Buffer Solution Discussion Examples | Explanation of pH Changes and Buffering Action - りすさんのしまりすコーポレーション　Squirrel's chipmunk Corporation

A buffer solution is a solution that suppresses changes in pH even when a small amount of acid or base is added.
Buffer solutions are widely used in biochemical experiments, analytical chemistry experiments, physical chemistry experiments, and other fields, and they play an important role in maintaining constant reaction conditions in enzyme reactions, protein experiments, cell experiments, titration experiments, and similar applications.

In a discussion of buffer solutions, it is not sufficient simply to write that “the pH did not change much even when acid or base was added.”
It is necessary to explain why the pH change becomes small, how a weak acid and its conjugate base, or a weak base and its conjugate acid, function, the pH range in which buffering action is strong, buffer capacity, the effects of concentration and dilution, and the causes of differences between measured and theoretical values.

This article clearly explains the basics of buffer solutions, pH changes and buffering action, how to use the Henderson-Hasselbalch equation, discussion of buffer capacity, sources of error, points for improvement, and example discussions that can be used in reports.

Note:
This article is a reference intended to assist with discussions of buffer-solution results obtained in chemistry and biochemistry experiments at universities and similar institutions.
For the actual type and concentration of buffer solution, pH adjustment, calibration of the pH meter, handling of reagents, and safety precautions, always follow the instructions in your university’s laboratory manual and those given by your instructor or TA.

What Is a Buffer Solution?
Main Items to Include in the Results
1. Main Items to Include in the Results
Reference Experimental Values for pH Changes and Buffering Action
1. Reference Experimental Conditions
2. Basic Concept of a Buffer Solution
3. Example Preparation of an Acetate Buffer
4. pH Calculation Using the Henderson-Hasselbalch Equation
5. pH Change When Acid Is Added
6. Example Calculation of pH After Acid Addition
7. pH Change When Base Is Added
8. Example Calculation of pH After Base Addition
9. Comparison of pH Changes Between Buffer Solution and Water
10. Differences in pH Caused by the Ratio of Acetic Acid to Acetate Ions
11. Differences in Buffer Capacity Caused by Buffer Concentration
12. Changes in pH and Buffering Action Caused by Dilution
13. Concept of the Buffering Range
14. Example pH Changes in a Phosphate Buffer
15. pH Change When the Buffering Limit Is Exceeded
16. Precautions and Examples of Errors When Measuring With a pH Meter
17. Example of How to Write the Results
18. Points for Connecting the Results to the Discussion
19. Example Discussion
20. Summary
Mechanism of Buffering Action
pH Change When Acid Is Added
pH Change When Base Is Added
Comparison Between Pure Water and a Buffer Solution
What Is the Henderson-Hasselbalch Equation?
Relationship Between pH and pKa
What Is Buffer Capacity?
Effect of Buffer Concentration
pH Change Upon Dilution
Effect of Mixing Ratio on pH
Discussion of the Buffering Range
Discussion of an Acetate Buffer
Discussion of a Phosphate Buffer
Relationship Between Buffer Solutions and Enzyme Experiments
Causes of Differences Between Theoretical and Measured pH
Errors Caused by the pH Meter
Effect of Temperature on pH
When a Buffer Solution Does Not Work Properly
Errors in Buffer Preparation
Discussion When Too Much Acid or Base Is Added
When the pH of a Buffer Solution Changes Over Time
When the Results Can Be Considered Good
Example Discussion When the Experiment Did Not Go Well
How to Write Points for Improvement
1. Improvements to Buffer Preparation
2. Improvements to pH Measurement
3. Improvements to Acid/Base Addition Experiments
Difference Between a Superficial Discussion and a Good Discussion
Examples of Expressions That Can Be Used in Reports
Points to Check When Discussing Buffer Solutions
Summary

What Is a Buffer Solution?

A buffer solution is a solution whose pH does not change greatly even when a small amount of acid or base is added.
In general, solutions containing a weak acid and its conjugate base, or a weak base and its conjugate acid, show buffering action.
Representative examples include an acetate buffer consisting of acetic acid and sodium acetate, and a phosphate buffer consisting of dihydrogen phosphate ions and hydrogen phosphate ions.

In a buffer solution, when acid is added, the conjugate base accepts hydrogen ions, and when base is added, the weak acid neutralizes hydroxide ions.
Therefore, the change in pH is smaller than in water alone.

