Potentiometric titration is an analytical chemistry experiment in which changes in potential or pH during titration are measured and the equivalence point is determined from those changes.
Unlike titration methods that rely on the color change of an indicator, potentiometric titration records measured values using electrodes, making it useful for colored samples and titrations in which the endpoint is difficult to determine visually.
In a potentiometric titration report, it is important to discuss the shape of the titration curve, the region where the potential or pH changes sharply, how the equivalence point is read, analysis using first and second derivatives, and sources of error related to the electrode and stirring.
In particular, it is necessary to clearly explain the difference between the equivalence point and the endpoint and how the equivalence point was determined from the titration curve.
This article clearly explains how to interpret potentiometric titration results, how to read titration curves and equivalence points, sources of error, points for improvement, and discussion examples that can be used in reports.
Note:
This article is a reference intended to assist with discussions of results obtained in chemistry experiments at universities and similar institutions.
For the actual measurement procedures, electrodes used, titration conditions, and methods for determining the equivalence point, always follow the instructions in your university’s laboratory manual and those given by your instructor or TA.
- What Is Potentiometric Titration?
- Results to Examine in Potentiometric Titration
- Reference Experimental Values for Potentiometric Titration and an Example of Equivalence-Point Analysis
- Reference Experimental Conditions
- Basic Interpretation of Potentiometric Titration
- Example of pH Change When a Strong Acid Is Titrated With a Strong Base
- Example of Determining the Equivalence Point Using the First Derivative
- Example of Determining the Equivalence Point Using the Second Derivative
- Example of Titrating a Weak Acid With a Strong Base
- Example of Potentiometric Redox Titration
- Example of Potentiometric Precipitation Titration
- Example of Calculating the Concentration of an Unknown Sample
- Comparison Between the Indicator Method and Potentiometric Titration
- Difference in Equivalence-Point Accuracy Depending on Titrant Increment
- Example of Error Caused by Delayed Electrode Response
- Main Sources of Error
- Example of How to Write the Results
- Points to Connect to the Discussion
- Example Discussion Text
- Summary
- What Is a Titration Curve?
- Difference Between the Equivalence Point and the Endpoint
- How to Read the Equivalence Point
- When the Steep Change in the Titration Curve Is Small
- Errors Caused by Coarse Measurement Intervals
- Errors Caused by Delayed Electrode Response
- Errors Caused by Insufficient Electrode Calibration
- Errors Caused by Insufficient Stirring
- Errors Caused by the Rate of Titrant Addition
- Effect of Temperature
- Causes of Deviation of the Equivalence Point From the Theoretical Value
- Example Discussion of a First-Derivative Curve
- Example Discussion of a Second-Derivative Curve
- When the Result Can Be Considered Good
- Example Discussion When the Experiment Did Not Go Well
- How to Write Points for Improvement
- Difference Between a Superficial Discussion and a Good Discussion
- Examples of Expressions That Can Be Used in Reports
- Points to Check When Discussing Potentiometric Titration
- Summary
What Is Potentiometric Titration?
Potentiometric titration is a titration method in which the potential difference or pH of a solution is measured during titration and the equivalence point is determined from the change.
In acid-base titration, changes in pH are often measured, while in redox titration, changes in oxidation-reduction potential may be measured.
In titration using an indicator, the endpoint is determined visually from a color change.
In potentiometric titration, on the other hand, changes in potential or pH are plotted against the amount of titrant added, and the equivalence point is read from the region where the value changes rapidly.
Therefore, potentiometric titration is effective for samples in which the color change of an indicator is difficult to observe, colored samples, and cases in which changes near the endpoint need to be confirmed numerically.
Results to Examine in Potentiometric Titration
In potentiometric titration results, organize the amount of titrant added, the potential or pH at each point, the titration curve, the position of the equivalence point, and the calculated concentration.
It is important not only to list the measured values in a table, but also to explain how the equivalence point was determined from the graph.
Main Items to Include in the Results
- Volume of the sample solution
- Concentration of the titrant
- Amount of titrant added
- Potential or pH at each added volume
- Titration curve
- Range where the potential or pH changed sharply
- Titrant volume at the equivalence point
- Results of first- or second-derivative analysis, if used
- Calculated sample concentration
- Variation or abnormal values in the measurements
Example of How to Write the Results:
A fixed amount of titrant was added to the sample solution, and the pH was measured after each addition.
The pH changed gradually until around 10.0 mL of titrant had been added, but changed rapidly around 10.5 to 11.0 mL.
The center of the steep-change region of the titration curve was judged to be the equivalence point, and the titrant volume at the equivalence point was determined to be 10.7 mL.
Reference Experimental Values for Potentiometric Titration and an Example of Equivalence-Point Analysis
Here, reference experimental values are organized for determining the equivalence point from changes in titrant volume and potential obtained in potentiometric titration.
