therefore, pretreatment such as dilution, acid treatment, deproteinization, ashing, and filtration may be performed before EDTA titration.

The purpose of pretreatment is to convert calcium into a measurable form, reduce interfering components, and make the endpoint easier to observe.
However, if calcium precipitates during pretreatment, remains in the filtration residue, or part of the solution is lost, errors occur in the measured value.
Pretreatment improves measurement accuracy but can also become a source of error.

Effect of Deproteinization

Milk contains casein and whey proteins.
These proteins are not only associated with calcium but may also make the solution turbid and make the indicator color change difficult to observe.
Therefore, treatment to remove proteins using acids or precipitating agents may be performed.

If deproteinization makes the solution transparent, endpoint determination becomes easier.
However, if calcium is incorporated into the precipitated proteins or calcium-containing solution remains in the filtration residue, the amount of calcium may be underestimated.
In deproteinization, the balance between removal of interfering substances and loss of components must be considered.

Effect of Fat Content

Fat contained in milk exists in a dispersed state different from the aqueous phase.
Fat globules make the solution cloudy and may make the indicator color change and endpoint determination difficult to observe.
In samples with high fat content, it may also be difficult to collect a uniform sample.

When measuring milk containing fat, it is important to mix the sample thoroughly and collect a representative portion.
Pretreatment such as defatting or ashing can reduce interference from fat when necessary.
However, care must be taken not to lose part of the sample during pretreatment.

Discussion of Ashing and Acid Digestion

When the aim is to measure calcium in milk in a form close to the total amount, ashing or acid digestion may be used to decompose organic matter and extract inorganic components into solution.
This treatment reduces the effects of proteins and fats and converts calcium into a form that readily reacts with EDTA.

However, during ashing and acid digestion, sample scattering, insufficient dissolution of residues, adhesion to equipment, and acid handling may become sources of error.
In addition, if the treatment conditions are too strong or inappropriate, sample loss or contamination may occur.
The choice of pretreatment method greatly affects the target of measurement and the accuracy.

Importance of pH Conditions

Complex formation between EDTA and metal ions is greatly affected by pH.
The form in which EDTA exists changes with pH, and its ease of reaction with metal ions also changes.
In addition, indicator color changes and precipitation of metal ions are affected by pH conditions.

When calcium is selectively titrated, it is important to adjust the solution to the pH conditions specified in the laboratory manual.
If the pH is too low, complex formation with EDTA may be insufficient, while if the pH is too high, precipitation of metal hydroxides, phosphates, and other compounds may have an effect.
Maintaining a constant pH using a buffer solution leads to reproducible measurements.

Indicator and Endpoint Determination

In EDTA titration, a metal indicator is used to determine the endpoint.
In calcium determination, calcium indicators such as murexide may be used.
The indicator changes color depending on whether it is bound to Ca2+ or whether the Ca2+ has been removed from it by EDTA.

If endpoint determination is unclear, an error occurs in the EDTA titration volume.
Turbidity and coloration originating from milk, insufficient pretreatment, inappropriate pH, and too much or too little indicator can make the endpoint difficult to observe.
Near the endpoint, EDTA is added one drop at a time and the solution is mixed well while confirming the color change.

Effects of Coexisting Ions Such as Mg2+

EDTA forms complexes not only with Ca2+ but also with many other metal ions such as Mg2+, Fe3+, and Zn2+.
Because milk contains inorganic ions other than calcium, these coexisting ions may consume EDTA depending on the conditions and cause the calcium amount to be overestimated.

To selectively measure calcium, the pH conditions, indicator, masking agent, pretreatment, and other factors must be appropriately selected.
If the conditions cause Ca2+ and Mg2+ to be titrated simultaneously, the result may be closer to hardness including both calcium and magnesium rather than calcium alone.

Effects of Phosphates and Citrates

Calcium in milk is also associated with phosphates and citrates.
Its free state changes by existing in forms such as calcium phosphate or by forming complexes with citrate.
These components may affect the state of calcium before it reacts with EDTA.

Pretreatment is necessary to change these binding states and convert calcium into a form that can be titrated.
However, depending on the pH conditions, calcium may precipitate as a phosphate and become difficult to react with EDTA.
In the determination of calcium in milk, it is important to consider the forms in which inorganic components exist in foods.

Concentration Error of the EDTA Standard Solution

In calcium determination, the concentration of the EDTA standard solution serves as the basis of the calculation.
If the EDTA concentration is inaccurate, all calculated calcium amounts will be systematically shifted.
Therefore, the EDTA standard solution is accurately prepared and standardized when necessary before use.

