Acid-Base Titration Discussion Examples | How to Write About the Neutralization Point, Endpoint, and Sources of Error

What Is Acid-Base Titration?

Acid-base titration is an analytical method that uses the neutralization reaction between an acid and a base to determine the concentration of an acid or base in a solution.
For example, an aqueous sodium hydroxide solution of known concentration can be used to determine the concentration of an aqueous acetic acid solution.

In titration, a standard solution of known concentration is gradually added from a burette, and the point at which the reaction has just been completed is determined.
The amount or concentration of the unknown sample is then calculated from the volume of standard solution used at that point.

Although the calculations in acid-base titration may appear relatively simple, in an actual report it is important to discuss matters such as “how the endpoint was determined,” “why the titration volumes varied,” and “whether the indicator was appropriate.”

Results to Examine in Acid-Base Titration

In the results of acid-base titration, organize the volume of standard solution used for titration, titration volumes from repeated measurements, the average titration volume, the calculated sample concentration, and the color change at the endpoint.

Main Items to Include in the Results

• Volume of the sample solution
• Concentration of the standard solution
• Titration volume for each trial
• Average titration volume
• Calculated sample concentration
• Type of indicator
• Color change at the endpoint
• Variation in titration values
• If any measured value was excluded, the reason for exclusion

Reference Experimental Values and Analysis Examples for the Neutralization Point and Concentration Calculation in Acid-Base Titration

Here, reference experimental values are organized for discussing titration volume, unknown sample concentration, neutralization point, titration curve, and indicator color changes obtained in acid-base titration.
Strong acid-strong base titration, weak acid-strong base titration, standardization of standard solutions, dilution factors, blank tests, and endpoint errors are summarized in a form that is easy to use in reports.

In acid-base titration, a standard solution of known concentration is used to neutralize an acid or base of unknown concentration, and the unknown concentration is determined from the volume required for the reaction.
At the equivalence point, the amount of H+ supplied by the acid and the amount of OH− supplied by the base become exactly equivalent according to the reaction ratio.

Reference Experimental Conditions

Basics of the Neutralization Reaction

The neutralization reaction between hydrochloric acid, a strong acid, and sodium hydroxide, a strong base, can be expressed as follows.

HCl + NaOH → NaCl + H2O

In this case, HCl and NaOH react in a 1:1 ratio.
Therefore, at the equivalence point, the amount of HCl is equal to the amount of NaOH.

Example of Titrating a Strong Acid With a Strong Base

The following are reference data obtained by titrating 25.00 mL of HCl of unknown concentration with 0.1000 mol/L NaOH standard solution.

This is an example in which the first trial is judged to have been slightly over-titrated while confirming the endpoint color, and the average of the second to fourth trials, 18.64 mL, is used as the representative value.

Example of Calculating the Unknown HCl Concentration

HCl and NaOH react in a 1:1 ratio.
When the NaOH concentration is 0.1000 mol/L and the average titration volume is 18.64 mL,

n(NaOH) = 0.1000 mol/L × 0.01864 L = 1.864×10−3 mol

From the 1:1 reaction ratio,

n(HCl) = 1.864×10−3 mol

The concentration in 25.00 mL of the HCl sample is,

C(HCl) = 1.864×10−3 mol ÷ 0.02500 L = 0.07456 mol/L

Therefore, the concentration of the unknown aqueous HCl solution is determined to be 0.07456 mol/L.

Example of Titrating a Weak Acid With a Strong Base

The following are reference data obtained by titrating 25.00 mL of aqueous acetic acid solution with 0.1000 mol/L NaOH standard solution.

In titration of a weak acid with a strong base, the pH at the equivalence point is greater than 7.
This is because acetate ions formed at the equivalence point act as the conjugate base of the weak acid and undergo partial hydrolysis with water.

Example of Determining the Acetic Acid Concentration in Vinegar

Suppose vinegar is diluted 10-fold and 10.00 mL of the diluted solution is titrated with 0.1000 mol/L NaOH.
The following is an example calculation when the average titration volume is 8.35 mL.

Using 60.05 g/mol as the molar mass of acetic acid, the amount of acetic acid in the original vinegar is calculated as follows.

0.835 mol/L × 60.05 g/mol = 50.1 g/L

This corresponds to approximately 5.01 g per 100 mL, so it can be expressed as approximately 5.0% as an approximate mass-volume percentage.