Titration curves, rapid changes in potential, first derivatives, second derivatives, acid-base titration, redox titration, precipitation titration, differences from indicator methods, and sources of error are summarized in a form that is easy to use in reports.
In potentiometric titration, the potential or pH of the solution is measured while the titrant is added little by little.
Near the equivalence point, the major chemical species in the solution change greatly, causing the potential or pH to change rapidly.
By graphing this change, the equivalence point can be estimated without using an indicator.
Reference Experimental Conditions
| Item | Details |
|---|---|
| Measurement target | Acid-base titration, redox titration, precipitation titration, complexometric titration, etc. |
| Measured values | Titrant volume, pH, potential, first-derivative value, second-derivative value |
| Examples of electrodes used | pH electrode, platinum electrode, silver electrode, reference electrode |
| Methods for determining the equivalence point | Steep-change point of the titration curve, maximum first derivative, sign change of the second derivative |
| Main sources of error | Delayed electrode response, insufficient stirring, coarse titrant increments, temperature changes, dirty electrodes, measurement interval |
Basic Interpretation of Potentiometric Titration
| Titration Stage | State of the Solution | Change in Potential or pH | Direction of Discussion |
|---|---|---|---|
| Before titration | A large amount of analyte is present | Change is small | Initial state |
| Before the equivalence point | Analyte remains | Changes gradually | Titrant is consumed |
| Near the equivalence point | The reactants have just finished reacting | Changes rapidly | Region for determining the equivalence point |
| After the equivalence point | Titrant becomes excessive | The change becomes gradual again | Excess titrant becomes dominant |
The greatest change in the titration curve appears near the equivalence point.
If the titrant-volume intervals are too large, it becomes difficult to accurately capture the steep-change point, so it is important to make finer measurements near the equivalence point.
Example of pH Change When a Strong Acid Is Titrated With a Strong Base
The following are reference data for titrating 25.00 mL of 0.100 mol/L HCl with 0.100 mol/L NaOH.
The theoretical equivalence point is around 25.00 mL.
| NaOH Added | pH | ΔpH/ΔV | State | Interpretation |
|---|---|---|---|---|
| 0.00 mL | 1.00 | – | Before titration | Strongly acidic |
| 10.00 mL | 1.37 | 0.037 | Before the equivalence point | Gradual increase |
| 20.00 mL | 1.95 | 0.058 | Before the equivalence point | Acid still remains |
| 24.00 mL | 2.70 | 0.188 | Immediately before the equivalence point | Change becomes larger |
| 24.50 mL | 3.00 | 0.600 | Immediately before the equivalence point | Enters the steep-change region |
| 24.90 mL | 3.70 | 1.75 | Near the equivalence point | Rapid increase |
| 25.00 mL | 7.00 | 33.0 | Equivalence point | Near neutral |
| 25.10 mL | 10.30 | 33.0 | Immediately after the equivalence point | Rapid increase |
| 25.50 mL | 11.00 | 1.75 | After the equivalence point | Excess base |
| 30.00 mL | 11.96 | 0.213 | After the equivalence point | Change becomes gradual |
The equivalence point is around 25.00 mL, where the pH change is greatest.
In a strong acid-strong base titration, the pH at the equivalence point is approximately 7.
Example of Determining the Equivalence Point Using the First Derivative
In the first-derivative method, the change in pH or potential relative to the change in titrant volume is calculated, and the point at which this value is greatest is estimated as the equivalence point.
First derivative = ΔpH / ΔV or ΔE / ΔV
| Interval | Midpoint Volume | pH Change | Volume Change | ΔpH/ΔV | Assessment |
|---|---|---|---|---|---|
| 24.00-24.50 mL | 24.25 mL | 0.30 | 0.50 mL | 0.60 | Before rapid change |
| 24.50-24.90 mL | 24.70 mL | 0.70 | 0.40 mL | 1.75 | Large change |
| 24.90-25.00 mL | 24.95 mL | 3.30 | 0.10 mL | 33.0 | Near maximum |
| 25.00-25.10 mL | 25.05 mL | 3.30 | 0.10 mL | 33.0 | Near maximum |
| 25.10-25.50 mL | 25.30 mL | 0.70 | 0.40 mL | 1.75 | After rapid change |
The midpoint of the interval in which the first-derivative value is greatest can be regarded as the equivalence point.
In this example, approximately 25.00 mL is a reasonable equivalence point.
Example of Determining the Equivalence Point Using the Second Derivative
In the second-derivative method, changes in the first-derivative values are examined.
Near the equivalence point, the second-derivative value may change sign from positive to negative or from negative to positive.
| Midpoint Volume | First-Derivative Value | Trend of the Second Derivative | Assessment |
|---|---|---|---|
| 24.25 mL | 0.60 | Increasing | Before the equivalence point |
| 24.70 mL | 1.75 | Increasing further | Before the equivalence point |
| 24.95 mL | 33.0 | Approaching 0 from positive values | Immediately before the equivalence point |
| 25.05 mL | 33.0 | Near 0 | Near the equivalence point |
| 25.30 mL | 1.75 | Decreasing | After the equivalence point |
In the second-derivative method, the inflection point of the curve is read as the equivalence point.