Example Discussion:
Because a buffer solution contains a weak acid and its conjugate base, or a weak base and its conjugate acid, it can neutralize small amounts of externally added acid or base.
As a result, the change in pH is smaller than when acid or base is added to pure water.
The small pH change observed for the buffer solution in this experiment is considered to have been due to this buffering action.

Main Items to Include in the Results

In a buffer-solution experiment, organize the type of buffer prepared, component concentrations, theoretical pH, measured pH, pH changes after adding acid or base, comparison with pure water, and pH after dilution.
Summarizing the pH changes in a table or graph makes the presence or absence of buffering action easier to understand.

Main Items to Include in the Results

Type of buffer solution
Combination of weak acid and conjugate base
Combination of weak base and conjugate acid
Concentration of each component
Mixing ratio
pKa
Theoretical pH
Measured pH
pH after adding acid
pH after adding base
Comparison of pH changes with pure water
pH after dilution
Magnitude of pH change
Magnitude of buffer capacity
Sources of error and points for improvement

Example of How to Write the Results:
When the pH of the prepared buffer solution was measured, a value close to the theoretical pH was obtained.
In addition, even when a small amount of acid or base was added, the pH change was smaller than when the same amount was added to pure water.
From this result, the prepared solution is considered to have shown buffering action.

Reference Experimental Values for pH Changes and Buffering Action

Here, pH changes when small amounts of acid or base are added to buffer solutions are organized as reference experimental values that are easy to discuss in reports.
Acetic acid/sodium acetate buffers, phosphate buffers, comparison with water, the effect of dilution, and pH changes caused by differences in concentration ratio are covered.

A buffer solution contains a weak acid and its conjugate base, or a weak base and its conjugate acid.
Even when a small amount of acid or base is added, the added H+ or OH− is taken up by the buffer components, so the change in pH is small.

Reference Experimental Conditions

Item	Details
Samples measured	Distilled water, acetate buffer, phosphate buffer
Buffer volume	50.0 mL
Acid added	0.100 mol/L hydrochloric acid
Base added	0.100 mol/L sodium hydroxide solution
Measurement method	Measurement with a pH meter
Measurement temperature	25°C
Evaluation items	Initial pH, pH after acid addition, pH after base addition, pH change, buffer capacity, effect of dilution

Basic Concept of a Buffer Solution

In a buffer solution consisting of acetic acid and acetate ions, when acid is added, acetate ions accept H+ and become acetic acid.
On the other hand, when base is added, acetic acid reacts with OH− and becomes acetate ions.

Substance Added	Main Component That Reacts	Concept of the Reaction	pH Change
Small amount of acid	Acetate ion CH₃COO−	Accepts H+ and becomes acetic acid	Small
Small amount of base	Acetic acid CH₃COOH	Neutralizes OH− and becomes acetate ion	Small
Large amount of acid	Acetate ion becomes insufficient	Buffer component is used up	Decreases greatly
Large amount of base	Acetic acid becomes insufficient	Buffer component is used up	Increases greatly

Example Preparation of an Acetate Buffer

The following is a reference example in which acetic acid and sodium acetate are mixed to prepare a buffer with a pH of approximately 4.76.

Solution	Concentration	Volume Used	Amount of Substance	Role
Acetic acid	0.100 mol/L	25.0 mL	2.50 mmol	Weak acid
Sodium acetate	0.100 mol/L	25.0 mL	2.50 mmol	Conjugate base
Total	–	50.0 mL	–	Buffer solution

When the amounts of acetic acid and acetate ions are equal, the pH becomes close to the pKa of acetic acid.
If the pKa of acetic acid is taken as 4.76, the pH of this buffer is approximately 4.76.

pH Calculation Using the Henderson-Hasselbalch Equation

The pH of a buffer consisting of a weak acid HA and its conjugate base A− can be approximated by the following equation.

pH = pKa + log([A−] ÷ [HA])

When equal amounts of acetic acid and acetate ions are present,

pH = 4.76 + log(2.50 ÷ 2.50) = 4.76 + log1 = 4.76

Therefore, when the ratio of acetic acid to acetate ions is 1:1, the pH is approximately equal to the pKa.

pH Change When Acid Is Added

The following is a reference example of pH changes when small amounts of 0.100 mol/L hydrochloric acid are added stepwise to distilled water and an acetate buffer.