Example of Standardizing NaOH Standard Solution

Aqueous NaOH solution readily absorbs CO2 from the air, so its exact concentration may change.
Therefore, it may be standardized using a standard substance such as oxalic acid.

H2C2O4 + 2NaOH → Na2C2O4 + 2H2O

Using the concentration of 0.09881 mol/L determined by standardization rather than the labeled concentration of 0.1000 mol/L allows the unknown sample concentration to be determined more accurately.

Example of Correction Using the Standardized Concentration

If the actual concentration of the NaOH standard solution is lower than the labeled value, calculating with the labeled concentration overestimates the acid concentration.

Examples of Indicator Selection

If the transition range of the indicator does not fall within the sharp pH-change range near the equivalence point, the endpoint and equivalence point are more likely to differ.

Example of Endpoint Determination Using Phenolphthalein

With phenolphthalein, the endpoint is taken not at a dark red color but at the point where a very pale red color remains for a certain period of time.
Attempting to make the color darker causes over-titration and overestimation of the acid concentration.

Examples Comparing Titration Curves

Example of Blank-Test Correction

If reagents or water contain components that consume acid or base, correction may be performed using a blank test.

Even if the blank-test correction volume is small, its relative effect may become large for low-concentration samples.

Effect of Over-Titration on Concentration Calculation

If too much standard solution is added beyond the endpoint, the amount of acid or base contained in the unknown sample is estimated to be greater than it actually is.

Effect of CO2 Absorption by the NaOH Standard Solution

Aqueous NaOH solution may absorb CO2 from the air and form carbonate.
This changes the effective concentration of NaOH and affects the titration result.

When NaOH is used as a standard solution, it is important to confirm its actual concentration by standardization.

Main Sources of Error

Example of How to Write the Results

A 25.00 mL aqueous HCl solution of unknown concentration was titrated with 0.1000 mol/L NaOH standard solution.
The average of three satisfactory titration volumes was 18.64 mL.
Because HCl and NaOH react in a 1:1 ratio, the amount of NaOH is equal to the amount of HCl.
The calculation gave an HCl concentration of 0.07456 mol/L.

When phenolphthalein was used as the indicator, the endpoint was taken as the point at which a very pale red color remained for a while.
If titration is continued until a dark red color appears, NaOH is added in excess and the HCl concentration is estimated higher than the actual value.
Therefore, judgment of the endpoint color greatly affects the titration result.

The aqueous NaOH solution used as the standard solution readily absorbs CO2 from the air, so its effective concentration may change.
If standardization gives an actual concentration of 0.09881 mol/L, recalculation using this value gives an HCl concentration of 0.07367 mol/L.
This difference shows that standardization of the standard solution is important for the accuracy of concentration calculations.

Points to Connect to the Discussion

In the discussion of acid-base titration, it is important not only to calculate the concentration from the titration volume, but also to explain the reaction ratio, indicator, difference between the equivalence point and endpoint, standardization of the standard solution, dilution factor, and sources of error in relation to one another.

• Can you correctly calculate the concentration using the reaction ratio between the acid and base?
• Can you determine the amount of substance from the concentration and titration volume of the standard solution?
• Can you determine the concentration by dividing by the amount of unknown sample?
• If vinegar or another sample was diluted, can you determine the original sample concentration by multiplying by the dilution factor?
• Can you explain that the pH at the equivalence point differs between strong acid-strong base titration and weak acid-strong base titration?
• Can you explain that the pH is close to pKa at the half-neutralization point?
• Can you discuss whether the transition range of the indicator is appropriate for the equivalence-point region?
• Can you explain why standardization of the standard solution is necessary?
• Can you discuss over-titration of the endpoint, CO2 absorption, burette reading, and blank testing as sources of error?

Example Discussion Text

Summary

In acid-base titration, the concentration of an unknown sample is determined from the titration volume of the standard solution based on the reaction ratio between the acid and base.
The equivalence point is the point at which the reaction is stoichiometrically just complete, while the endpoint is the observed end of titration determined using an indicator or other method.

This reference example covered strong acid-strong base titration, weak acid-strong base titration, acetic acid concentration in vinegar, standardization of NaOH standard solution, indicator selection, titration curves, blank-test correction, over-titration, CO2 absorption, and sources of error.
In a report, it is useful to discuss not only the calculation results, but also the difference between the equivalence point and endpoint, the suitability of the indicator, and the reliability of the standard solution.