If experimental values show variation, it is useful to make the judgment together with the first-derivative method.
Example of Titrating a Weak Acid With a Strong Base
The following are reference data for titrating 25.00 mL of 0.100 mol/L acetic acid with 0.100 mol/L NaOH.
The pH at the equivalence point is greater than 7.
| NaOH Added | pH | State | Direction of Discussion |
|---|---|---|---|
| 0.00 mL | 2.88 | Before titration | pH is higher than that of a strong acid because it is a weak acid |
| 5.00 mL | 4.14 | Buffer region | Acetic acid and acetate ions coexist |
| 12.50 mL | 4.76 | Half-neutralization point | pH ≈ pKa |
| 20.00 mL | 5.36 | Before the equivalence point | Gradual increase |
| 24.50 mL | 6.75 | Immediately before the equivalence point | Change becomes larger |
| 25.00 mL | 8.72 | Equivalence point | Basic because of hydrolysis of acetate ions |
| 25.50 mL | 10.70 | After the equivalence point | Excess NaOH |
| 30.00 mL | 11.80 | After the equivalence point | Influence of the strong base becomes large |
In a weak acid-strong base titration, the pH is close to the pKa at the half-neutralization point, and the pH at the equivalence point becomes greater than 7 because of hydrolysis of the conjugate base that is formed.
Example of Potentiometric Redox Titration
In a redox titration in which Fe2+ is titrated with an oxidizing agent, the oxidation-reduction potential changes rapidly near the equivalence point.
| Titrant Volume | Potential E | ΔE/ΔV | State | Interpretation |
|---|---|---|---|---|
| 0.00 mL | 0.32 V | – | Before titration | Large amount of Fe2+ |
| 5.00 mL | 0.39 V | 0.014 | Before the equivalence point | Gradual increase |
| 10.00 mL | 0.47 V | 0.016 | Before the equivalence point | Oxidation proceeds |
| 14.50 mL | 0.58 V | 0.024 | Immediately before the equivalence point | Change becomes larger |
| 15.00 mL | 0.81 V | 0.460 | Near the equivalence point | Rapid change |
| 15.50 mL | 1.04 V | 0.460 | Immediately after the equivalence point | Excess oxidizing agent |
| 20.00 mL | 1.12 V | 0.018 | After the equivalence point | Change becomes gradual |
Potentiometric titration can determine the equivalence point not only from pH changes but also from changes in oxidation-reduction potential.
Even for samples in which color changes are difficult to observe, using changes in potential makes it easier to judge the equivalence point objectively.
Example of Potentiometric Precipitation Titration
When Cl− is titrated with AgNO3, the potential of a silver electrode changes according to the change in Ag+ concentration.
| AgNO3 Added | Potential E | State | Direction of Discussion |
|---|---|---|---|
| 0.00 mL | 0.12 V | Excess Cl− | Low Ag+ concentration |
| 5.00 mL | 0.18 V | Before the equivalence point | AgCl precipitate forms |
| 9.50 mL | 0.25 V | Immediately before the equivalence point | Cl− decreases |
| 10.00 mL | 0.48 V | Equivalence point | Potential changes greatly |
| 10.50 mL | 0.70 V | Immediately after the equivalence point | Excess Ag+ |
| 15.00 mL | 0.78 V | Excess region | Change becomes gradual |
In precipitation titration, the concentration of free ions changes greatly as the precipitate forms, so a rapid change in potential is observed near the equivalence point.
Example of Calculating the Concentration of an Unknown Sample
Suppose 25.00 mL of an unknown HCl solution is potentiometrically titrated with 0.100 mol/L NaOH and the equivalence point is determined to be 18.60 mL.
HCl + NaOH → NaCl + H2O
Because the reaction ratio is 1:1, the amount of HCl is equal to the amount of NaOH.
n(NaOH) = 0.100 mol/L × 0.01860 L = 1.86×10−3 mol
n(HCl) = 1.86×10−3 mol
C(HCl) = 1.86×10−3 mol ÷ 0.02500 L = 0.0744 mol/L
Therefore, the concentration of the unknown HCl solution is determined to be 0.0744 mol/L.
Comparison Between the Indicator Method and Potentiometric Titration
| Method | How the Equivalence Point Is Judged | Advantage | Points to Note |
|---|---|---|---|
| Indicator method | Judged from color change | Simple and requires little equipment | There are individual differences in judging the color |
| Potentiometric titration | Judged from rapid changes in pH or potential | Equivalence point can be determined more objectively | Electrode maintenance and calibration are required |
| Derivative method | Maximum first derivative or sign change of the second derivative | The steep-change point can be evaluated numerically | Accuracy decreases when data intervals are coarse |
| Automatic titration | The instrument judges the curve | High reproducibility | Affected by instrument settings and electrode condition |
Potentiometric titration is effective for colored or turbid samples in which the color change of an indicator is difficult to judge.