If the EDTA concentration is treated as higher than the actual value, the calculated calcium amount becomes higher for the same titration volume.
Conversely, if the EDTA concentration is treated as lower, the calculated calcium amount becomes lower.
Management of the standard-solution concentration is directly related to the reliability of chelometric titration.

Comparison With Food-Label Values

Milk may have its calcium content listed as nutritional information.
Comparing the calcium amount obtained experimentally with the labeled value makes it easier to discuss the validity of the measurement results.
However, the labeled value is an average or standard value for the product and does not necessarily completely agree with the experimental value.

Possible causes of differences from the labeled value include calcium loss during pretreatment, EDTA consumption by coexisting ions, endpoint-determination errors, mistakes in the dilution factor, variation among samples, and differences among product lots.
When comparing values, it is important to use the same units, such as per 100 mL or per 100 g.

Discussion When the Calcium Amount Is High

If the experimentally determined calcium amount is high, the milk sample may contain a large amount of calcium.
Low-fat milk, processed milk, calcium-fortified milk, and similar products may have different calcium contents from ordinary milk.
Comparing the result with the food label and type of product makes the discussion easier.

However, a high value does not necessarily mean only that the calcium content itself was high.
The value may also be high if coexisting metal ions such as Mg2+ consumed EDTA, if the titration was continued beyond the endpoint, or if there was an error in the EDTA concentration or dilution factor.

Discussion When the Calcium Amount Is Low

If the calcium amount is low, the sample may contain little calcium.
However, in calcium determination in milk, the value may also become low because of losses or incomplete reactions during pretreatment.
In particular, if calcium remains in precipitates or filtration residues, the amount of Ca2+ being titrated decreases.

In addition, if the pH conditions are inappropriate and complex formation with EDTA is insufficient, or if the titration is stopped before the endpoint, the calcium amount is determined as too low.
If the value is much lower than the labeled value, the pretreatment, pH, titration procedure, and calculation must be checked.

Discussion of the Dilution Factor and Calculations

When a milk sample is diluted before measurement, the dilution factor must be correctly reflected in the calculation.
The amount of Ca2+ obtained by titrating the diluted sample is the amount contained in the aliquot of the diluted solution.
To convert this back to the amount of calcium in the original milk, the dilution factor, aliquot volume, and total volume must be handled accurately.

Forgetting to apply the dilution factor causes a large underestimation of the calcium amount in the original milk.
Conversely, applying the dilution factor twice causes overestimation.
When comparing with food-label values, it is also important to convert to the same units, such as per 100 mL or per 100 g.

Causes of Error in Calcium Determination in Milk

Causes of error in calcium determination in milk include nonuniformity of the sample, calcium loss during pretreatment, coprecipitation during deproteinization, loss of liquid during filtration, turbidity caused by fat, inappropriate pH conditions, effects of coexisting metal ions, concentration errors in the EDTA standard solution, endpoint-determination errors, and mistakes in the dilution factor.
Because milk is a complex food sample, both pretreatment and titration affect the result.

Causes that make the value high include EDTA consumption by coexisting ions such as Mg2+, titration beyond the endpoint, and errors in the EDTA concentration or dilution factor.
Causes that make the value low include calcium loss during pretreatment, incorporation into precipitates, stopping the titration before the endpoint, and insufficient complex formation.
Classifying error causes into overestimation and underestimation makes the discussion easier.

When the Results Can Be Considered Good

Results can be considered good in calcium determination in milk when multiple titration volumes are close to one another, the endpoint is clear, the pretreated solution is easy to measure, and the obtained calcium amount does not greatly contradict the food-label value or literature values.
It is also important that the dilution factor and unit conversions are correct and that the concentration of the EDTA standard solution is reliable.

If differences in calcium content among types of milk correspond to the characteristics and labeled values of the products, the results become easier to discuss.
However, exact agreement with the labeled value is not necessary, and differences in measurement methods and pretreatment conditions must be considered.

Example Discussion When the Experiment Did Not Go Well

When calcium determination in milk does not go well, possible causes are considered from results such as difficulty observing the endpoint, variation in titration values, a large difference from the labeled value, turbidity remaining after pretreatment, remaining precipitate, or an unnatural calculated value.
Organizing the causes according to pretreatment, pH conditions, coexisting ions, titration operation, standard solution, and calculation makes the discussion easier.