HCl Added	Amount of H+ Added	pH of Distilled Water	pH of Acetate Buffer	How to Interpret the Result
0.0 mL	0.00 mmol	6.80	4.76	Initial pH
0.5 mL	0.05 mmol	3.00	4.74	Change is small in the buffer
1.0 mL	0.10 mmol	2.70	4.72	pH decrease is small
2.0 mL	0.20 mmol	2.40	4.69	Acetate ions accept H+
5.0 mL	0.50 mmol	2.00	4.58	Buffering action still remains
10.0 mL	1.00 mmol	1.70	4.36	pH change begins to become larger

In distilled water, the pH decreases greatly when a small amount of hydrochloric acid is added, whereas the decrease in pH is kept small in the acetate buffer.
This is because acetate ions accepted the added H+.

Example Calculation of pH After Acid Addition

Consider a buffer containing 2.50 mmol of acetic acid and 2.50 mmol of acetate ions to which 2.0 mL of 0.100 mol/L hydrochloric acid is added.
The amount of H+ added is 0.20 mmol.

Component	Before Addition	Change	After Addition
Acetic acid HA	2.50 mmol	+0.20 mmol	2.70 mmol
Acetate ion A−	2.50 mmol	−0.20 mmol	2.30 mmol

The pH can be calculated as follows.

pH = 4.76 + log(2.30 ÷ 2.70)

pH = 4.76 + log0.852 = 4.76 − 0.069 = 4.69

This value is close to the measured value of 4.69, showing that the acid in the buffer was taken up by acetate ions.

pH Change When Base Is Added

The following is a reference example of pH changes when small amounts of 0.100 mol/L sodium hydroxide solution are added stepwise to distilled water and an acetate buffer.

NaOH Added	Amount of OH− Added	pH of Distilled Water	pH of Acetate Buffer	How to Interpret the Result
0.0 mL	0.00 mmol	6.80	4.76	Initial pH
0.5 mL	0.05 mmol	11.00	4.78	Change is small in the buffer
1.0 mL	0.10 mmol	11.30	4.79	pH increase is small
2.0 mL	0.20 mmol	11.60	4.83	Acetic acid neutralizes OH−
5.0 mL	0.50 mmol	12.00	4.94	Buffering action remains
10.0 mL	1.00 mmol	12.30	5.16	pH increase begins to become larger

In distilled water, the pH rises greatly when a small amount of NaOH is added, whereas the pH change is small in the acetate buffer.
This is because acetic acid neutralized OH− and became acetate ions.

Example Calculation of pH After Base Addition

Consider a buffer containing 2.50 mmol of acetic acid and 2.50 mmol of acetate ions to which 2.0 mL of 0.100 mol/L NaOH is added.
The amount of OH− added is 0.20 mmol.

Component	Before Addition	Change	After Addition
Acetic acid HA	2.50 mmol	−0.20 mmol	2.30 mmol
Acetate ion A−	2.50 mmol	+0.20 mmol	2.70 mmol

pH = 4.76 + log(2.70 ÷ 2.30)

pH = 4.76 + log1.174 = 4.76 + 0.070 = 4.83

This value is close to the measured value of 4.83, showing that the added OH− was neutralized by acetic acid.

Comparison of pH Changes Between Buffer Solution and Water

The following example compares the pH changes when 2.0 mL of acid or base is added.

Sample	Additive	pH Before Addition	pH After Addition	pH Change	Buffering Action
Distilled water	HCl 2.0 mL	6.80	2.40	−4.40	Almost none
Acetate buffer	HCl 2.0 mL	4.76	4.69	−0.07	Present
Distilled water	NaOH 2.0 mL	6.80	11.60	+4.80	Almost none
Acetate buffer	NaOH 2.0 mL	4.76	4.83	+0.07	Present

Even when the same amount of acid or base is added, the pH changes greatly in distilled water, whereas the pH change is kept small in the buffer solution.

Differences in pH Caused by the Ratio of Acetic Acid to Acetate Ions

The pH of a buffer solution changes according to the concentration ratio of the weak acid and conjugate base.

Amount of Acetic Acid	Amount of Acetate Ions	[A−] / [HA]	Calculated pH	How to Interpret the Result
4.0 mmol	1.0 mmol	0.25	4.16	Acidic side
3.0 mmol	2.0 mmol	0.67	4.58	Slightly acidic side
2.5 mmol	2.5 mmol	1.00	4.76	Near pH = pKa
2.0 mmol	3.0 mmol	1.50	4.94	Slightly more basic side
1.0 mmol	4.0 mmol	4.00	5.36	Moves toward the basic side

The larger the proportion of acetate ions, which are the conjugate base, the higher the pH becomes.
On the other hand, when the proportion of acetic acid is larger, the pH becomes lower.