Difference in Equivalence-Point Accuracy Depending on Titrant Increment
| Measurement Condition | Titrant Increment Near the Equivalence Point | Estimated Equivalence Point | Error Trend | Direction of Discussion |
|---|---|---|---|---|
| Coarse measurement | Every 1.00 mL | Between 25.0 and 26.0 mL | Large | The steep-change point becomes unclear |
| Moderate | Every 0.50 mL | Around 25.0 mL | Moderate | Approximate judgment is possible |
| Fine measurement | Every 0.10 mL | 25.00 mL | Small | Suitable for derivative methods |
| Fine measurement only near the equivalence point | 0.05-0.10 mL only before and after the equivalence point | 25.00 mL | Small | Accuracy can be improved efficiently |
Because pH or potential changes rapidly near the equivalence point, measuring with smaller titrant increments improves the accuracy of equivalence-point estimation.
Example of Error Caused by Delayed Electrode Response
In potentiometric titration, it is necessary to wait until the electrode reading stabilizes after the titrant is added.
If the value is recorded before stabilization, the equivalence point may appear to be shifted.
| Recording Timing | pH Near the Equivalence Point | Estimated Equivalence Point | Problem |
|---|---|---|---|
| Immediately after addition | Unstable | 24.8 mL | Reads low because of response delay |
| After 10 seconds | Somewhat stable | 24.9 mL | Still slightly shifted |
| After 30 seconds | Stable | 25.0 mL | High reliability |
| Insufficient stirring | Locally uneven | Varies | Reproducibility decreases |
Delayed electrode response and insufficient stirring can prevent accurate recording of the rapid change near the equivalence point.
Main Sources of Error
| Source of Error | Effect on Measured Values | Trend in the Result | Improvement |
|---|---|---|---|
| Insufficient electrode calibration | pH or potential is shifted | Values are shifted overall | Calibrate with standard solutions |
| Delayed electrode response | Reading taken before stabilization | Equivalence point appears shifted | Record after the value stabilizes |
| Insufficient stirring | Local concentrations become uneven | Curve becomes irregular | Stir at a constant rate |
| Error in reading the titrant volume | Volume is incorrect | Affects concentration calculation | Read the burette correctly |
| Coarse measurement intervals near the equivalence point | Difficult to capture the rapid change | Equivalence-point estimate becomes rough | Measure more finely only near the equivalence point |
| Temperature change | Electrode potential and equilibrium change | Measured values shift | Measure at a constant temperature |
| Dirty electrode | Response becomes slower | Reproducibility decreases | Clean and store the electrode properly |
Example of How to Write the Results
25.00 mL of 0.100 mol/L HCl was potentiometrically titrated with 0.100 mol/L NaOH.
Immediately after the start of titration, the pH increased gradually, but it changed rapidly around 25.00 mL.
Because this steep-change point corresponds to the point where HCl and NaOH reacted in nearly equivalent amounts, the equivalence point can be judged to be around 25.00 mL.
When ΔpH/ΔV was calculated using the first-derivative method, the maximum value was observed near the equivalence point.
In the second-derivative method, a tendency for the sign to change near the equivalence point was also observed.
These results confirmed the equivalence point numerically as well as visually from the titration curve.
When acetic acid, a weak acid, was titrated with a strong base, the pH at the half-neutralization point was close to the pKa, and the pH at the equivalence point was greater than 7.
This is because the acetate ions formed at the equivalence point react with water and make the solution basic.
Therefore, the pH at the equivalence point varies depending on the strengths of the acid and base.
Points to Connect to the Discussion
In a discussion of potentiometric titration, it is important not only to read the steep-change point of the titration curve, but also to explain why the pH or potential changes rapidly at the equivalence point, how derivative methods determine the equivalence point, and where errors arise.
- Can the rapid change near the equivalence point be identified from the titration curve?
- Can the equivalence point be judged using the maximum first-derivative value?
- Can the sign change or inflection point of the second derivative be related to the equivalence point?
- In acid-base titration, can differences among strong acids, weak acids, strong bases, and weak bases be reflected in the pH curve?
- In redox titration, can the rapid potential change be explained in relation to changes in the proportions of oxidized and reduced species?
- In precipitation titration, can it be explained that changes in free-ion concentration affect the potential?
- Can the concentration of an unknown sample be calculated from the equivalence-point volume and reaction ratio?
- Can differences from the indicator method be explained in terms of objectivity and the absence of visual color judgment?
- Can electrode response, stirring, titrant increments, temperature, and electrode contamination be discussed as sources of error?