Difference Between the Neutralization Point and the Endpoint

An important point in the discussion of acid-base titration is the difference between the “neutralization point” and the “endpoint.”
The neutralization point is the point at which the acid and base have reacted in exactly the stoichiometric ratio.
The endpoint, on the other hand, is the point at which the experimenter stops the titration based on an indicator color change or similar observation.

Ideally, the neutralization point and endpoint should coincide, but in practice they may not completely coincide because of the transition range of the indicator and visual judgment.
This difference causes titration error.

Indicator Transition Range and Error

In acid-base titration, an indicator may be used to determine the endpoint.
An indicator changes color over a certain pH range.
Therefore, the indicator used for the titration must change color near the neutralization point.

For example, in titration of a strong acid with a strong base, the pH changes sharply near the neutralization point, so a relatively wide range of indicators can be used.
On the other hand, in titration of a weak acid with a strong base or a strong acid with a weak base, the pH at the neutralization point shifts away from 7, so indicator selection becomes important.

Discussion When Using Phenolphthalein

Phenolphthalein is an indicator that is colorless under acidic to near-neutral conditions and shows a red or pale red color on the basic side.
It is often used in titrations such as those between a weak acid and a strong base.

At the endpoint, a pale red color that remains for a while, rather than a dark red color, is often used as a guide.
If titration is continued until the solution becomes dark red, the endpoint may have been exceeded.

Discussion of Variation in Titration Volumes

In titration experiments, repeated measurements may not produce exactly the same titration volume.
Possible causes of variation include differences in endpoint determination, burette-reading errors, deviations in the amount of sample collected, insufficient stirring, and differences in dropwise addition rate.

Discussion When the Endpoint Is Exceeded

A common source of error in acid-base titration is adding too much standard solution beyond the endpoint.
If the endpoint is exceeded, the recorded titration volume becomes larger than the amount actually required.
As a result, the concentration calculation is also affected.

For example, when determining the concentration of an acid by titrating it with a base, if the titration volume is read as too large, the amount of acid is estimated to be greater than it actually is.
Therefore, the calculated acid concentration may become higher than the actual value.

Burette-Reading Error

With a burette, the initial value before titration and the endpoint value after titration are read, and the titration volume is determined from the difference.
If either reading contains an error, an error also occurs in the titration volume.

If the line of sight is not at the same height as the scale when reading the meniscus, parallax may cause the volume to be read as larger or smaller than the actual value.

Error Due to Air Bubbles in the Burette Tip

If an air bubble remains in the tip of the burette, the liquid level appears to decrease when the bubble is expelled during titration.
However, that volume of liquid has not actually been added to the sample solution, so the titration volume may be overestimated.

Error in Sample Volume Collected With a Volumetric Pipette

In acid-base titration, a fixed volume of sample solution may be collected using a volumetric pipette.
If the liquid level is not aligned correctly with the calibration mark, if air bubbles are present, or if rinsing with the solution is insufficient, the collected sample volume may deviate from the specified amount.

Error Due to Standard-Solution Concentration

Titration assumes that the concentration of the standard solution is accurate.
If the actual concentration of the standard solution differs from the labeled or calculated value, the determined concentration of the unknown sample also shifts.

For example, aqueous sodium hydroxide solution may absorb carbon dioxide from the air, causing its concentration to change.
Errors in weighing and volumetric-flask operation during preparation of the standard solution may also have an effect.

Error Due to Insufficient Stirring

During titration, the added standard solution must mix uniformly throughout the sample solution.
If stirring is insufficient, the pH may change locally and the color of the indicator may change temporarily.
As a result, the endpoint may be judged too early, or conversely, too much additional titrant may be added.

What Can Be Discussed From the Titration Curve

If the pH during titration is measured using a pH meter or similar device, a titration curve can be created.
The titration curve shows the change in pH with respect to the volume of standard solution added.
Because pH changes greatly near the neutralization point, the equivalence point and suitability of the indicator can be discussed more easily.

Concept of Concentration Calculation

In acid-base titration, concentration is determined using the quantitative relationship of the neutralization reaction.
If the acid and base react in a 1:1 ratio, the point where the amounts of acid and base are equal is used.
However, if the valences of the acid or base differ, the coefficients of the reaction equation must be taken into account.

Amount of substance mol = concentration mol/L × volume L

In calculations, it is important to convert mL to L, use consistent significant figures, and select appropriate values when using an average titration volume.