Differences in Buffer Capacity Caused by Buffer Concentration

Even when the pH is the same, the ability to take up acid or base changes if the total concentration of the buffer components differs.

Buffer Condition	Amount of Acetic Acid	Amount of Acetate Ions	Initial pH	pH After Addition of 2.0 mL HCl	pH Change
Low concentration	0.50 mmol	0.50 mmol	4.76	4.36	−0.40
Medium concentration	2.50 mmol	2.50 mmol	4.76	4.69	−0.07
High concentration	5.00 mmol	5.00 mmol	4.76	4.72	−0.04

Even with the same initial pH, the higher-concentration buffer shows a smaller pH change.
This is because a larger amount of acetate ions is available to accept the acid.

Changes in pH and Buffering Action Caused by Dilution

Even when a buffer solution is diluted with water, the pH does not change greatly if the ratio of the weak acid to the conjugate base remains unchanged.
However, because the total amount of buffer components decreases, resistance to acid or base becomes weaker.

Dilution Condition	Initial pH	pH After Addition of 1.0 mL HCl	pH After Addition of 1.0 mL NaOH	How to Interpret the Result
Original solution	4.76	4.72	4.79	Strong buffering action
2-fold dilution	4.76	4.68	4.84	Change is somewhat larger
5-fold dilution	4.77	4.50	5.05	Buffering action becomes weaker
10-fold dilution	4.78	4.18	5.42	pH change is large

Although the initial pH does not change greatly after dilution, the pH change becomes larger when acid or base is added.
This is because the total amount of buffer components has decreased.

Concept of the Buffering Range

A buffer solution works most effectively near the pKa of the weak acid.
In general, buffering action is considered effective within approximately pKa ± 1.

Buffer System	pKa	Approximate Effective pH Range	Example Use
Acetic acid / acetate ion	4.76	Approximately 3.8–5.8	Weakly acidic region
Dihydrogen phosphate / hydrogen phosphate	7.21	Approximately 6.2–8.2	Near neutral pH
Ammonia / ammonium ion	9.25	Approximately 8.3–10.3	Weakly basic region

When it is necessary to maintain a stable pH around 7, a phosphate buffer is more suitable than an acetate buffer.

Example pH Changes in a Phosphate Buffer

The following is a reference example in which acid or base is added to a phosphate buffer with a pH of approximately 7.2.

Sample	Additive	pH Before Addition	pH After Addition	pH Change	How to Interpret the Result
Distilled water	HCl 1.0 mL	6.80	2.70	−4.10	No buffering action
Phosphate buffer	HCl 1.0 mL	7.20	7.12	−0.08	Buffers against acid
Distilled water	NaOH 1.0 mL	6.80	11.30	+4.50	No buffering action
Phosphate buffer	NaOH 1.0 mL	7.20	7.29	+0.09	Buffers against base

In the phosphate buffer, the pH change caused by the addition of acid or base is small near pH 7.
This is because H+ and OH− are taken up through the equilibrium between H₂PO₄− and HPO₄²⁻.

pH Change When the Buffering Limit Is Exceeded

Even in a buffer solution, if too much acid or base is added, the buffer components are used up and the pH changes rapidly.

Amount of HCl Added	Remaining Acetate Ion	Amount of Acetic Acid	pH	How to Interpret the Result
0.0 mmol	2.50 mmol	2.50 mmol	4.76	Buffer solution
1.0 mmol	1.50 mmol	3.50 mmol	4.39	Within buffering range
2.0 mmol	0.50 mmol	4.50 mmol	3.81	Near the limit
2.5 mmol	0.00 mmol	5.00 mmol	Approximately 2.9	Conjugate base is used up
3.0 mmol	0.00 mmol	5.00 mmol + excess strong acid	Approximately 2.2	Buffering action is lost

A buffer solution suppresses pH changes against small amounts of acid or base, but it cannot maintain the pH indefinitely.
Once one of the buffer components is used up, the pH changes greatly.

Precautions and Examples of Errors When Measuring With a pH Meter

Condition	Measured pH	Possible Cause	Improvement
Immediately after calibration	4.76	Standard measurement	Reference value
No calibration	4.90	Electrode deviation	Calibrate with standard solutions
Insufficient stirring	4.70–4.85	Added acid or base is not mixed uniformly	Stir lightly before measurement
Insufficient electrode cleaning	Unstable value	Residue from the previous sample	Rinse with pure water and lightly remove droplets
Temperature change	4.73–4.80	Changes in pKa or electrode response	Keep the temperature constant

A pH meter is affected by calibration, electrode cleaning, stirring, and temperature.
Because pH changes are small in buffering-action experiments, measurement errors must also be considered carefully.