Example Discussion Text
In this experiment, the equivalence point of an acid-base reaction was determined by potentiometric titration.
When HCl was titrated with NaOH, the pH increased gradually at the beginning of the titration but changed rapidly around 25.00 mL.
This occurred because H+ was almost completely consumed near the equivalence point, so even a small excess of NaOH caused a large change in the pH of the solution.
In the first-derivative method, the volume at which ΔpH/ΔV was greatest was judged to be the equivalence point.
This method can numerically indicate the point where the slope of the titration curve is greatest.
In the second-derivative method, the sign of the second-derivative value changes at the position corresponding to the inflection point of the titration curve.
Therefore, using derivative methods makes it possible to determine the equivalence point more objectively than by visual inspection alone.
When acetic acid was titrated with NaOH, the pH at the equivalence point was greater than 7.
This is because acetate ions, which are mainly present at the equivalence point, act as the conjugate base of a weak acid and accept H+ from water.
In contrast, in titration between a strong acid and a strong base, the salt formed at the equivalence point undergoes almost no hydrolysis, so the pH is approximately 7.
In redox titration, the potential changed rapidly near the equivalence point because the ratio of oxidized to reduced species changed greatly.
In precipitation titration, the electrode potential also changed greatly because the concentration of free ions changed rapidly as precipitation proceeded.
Thus, regardless of the type of reaction, potentiometric titration can detect changes in the major chemical species in solution as changes in potential or pH.
Possible sources of error include insufficient electrode calibration, delayed electrode response, insufficient stirring, errors in reading the titrant volume, and coarse measurement intervals near the equivalence point.
In particular, because pH or potential changes rapidly near the equivalence point, adding too much titrant at once may pass beyond the equivalence point and make it difficult to determine the exact volume.
Therefore, it is important to reduce the amount of titrant added near the equivalence point and record the value only after it has stabilized.
Summary
In potentiometric titration, changes in pH or potential relative to the titrant volume are measured, and the equivalence point can be determined from the steep-change point.
In the first-derivative method, the equivalence point is estimated from the point where the change is greatest, while in the second-derivative method, the inflection point is used.
This reference example covered strong acid-strong base titration, weak acid-strong base titration, redox titration, precipitation titration, calculation of an unknown sample concentration, comparison with the indicator method, titrant increments, electrode response, and sources of error.
In a report, it is useful to discuss the shape of the titration curve, derivative values, equivalence-point volume, reaction ratio, and measurement errors in relation to one another.
What Is a Titration Curve?
A titration curve is a graph in which the amount of titrant added is plotted on the horizontal axis and the potential or pH is plotted on the vertical axis.
As titration proceeds, the amounts of components in the solution change, and the potential or pH changes accordingly.
Near the equivalence point, the quantitative relationship between the reacting components changes greatly, causing the potential or pH to change rapidly.
The equivalence point is judged based on this steep-change region.
| Part of the Titration Curve | Characteristic | Perspective for Discussion |
|---|---|---|
| Before the equivalence point | Potential or pH changes gradually | The sample component still remains |
| Near the equivalence point | Potential or pH changes rapidly | The reaction is nearly quantitatively complete |
| After the equivalence point | The change becomes gradual again | The titrant is in excess |
Example Discussion:
In the titration curve, the pH changed rapidly when the titrant volume reached a certain range.
This rapid change indicates that the sample component and titrant reacted in nearly equivalent amounts.
Therefore, the region around the center of the largest pH change can be judged to be the equivalence point.
Difference Between the Equivalence Point and the Endpoint
In discussing potentiometric titration, it is necessary to understand the difference between the equivalence point and the endpoint.
The equivalence point is the point at which the sample and titrant have reacted in exactly stoichiometric amounts.
The endpoint, on the other hand, is the point at which the titration is experimentally stopped.
In titration using an indicator, the endpoint is judged from a color change.
In potentiometric titration, the equivalence point is read from the steep-change region of the titration curve or from derivative curves, so it may be easier to judge objectively than by visual observation of a color change.
| Item | Meaning | How It Is Determined |
|---|---|---|
| Equivalence point | The point where the reactants have reacted in stoichiometrically equivalent amounts | Judged from the reaction equation or titration curve |
| Endpoint | The point where the titration is experimentally stopped | Judged from a color change or change in measured values |
Example Discussion:
The equivalence point is the point at which the sample and titrant have reacted in exactly stoichiometric amounts, whereas the endpoint is the point at which the titration is experimentally stopped.
In potentiometric titration, the equivalence point is read from the steep-change region of the titration curve, so it is easier to judge objectively than when relying on the color change of an indicator.
However, coarse measurement intervals or delayed electrode response may cause the read equivalence point to differ from the actual equivalence point.
How to Read the Equivalence Point
Methods for reading the equivalence point from a titration curve include reading the center of the steep-change region, using the first derivative, and using the second derivative.
Follow the method specified in the course or laboratory manual.