How to Write About Excluding Titration Values

In titration, a value that clearly exceeded the endpoint or differed greatly from the other measurements may be excluded when calculating the average.
However, when excluding a value, the reason for exclusion must be explained in the report.

It is important to base the reason on observed facts so that it does not appear that the value was excluded simply because it was inconvenient.
Examples include “the solution became dark red,” “the endpoint was clearly exceeded,” or “the value differed greatly from the other titration values.”

When the Result Can Be Considered Good

A good result in acid-base titration is indicated when multiple titration volumes agree closely, the color change at the endpoint is appropriate, and the determined concentration is close to the theoretical or labeled value.
If a titration curve is created, it is also important that a clear sharp pH-change region can be observed.

Example Discussion When the Experiment Did Not Go Well

If titration values varied, differed greatly from the theoretical value, or the endpoint color was difficult to determine, consider where the cause may have been among endpoint determination, the standard solution, apparatus, and procedure.

How to Write Points for Improvement

In the discussion of acid-base titration, including points for improvement as well as sources of error makes the report easier to organize.
It is important to write improvements that correspond to the actual sources of error considered.

Methods for Improving Endpoint Determination

• Add the standard solution one drop at a time near the endpoint
• Titrate while thoroughly stirring the solution
• Use the point at which a pale color change persists for a certain period of time as the endpoint
• Do not continue titration until a dark color appears
• Perform multiple titrations to confirm reproducibility

Methods for Reducing Errors Caused by Apparatus

• Read the burette scale at the same height as the meniscus
• Remove air bubbles from the burette tip before titration
• Align the volumetric-pipette calibration mark accurately
• Rinse the apparatus with the solution to be used
• Check the concentration and storage condition of the standard solution

Difference Between a Superficial Discussion and a Good Discussion

In a discussion of acid-base titration, simply writing that “the endpoint shifted” or “the titration volumes varied” results in a superficial discussion.
A persuasive discussion can be produced by explaining how each operation affected the titration volume and concentration calculation.

Examples of Expressions That Can Be Used in Reports

The following expressions can be used when writing the results and discussion of acid-base titration.
Adjust the necessary parts according to your own experimental results.

• The neutralization point is the point at which the acid and base have reacted in stoichiometrically equivalent amounts, while the endpoint is the point determined by the color change of the indicator.
• If the transition range of the indicator and the pH at the neutralization point do not completely coincide, the endpoint may shift from the neutralization point.
• Because endpoint determination was performed visually, individual differences may have occurred in the timing used to judge the color change.
• If titration continued beyond the endpoint, the titration volume would become larger than the actual value and the calculated concentration might be overestimated.
• Parallax when reading the burette scale may have caused an error in the titration volume.
• If an air bubble remained in the burette tip, the titration volume may have been overestimated.
• If the concentration of the standard solution was not accurate, a systematic error would also occur in the calculated sample concentration.
• Because the titration volumes from multiple trials were close to one another, the reproducibility of endpoint determination is considered relatively high.
• Adding the standard solution one drop at a time near the endpoint can reduce errors caused by excess titration.

Points to Check When Discussing Acid-Base Titration

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

• Can you explain the difference between the neutralization point and the endpoint?
• Was the indicator used appropriate?
• Was the color change at the endpoint clear?
• Did you avoid titrating beyond the endpoint?
• Was there variation in the titration volumes?
• If any measured value was excluded, did you state the reason?
• Have you considered burette-reading errors?
• Was there any air bubble in the burette tip?
• Was there any error in the sample volume collected with the volumetric pipette?
• Was the concentration of the standard solution accurate?
• Was stirring sufficient?
• Have you explained how the error affected the concentration calculation?

Summary

Acid-base titration is a basic analytical experiment that determines the concentration of an unknown sample using a neutralization reaction.
In a report, it is important to discuss not only the titration volume and concentration calculation, but also the difference between the neutralization point and endpoint, the transition range of the indicator, and sources of error in endpoint determination.

Sources of error in titration volume include titration beyond the endpoint, burette-reading errors, air bubbles in the burette tip, deviations in the amount collected with a volumetric pipette, changes in the concentration of the standard solution, and insufficient stirring.
These errors directly affect the calculated sample concentration.

In the discussion, rather than simply writing that “the titration did not go well,” specifically explain which operation made the titration volume larger or smaller and how that affected the concentration calculation.
More reliable results can be obtained by carefully adding the titrant near the endpoint and comparing multiple titration values.