Example of How to Write the Results

The initial pH of the buffer prepared by mixing equal amounts of acetic acid and sodium acetate was 4.76.
If the pKa of acetic acid is taken as 4.76, the amounts of acetic acid and acetate ions are equal, so the pH is calculated to be 4.76 from the Henderson-Hasselbalch equation.
The measured value was also close to this value, indicating that the buffer was prepared at approximately the intended pH.

When 2.0 mL of 0.100 mol/L hydrochloric acid was added to distilled water, the pH decreased greatly from 6.80 to 2.40.
In contrast, when the same amount of hydrochloric acid was added to the acetate buffer, the pH decreased only from 4.76 to 4.69.
This is considered to have occurred because acetate ions in the buffer accepted the added H+ and became acetic acid.

In addition, when 2.0 mL of 0.100 mol/L NaOH was added to distilled water, the pH rose to 11.60.
In contrast, the pH of the acetate buffer remained at 4.83.
This is because acetic acid neutralized OH− and changed into acetate ions.
From these results, the acetate buffer was confirmed to show buffering action that suppresses pH changes against the addition of small amounts of both acid and base.

Points for Connecting the Results to the Discussion

In a discussion of buffer solutions, it is important to explain not only that the pH is difficult to change, but also to use changes in the amounts of the weak acid and conjugate base.

Can it be explained that the buffer consists of a weak acid and its conjugate base?
Can it be explained that the conjugate base accepts H+ when acid is added?
Can it be explained that the weak acid neutralizes OH− when base is added?
Can the pH change be calculated using the Henderson-Hasselbalch equation?
Can the pH changes in distilled water and the buffer be compared numerically to show buffering action?
Can it be explained that the ratio of the weak acid to the conjugate base determines the pH?
Can it be discussed that a higher total concentration of buffer components gives a larger buffer capacity?
Can it be explained that dilution weakens buffering action even if the initial pH does not change greatly?
Can it be explained that pH changes greatly when the buffering range or buffering limit is exceeded?
Can measurement errors such as pH-meter calibration, stirring, and temperature be discussed?

Example Discussion

In this experiment, a buffer solution consisting of acetic acid and sodium acetate was prepared, and the pH changes caused by the addition of acid and base were investigated.
The pH of the buffer containing equal amounts of acetic acid and acetate ions was 4.76, which was almost identical to the pKa of acetic acid.
This is because, in the Henderson-Hasselbalch equation, [A−] / [HA] = 1 and log1 = 0.

When a small amount of hydrochloric acid was added to distilled water, the pH decreased greatly, whereas the pH change was small in the acetate buffer.
In the acetate buffer, the added H+ reacted with acetate ions to form acetic acid.
Therefore, the increase in the concentration of free H+ in the solution was suppressed, and the decrease in pH is considered to have been small.

On the other hand, when NaOH was added, the pH also increased greatly in distilled water, whereas the pH change was small in the acetate buffer.
This occurred because the added OH− reacted with acetic acid to form water and acetate ions.
When acid was added, acetate ions decreased and acetic acid increased, whereas when base was added, acetic acid decreased and acetate ions increased.
In this way, a buffer suppresses rapid pH changes by changing the ratio of the weak acid to the conjugate base.

When the buffer solution was diluted, the initial pH hardly changed.
This is because the ratio of acetic acid to acetate ions remained almost unchanged after dilution.
However, the pH change after adding acid or base became larger.
This is because the total amount of buffer components decreased and the ability to take up H+ or OH− decreased.

In addition, when a large amount of acid or base was added even to the buffer solution, the pH changed greatly.
This is because either acetic acid or acetate ions became insufficient and the buffering action could no longer be maintained.
Therefore, buffer solutions have an effective pH range and a limited amount that can be buffered, and the pKa and buffer concentration must be selected according to the intended use.

Possible sources of error include insufficient calibration of the pH meter, insufficient cleaning of the electrode, temperature changes, and insufficient stirring after adding acid or base.
Because the pH changes in a buffer solution are small, measurement errors can easily affect interpretation of the results.
Therefore, it is important to calibrate the pH meter with standard solutions before measurement and to mix the solution thoroughly after addition before measuring the pH.

Summary

A buffer solution is a solution that suppresses pH changes when small amounts of acid or base are added through a combination of a weak acid and its conjugate base.
In an acetate buffer, acetate ions accept H+ when acid is added, and acetic acid neutralizes OH− when base is added.