How to Write Points for Improvement

In a discussion of calcium determination in milk, writing not only the causes of error but also points for improvement makes the report easier to organize.
Points for improvement can be divided into sample preparation, pretreatment, titration operation, standard solution, and calculation and analysis.

Improvements to Sample Preparation and Pretreatment

• Thoroughly mix the milk sample before collecting it
• Measure the sample amount accurately
• Keep the pretreatment conditions constant
• Avoid losing calcium during deproteinization
• Properly wash the filtration residue
• Prevent sample scattering during ashing or acid digestion
• Accurately record the dilution factor

Improvements to the Titration Operation

• Adjust the pH to the specified range
• Use the buffer solution appropriately
• Confirm the concentration of the EDTA standard solution
• Add the titrant one drop at a time near the endpoint
• Carefully observe the indicator color change
• Review the pretreatment if turbidity remains
• Perform multiple measurements and calculate the average value

Improvements to Calculations and Analysis

• Use the 1:1 reaction between Ca2+ and EDTA in the calculation
• Correctly reflect the dilution factor
• Convert the result to units per 100 mL or per 100 g
• Apply blank correction when necessary
• Use consistent units when comparing with food-label values
• Consider the effects of coexisting ions
• Include losses caused by pretreatment in the discussion

Difference Between a Superficial Discussion and a Good Discussion

In a discussion of calcium determination in milk, simply writing that “there was a lot of calcium” or “it was titrated with EDTA” results in a superficial discussion.
A good discussion relates the 1:1 reaction with EDTA, the forms of calcium present in milk, pretreatment, pH conditions, coexisting ions, and endpoint determination.

Examples of Expressions That Can Be Used in Reports

The following expressions can be used when writing the results and discussion of calcium determination in milk.
Adjust the necessary parts according to your own experimental results.

• Because EDTA forms a 1:1 complex with Ca2+, the amount of calcium can be determined from the EDTA titration volume.
• Calcium in milk exists not only as free ions but also in forms associated with casein micelles and phosphates.
• Pretreatment is important for converting calcium into a form that readily reacts with EDTA.
• Turbidity caused by proteins and fats may make endpoint determination difficult.
• If calcium is incorporated into the precipitate during deproteinization, the calcium amount may be underestimated.
• pH conditions affect complex formation with EDTA and the color change of the indicator.
• If coexisting metal ions such as Mg2+ consume EDTA, the calcium amount may be overestimated.
• For diluted samples, the dilution factor must be correctly reflected in the calculation.
• When comparing with food-label values, the units must be made consistent, such as per 100 mL.
• Titrating beyond the endpoint makes the EDTA titration volume too large and may cause the calcium amount to be overestimated.

Points to Check When Discussing Calcium Determination in Milk

Checking the following points before writing the report makes the discussion easier to write.

• Is the principle of EDTA chelometric titration explained?
• Is the 1:1 reaction between Ca2+ and EDTA written?
• Are the forms of calcium present in milk considered?
• Is the reason pretreatment is necessary explained?
• Are the effects of deproteinization and fat content considered?
• Is the importance of pH conditions described?
• Is the relationship between the indicator and endpoint determination explained?
• Are the effects of coexisting ions such as Mg2+ considered?
• Has the concentration error of the EDTA standard solution been checked?
• Are the dilution factor and unit conversions handled correctly?
• Is the difference from the food-label value discussed?
• Do the points for improvement correspond to the causes of error?

Summary

Determination of calcium in milk is an experiment in which Ca2+ contained in milk is determined by EDTA chelometric titration.
Because EDTA forms a stable 1:1 complex with Ca2+, the amount of calcium can be calculated from the concentration and titration volume of the EDTA standard solution.
The obtained value can be discussed by comparison with the nutritional composition of milk and food-label values.

However, calcium in milk exists not only as free ions but also in forms associated with casein micelles, phosphates, and citrates.
In addition, because milk contains proteins and fats, insufficient pretreatment affects endpoint determination and calcium recovery.
Therefore, the effects of pretreatment conditions, pH, indicators, and coexisting ions must be considered.

In a report, rather than simply writing that “the calcium amount was high or low,” organize and discuss the principle of EDTA chelometric titration, the 1:1 reaction between Ca2+ and EDTA, the forms of calcium present in milk, the effects of pretreatment, pH conditions, endpoint determination, coexisting ions, causes of error, and points for improvement.
In calcium determination in milk, it is important to understand the connection between food components and chelometric titration in analytical chemistry.