Reading the Center of the Steep-Change Region
This method identifies the region of the titration curve in which the potential or pH changes rapidly and takes the center of that region as the equivalence point.
It is intuitive and easy to understand, but individual differences may arise in reading the graph.
Example Discussion:
In this experiment, the center of the steep-change region of the titration curve was read as the equivalence point.
The steep-change region is the range in which the quantitative relationship between the sample and titrant changes greatly, and its center is considered to correspond to the equivalence point.
However, because the value was read visually from the graph, a small reading error may be included.
Determining the Equivalence Point Using the First Derivative
In the first-derivative method, the change in potential or pH relative to the titrant volume is examined.
The point where the change is greatest corresponds to the region near the equivalence point.
ΔpH ÷ ΔV or ΔE ÷ ΔV is checked for its maximum value.
Example Discussion:
In the first-derivative curve, a peak was observed near the titrant volume where the pH change was greatest.
This point corresponds to the steep-change region of the titration curve and indicates the position where the sample and titrant reacted in nearly equivalent amounts.
Therefore, the titrant volume showing the maximum first-derivative value can be used as the equivalence point.
Determining the Equivalence Point Using the Second Derivative
In the second-derivative method, changes in the first derivative are examined further.
The point where the second-derivative value becomes 0 corresponds to the inflection point of the titration curve and may be judged as the equivalence point.
Example Discussion:
In the second-derivative curve, a point where the sign changed from positive to negative or from negative to positive was observed.
This point corresponds to the inflection point of the titration curve and provides a clue for reading the equivalence point more objectively.
Compared with visually reading the center of the steep-change region, the second-derivative method is considered less susceptible to individual differences in determining the equivalence point.
When the Steep Change in the Titration Curve Is Small
If the steep change in the titration curve is small, reading the equivalence point becomes difficult.
The steep-change region may be unclear in titrations of a weak acid with a weak base, low-concentration samples, incomplete reactions, or when the electrode response is slow.
Example Discussion:
One possible reason the steep-change region of the titration curve was unclear is that the change in pH caused by the reaction between the sample and titrant was small.
When the steep change is small, it becomes difficult to read the equivalence point visually and the reading error becomes larger.
In such cases, using the first or second derivative may make it possible to judge the equivalence point more objectively.
Errors Caused by Coarse Measurement Intervals
In potentiometric titration, the potential or pH is measured while a fixed amount of titrant is added each time.
If the titrant increment is too large near the equivalence point, the steep-change region cannot be recorded in sufficient detail, reducing the accuracy of equivalence-point determination.
In particular, because a small amount of titrant causes a large change in potential or pH near the equivalence point, it is important to reduce the amount added at each measurement.
Example Discussion:
If the titrant increment near the equivalence point was too large, the steep change in potential or pH could not be recorded in sufficient detail.
Therefore, an error may occur in the position of the equivalence point read from the titration curve.
To determine the equivalence point more accurately, it is necessary to add the titrant in smaller amounts near the equivalence point and increase the number of measurement points.
Errors Caused by Delayed Electrode Response
In potentiometric titration, it may take time for the electrode to respond to the state of the solution and show a stable value.
If the measured value is recorded before stabilization, it may differ from the actual potential or pH.
In particular, because potential or pH changes rapidly near the equivalence point, delayed electrode response can strongly affect the reading of the equivalence point.
Example Discussion:
If a measured value was recorded before the electrode response had stabilized, a value different from the actual pH or potential may have been read.
In particular, because the measured value changes rapidly near the equivalence point, the influence of response delay tends to become large.
As a result, the steep-change region of the titration curve may have shifted and caused an error in reading the equivalence point.
Errors Caused by Insufficient Electrode Calibration
When a pH electrode is used, calibration before measurement is important.
If calibration is insufficient, all measured pH values may be shifted higher or lower.
Even when a redox electrode is used, the condition of the electrode and the stability of the reference electrode affect the results.
Example Discussion:
One possible reason the measured values differed from the expected titration curve is insufficient electrode calibration.
If the pH electrode is not calibrated correctly, the measured values as a whole may shift higher or lower.
However, because the equivalence point is judged from the steep-change region, it is necessary to discuss not only shifts in the absolute values but also the shape and position of the steep-change region.
Errors Caused by Insufficient Stirring
In potentiometric titration, the entire solution must become uniform after the titrant is added.
If stirring is insufficient, the concentration or pH near the electrode may not represent the entire solution, causing variation in the measured values.
If the titrant becomes locally excessive, a rapid change may sometimes be observed even before the equivalence point has been reached.
Example Discussion:
If stirring was insufficient, the added titrant may not have mixed uniformly throughout the solution, causing the pH or potential to change only near the electrode.
In that case, the measured value would not correctly represent the state of the entire solution and variation could appear in the titration curve.
Therefore, sufficient stirring during titration is necessary to accurately read the equivalence point.