This reference example covered pH changes after acid and base addition, pH calculations using the Henderson-Hasselbalch equation, concentration ratios, buffer concentration, dilution, buffering range, buffering limit, and pH measurement errors using acetate and phosphate buffers as examples.
In a report, it is useful to compare pH changes numerically and discuss them in relation to changes in the amounts of the weak acid and conjugate base.

Mechanism of Buffering Action

Buffering action can be explained by the equilibrium between a weak acid and its conjugate base present in the solution.
If the weak acid is represented by HA and the conjugate base by A−, the following equilibrium exists.

HA ⇄ H+ + A−

When acid is added and H+ increases, A− accepts H+ and becomes HA.
This suppresses the increase in H+ concentration and keeps the decrease in pH small.
Conversely, when base is added and OH− increases, HA supplies H+ to neutralize OH−, thereby suppressing the increase in pH.

Example Discussion:
In a buffer solution, the weak acid HA and conjugate base A− coexist.
When acid is added, A− accepts H+ and becomes HA, so a rapid increase in H+ concentration is suppressed.
When base is added, HA supplies H+ and neutralizes OH−, so the increase in pH is suppressed.

pH Change When Acid Is Added

When a small amount of acid is added to a buffer solution, the H+ concentration in the solution tends to increase.
However, the conjugate base A− accepts H+ and becomes the weak acid HA, so the increase in H+ concentration is kept small.
As a result, the decrease in pH is smaller than in pure water.

However, if too much acid is added, the conjugate base is consumed and the buffering action becomes weaker.
When insufficient buffer components remain, the pH changes greatly.

Example Discussion:
Even when acid was added to the buffer solution, the decrease in pH was small.
This is because the conjugate base in the solution accepted the added H+ and changed into the weak acid.
As a result, the increase in free H+ concentration was suppressed, and the pH change was smaller than when acid was added to pure water.

pH Change When Base Is Added

When a small amount of base is added to a buffer solution, OH− tends to increase.
At this time, the weak acid HA supplies H+ and reacts with OH− to form water.
Therefore, the increase in OH− concentration is suppressed and the increase in pH remains small.

However, if too much base is added, the weak acid HA is consumed and the buffering action becomes weaker.
As a result, the pH may rise rapidly.

Example Discussion:
Even when base was added to the buffer solution, the increase in pH was small.
This is because the weak acid HA in the solution supplied H+ and neutralized the added OH−.
Through this reaction, the increase in OH− concentration was suppressed, and the pH change was smaller than when base was added to pure water.

Comparison Between Pure Water and a Buffer Solution

Pure water does not contain sufficient buffer components to neutralize added acid or base.
Therefore, even a small amount of acid or base causes a large change in pH.
In contrast, in a buffer solution, the weak acid and conjugate base consume the added acid or base, so the pH change becomes small.

In experiments, the same amount of acid or base may be added to pure water and a buffer solution to compare their pH changes.
This comparison confirms that a buffer solution has the ability to suppress pH changes.

Example Discussion:
When acid or base was added to pure water, the pH changed greatly.
In contrast, even when the same amount of acid or base was added to the buffer solution, the pH change was small.
This is because pure water contains almost no buffer components capable of neutralizing acid or base, whereas the buffer solution contains a weak acid and conjugate base that can consume the added H+ or OH−.

What Is the Henderson-Hasselbalch Equation?

The pH of a buffer solution consisting of a weak acid HA and its conjugate base A− can be expressed by the Henderson-Hasselbalch equation.
This equation is commonly used when considering the pH of a buffer solution.

pH = pKa + log([A−] / [HA])

This equation shows that the pH is determined by the concentration ratio of the weak acid and conjugate base.
When [A−] and [HA] are equal, log(1) = 0, so pH = pKa.
In other words, when the weak acid and conjugate base have the same concentration, the pH of the buffer solution is close to the pKa.

Example Discussion:
According to the Henderson-Hasselbalch equation, the pH of a buffer solution is determined by the concentration ratio of the weak acid HA and conjugate base A−.
In the buffer prepared in this experiment, if the ratio [A−] / [HA] is close to the set value, a pH close to the theoretical pH is expected.
If the measured pH differs from the theoretical value, possible causes include errors in concentration preparation and calibration errors of the pH meter.

Relationship Between pH and pKa

A buffer solution works most effectively near the pKa of the weak acid.
This is because when the pH is close to the pKa, the weak acid HA and conjugate base A− are present in similar amounts, making it easy to respond to both acid and base.
When the pH is far from the pKa, either HA or A− becomes scarce and the buffering action becomes weaker.