Errors Caused by the Rate of Titrant Addition
If the titrant is added too quickly, the electrode response and mixing of the solution may not keep up, making the measured values difficult to stabilize.
In particular, if the titrant is added too rapidly near the equivalence point, the steep-change region may be passed over and the equivalence-point reading may become coarse.
Example Discussion:
If the titrant was added too quickly near the equivalence point, the steep-change region of the pH or potential could not be measured in detail and the equivalence point may not have been read accurately.
In addition, if the measured value was recorded before the titrant had mixed uniformly, variation may have occurred in the titration curve.
Therefore, near the equivalence point, the titrant should be added in small amounts and the value should be recorded only after it stabilizes.
Effect of Temperature
pH and potential may be affected by temperature.
When the temperature changes, the electrode response and equilibrium conditions in the solution change, possibly causing shifts in the measured values.
If the temperature changes greatly during measurement, it may affect the shape of the titration curve and the measured values near the equivalence point.
Therefore, for high-accuracy measurements, it is desirable to keep the temperature constant.
Example Discussion:
Temperature changes during measurement may have caused the variation in measured values.
Because pH and potential are affected by temperature, a change in temperature may alter the electrode response and the equilibrium conditions in the solution.
As a result, errors may have occurred in the shape of the titration curve and the reading of the equivalence point.
Causes of Deviation of the Equivalence Point From the Theoretical Value
If the equivalence point read experimentally differs from the theoretical value, possible causes include the sample concentration, titrant concentration, electrode condition, measurement interval, stirring, and temperature.
If interfering components are present in the sample, the amount of titrant consumed may also change.
| Cause | Effect on the Equivalence Point |
|---|---|
| Error in titrant concentration | The calculated sample concentration shifts |
| Coarse measurement intervals | The center of the steep-change region cannot be read accurately |
| Delayed electrode response | The measured change is recorded later than the actual change |
| Insufficient stirring | A local value near the electrode is measured |
| Presence of interfering components | Titrant is consumed by components other than the target component |
Example Discussion:
Possible reasons the experimentally determined equivalence point differed from the theoretical value include coarse measurement intervals near the equivalence point and delayed electrode response.
Because the pH or potential changes rapidly near the equivalence point, it is difficult to accurately read the center of the steep-change region when there are few measurement points.
In addition, if the measured value was recorded before stabilization, the shape of the titration curve may differ from the actual curve and cause an error in determining the equivalence point.
Example Discussion of a First-Derivative Curve
When a first-derivative curve is prepared, the point at which the change in potential or pH is greatest can be judged as the equivalence point.
Even when the steep-change region of the titration curve is difficult to read visually, the first derivative makes it easier to determine the position of the equivalence point.
Example Discussion:
In the first-derivative curve, a point was observed at which the change in pH relative to the titrant volume was greatest.
This point corresponds to the steep-change region of the titration curve and indicates the position where the sample and titrant reacted in nearly equivalent amounts.
Therefore, in this experiment, the titrant volume at which the first-derivative value was greatest was used as the equivalence point.
Example Discussion of a Second-Derivative Curve
In a second-derivative curve, the point where the value passes through 0 or where its sign changes is checked.
This point corresponds to the inflection point of the titration curve and is used as a more objective method for determining the equivalence point.
Example Discussion:
In the second-derivative curve, a point was observed where the second-derivative value was near 0 and changed sign.
Because this point corresponds to the inflection point of the titration curve, it can be judged as the equivalence point.
Compared with visually reading the center of the steep-change region, using the second derivative made it possible to determine the equivalence point more objectively.
When the Result Can Be Considered Good
A good potentiometric titration result is indicated when the titration curve has a clear steep-change region and the equivalence point can be easily read from the first or second derivative.
It is also important to have enough measurement points near the equivalence point and stable measured values.
Example Discussion:
A clear steep-change region was observed in the titration curve, and the first-derivative curve also showed a point where the change was greatest.
Therefore, the equivalence point is considered to have been relatively clearly identified.
In addition, because the titrant was added in small amounts near the equivalence point, the steep-change region could be recorded in detail, and the accuracy of the equivalence-point reading is considered relatively high.
Example Discussion When the Experiment Did Not Go Well
When potentiometric titration does not go well, possible causes can be considered from results such as an unclear steep change in the titration curve, scattered measured values, or an equivalence point that differs greatly from the theoretical value.
Checking the condition of the electrode, measurement intervals, stirring, and the rate of titrant addition makes the discussion easier to write.
Example Discussion:
The steep-change region of the titration curve was unclear, making it difficult to read the equivalence point.
Possible causes include large titrant increments near the equivalence point, recording the measured values before they stabilized, and insufficient stirring.
In particular, because pH or potential changes rapidly near the equivalence point, having too few measurement points makes it impossible to accurately determine the center of the steep-change region and causes an error in the equivalence-point reading.