In general, buffer solutions are sometimes described as working well within approximately pKa ± 1.
Therefore, it is important to select a weak-acid or weak-base system with a pKa close to the desired pH.

Example Discussion:
A buffer solution works most effectively when the pH is close to the pKa of the weak acid.
Near pH = pKa, the weak acid HA and conjugate base A− are present in similar amounts, making it easy to respond both when acid is added and when base is added.
Therefore, selecting a buffer system with a pKa close to the desired pH is important for maintaining a stable pH.

What Is Buffer Capacity?

Buffer capacity is the ability of a buffer solution to suppress pH changes.
The larger the buffer capacity, the smaller the pH change when the same amount of acid or base is added.
Buffer capacity is affected by the total concentration of buffer components and the ratio of the weak acid to the conjugate base.

The higher the concentration of buffer components, the greater the amount of added acid or base that can be taken up, so the buffer capacity becomes larger.
In addition, near the pH where the weak acid and conjugate base are present in similar amounts, the buffer can more readily respond to both acid and base.

Example Discussion:
Buffer capacity is the ability of a buffer solution to suppress pH changes caused by the addition of acid or base.
The higher the total concentration of buffer components, the greater the amount of added H+ or OH− that can be consumed, so the pH change becomes smaller.
If the higher-concentration buffer showed a smaller pH change in this experiment, it is considered to have had a larger buffer capacity.

Effect of Buffer Concentration

The higher the total concentration of a buffer solution, the greater the amount of acid or base it can take up.
For example, even for buffer solutions with the same pH, a 0.1 mol/L buffer can neutralize more acid or base than a 0.01 mol/L buffer.
Therefore, the pH change is smaller in the more concentrated buffer.

However, if the buffer concentration is too high, the effects of ionic strength and effects on the reaction system may become larger.
In biochemical experiments, the effects of salt concentration on enzymes and proteins must also be considered.

Example Discussion:
Under conditions with a higher buffer concentration, the pH change after adding acid or base was smaller.
This is because a larger amount of buffer components was present and more of the added H+ or OH− could be consumed.
In contrast, in a low-concentration buffer, the amount of buffer components was smaller, so even a small amount of acid or base caused a larger pH change.

pH Change Upon Dilution

When a buffer solution is diluted, the concentrations of both the weak acid and conjugate base decrease.
However, ideally, if the concentration ratio [A−] / [HA] does not change, the pH in the Henderson-Hasselbalch equation does not change greatly.
Therefore, simple dilution may not cause a large change in pH.

However, dilution reduces the total amount of buffer components, so the buffer capacity decreases.
In other words, even if the pH does not immediately change greatly after dilution, it becomes easier for the pH to change when acid or base is added.

Example Discussion:
The pH did not change greatly when the buffer solution was diluted because the concentration ratio of the weak acid and conjugate base remained almost unchanged.
According to the Henderson-Hasselbalch equation, the pH is mainly determined by the ratio [A−] / [HA].
However, because dilution lowers the total concentration of buffer components, the buffer capacity decreases and the pH becomes easier to change when acid or base is added.

Effect of Mixing Ratio on pH

The pH of a buffer solution is greatly affected by the mixing ratio of the weak acid and conjugate base.
The larger the amount of conjugate base A−, the larger the term log([A−] / [HA]) in the Henderson-Hasselbalch equation becomes and the higher the pH becomes.
Conversely, the larger the amount of weak acid HA, the smaller this ratio becomes and the lower the pH becomes.

Therefore, the mixing ratio of the weak acid and conjugate base is adjusted according to the desired pH.
Errors in preparing the mixing ratio cause differences between the theoretical pH and measured pH.

Example Discussion:
The pH of a buffer solution changes according to the mixing ratio of the weak acid HA and conjugate base A−.
The greater the proportion of conjugate base, the higher the pH becomes, and the greater the proportion of weak acid, the lower the pH becomes.
A possible cause of the difference between the measured pH and theoretical value is an error in the volume ratio or concentration of the weak-acid solution and conjugate-base solution.

Discussion of the Buffering Range

The pH range in which a buffer solution works effectively is called the buffering range.
In general, buffering action is strongest in the pH range close to the pKa of the weak acid.
When the pH is far from the pKa, either the weak acid or the conjugate base becomes scarce, reducing the ability to respond to acid or base.