How to Write Points for Improvement
In a discussion of potentiometric titration, including points for improvement as well as sources of error makes the report easier to organize.
It is important to write the improvements specifically in relation to the actual sources of error considered.
Improvements for Making the Equivalence Point Easier to Read
- Add the titrant in small amounts near the equivalence point
- Increase the number of measurement points and record the steep-change region in detail
- Use the first or second derivative to judge the equivalence point
- Record measured values only after they stabilize
- Check both the titration curve and derivative curves
Improvements for Reducing Measurement Error
- Calibrate the electrode appropriately before measurement
- Clean the electrode thoroughly
- Stir the solution sufficiently
- Avoid adding the titrant too rapidly
- Keep the temperature as constant as possible
- Confirm that the electrode is appropriately immersed in the sample solution
Example of How to Write Points for Improvement:
To determine the equivalence point more accurately, the titrant should be added in small amounts near the equivalence point and the number of measurement points should be increased.
In addition, recording the value only after the electrode response stabilizes and stirring the solution sufficiently can reduce variation in the measured values.
Furthermore, using the first or second derivative can make it possible to judge the steep-change region of the titration curve more objectively.
Difference Between a Superficial Discussion and a Good Discussion
In a discussion of potentiometric titration, simply writing that “a titration curve was obtained” or “the equivalence point was read” results in a superficial discussion.
It is important to explain the steep-change region of the titration curve, derivative curves, reading of the equivalence point, and sources of error in relation to one another.
| Superficial Discussion | Good Discussion |
|---|---|
| The equivalence point was determined from the titration curve. | In the titration curve, the pH or potential changed rapidly when the titrant volume reached a certain range. Because this steep-change region corresponds to the range where the sample and titrant reacted in nearly equivalent amounts, the center of the steep-change region was read as the equivalence point. |
| The equivalence point shifted. | Possible reasons the equivalence point differed from the theoretical value include coarse measurement intervals near the equivalence point and recording measured values before the electrode response had stabilized. If there are few measurement points in the steep-change region, the accuracy of the equivalence-point reading decreases. |
| The measured values varied. | Possible causes of variation in the measured values include insufficient stirring and delayed electrode response. If measurements are made before the solution becomes uniform, a local pH or potential near the electrode may be measured, resulting in variation in the titration curve. |
Examples of Expressions That Can Be Used in Reports
The following expressions can be used when writing the results and discussion of potentiometric titration.
Adjust the necessary parts according to your own experimental results.
- In potentiometric titration, the change in pH or potential relative to the amount of titrant added is measured to prepare a titration curve.
- The steep-change region of the titration curve corresponds to the range where the sample and titrant reacted in nearly equivalent amounts.
- The center of the steep-change region was read as the equivalence point.
- The point where the change was greatest in the first-derivative curve was taken as the equivalence point.
- The point where the sign changed in the second-derivative curve was used as a guide to the equivalence point.
- If the measurement interval near the equivalence point is large, an error may occur in reading the equivalence point.
- If the value is recorded before the electrode response stabilizes, a shift may occur in the titration curve.
- If stirring is insufficient, a local value near the electrode may be measured, causing variation in the measured values.
- Near the equivalence point, the titrant should be added in small amounts and the value should be recorded after it stabilizes.
- Using the first or second derivative makes it possible to judge the equivalence point more objectively.
Points to Check When Discussing Potentiometric Titration
Checking the following points before writing the report makes the discussion easier to write.
- Have you prepared the titration curve correctly?
- Is the titrant volume on the horizontal axis and the pH or potential on the vertical axis?
- Have you explained where the steep-change region is?
- Have you written which method was used to read the equivalence point?
- If the first or second derivative was used, have you explained its meaning?
- Are there enough measurement points near the equivalence point?
- Have you considered electrode calibration and delayed electrode response?
- Were measured values recorded after stabilization?
- Was stirring sufficient?
- Was the titrant addition rate appropriate?
- Have you considered the effect of temperature changes?
- Have you explained how error in reading the equivalence point affects the concentration calculation?
Summary
Potentiometric titration is an analytical method in which changes in pH or potential during titration are measured and the equivalence point is determined from the titration curve.
Because the equivalence point can be judged from numerical values and a graph without relying on an indicator color change, the method is also effective for colored samples and titrations in which the endpoint is difficult to observe.
In the discussion of potentiometric titration, it is important to explain the steep-change region of the titration curve, how the equivalence point is read, the meaning of the first and second derivatives, measurement intervals, electrode response, and stirring conditions.
If there are too few measurement points near the equivalence point or values are recorded before the electrode stabilizes, errors may occur in reading the equivalence point.
In a report, do not simply write that “the equivalence point was determined from the titration curve.”
Explain specifically why that position was judged to be the equivalence point and what sources of error may have affected the reading.
By adding the titrant in small amounts near the equivalence point and recording values only after they stabilize, more reliable results can be obtained.