For example, when the pH is considerably lower than the pKa, HA is abundant in the solution and A− is scarce.
In this case, the buffer can respond to base to some extent, but its buffering action against acid becomes weak.
Conversely, when the pH is considerably higher than the pKa, A− is abundant and HA is scarce, so the buffering action against base becomes weak.

Example Discussion:
A buffer solution shows its strongest buffering action near the pKa.
When the pH is far from the pKa, either the weak acid HA or conjugate base A− becomes scarce, reducing the ability to neutralize acid or base.
Therefore, when the desired pH is outside the buffering range, the pH is more likely to change greatly upon the addition of acid or base.

Discussion of an Acetate Buffer

An acetate buffer is a representative weak-acid buffer consisting of acetic acid CH₃COOH and acetate ions CH₃COO−.
It shows buffering action near the pKa of acetic acid.
When acid is added, acetate ions accept H+, and when base is added, acetic acid supplies H+.

The pH of an acetate buffer is determined by the concentration ratio of acetic acid to acetate ions.
Increasing the proportion of sodium acetate raises the pH, whereas increasing the proportion of acetic acid lowers the pH.

Example Discussion:
An acetate buffer shows buffering action because acetic acid and acetate ions coexist.
When acid is added, acetate ions accept H+, and when base is added, acetic acid supplies H+, so the pH change remains small.
Under conditions in this experiment where the pH was close to the pKa of acetic acid, both acetic acid and acetate ions were present in sufficient amounts, and the buffer is considered to have shown strong buffering action.

Discussion of a Phosphate Buffer

A phosphate buffer is one of the buffer solutions commonly used in biochemical experiments.
Typically, the combination of H₂PO₄− and HPO₄²⁻ provides buffering action near neutral pH.
It may be used in enzyme reactions and protein experiments to maintain the pH of the reaction solution at a constant value.

The pH of a phosphate buffer is also determined by the ratio of the acidic and basic components.
However, because phosphoric acid is a polyprotic acid and has multiple pKa values, it is important to confirm which dissociation step is being used.

Example Discussion:
In a phosphate buffer, H₂PO₄− and HPO₄²⁻ coexist and act to suppress pH changes.
When acid is added, HPO₄²⁻ accepts H+, and when base is added, H₂PO₄− supplies H+.
Therefore, the buffer is considered to have shown relatively stable buffering action near neutral pH.

Relationship Between Buffer Solutions and Enzyme Experiments

Because enzyme activity is greatly affected by pH, buffer solutions are important in enzyme experiments.
When pH changes, the charge state and three-dimensional structure of the enzyme’s active site change, affecting substrate binding and catalytic reactions.
By using a buffer solution, pH changes during the reaction can be suppressed and enzyme activity can be compared under constant conditions.

However, the type and concentration of the buffer solution may also affect enzyme activity.
For enzymes that require metal ions, buffer components may interact with the metal ions.
Therefore, not only the pH but also the buffer components themselves may affect the experimental results.

Example Discussion:
In enzyme experiments, it is important to maintain the pH of the reaction solution at a constant value using a buffer solution.
When the pH changes, the charge state of the enzyme’s active site changes, affecting substrate binding and catalytic reactions.
Therefore, using a buffer solution is considered to reduce variation in enzyme activity caused by pH changes.

Causes of Differences Between Theoretical and Measured pH

The theoretical pH calculated from the Henderson-Hasselbalch equation and the pH actually measured with a pH meter may differ.
Possible causes include errors in reagent concentrations, errors in volume measurement, insufficient calibration of the pH meter, temperature differences, effects of ionic strength, and insufficient mixing of the solution.

In addition, because the Henderson-Hasselbalch equation assumes ideal conditions, deviations may occur in actual solutions because of factors such as activity coefficients.
In student experiments, the effects of concentration preparation, measurement procedures, and pH-meter calibration should first be considered.

Example Discussion:
Possible causes of the difference between the measured pH and theoretical pH include errors in volume measurement during buffer preparation and calibration errors of the pH meter.
Because the Henderson-Hasselbalch equation determines pH from the concentration ratio of the weak acid and conjugate base, deviation in the mixing ratio causes deviation from the theoretical pH.
Differences in temperature and ionic strength may also have affected the measured pH.

Errors Caused by the pH Meter

When measuring pH with a pH meter, calibration, electrode condition, temperature compensation, cleaning, and waiting for the measurement value to stabilize are important.
If calibration is insufficient, all measured values may be systematically shifted.
If the electrode is dirty or residue from the previous sample remains, the pH may not be measured correctly.

In addition, reading the pH meter before the value has stabilized causes variation in the measured values.
In experiments comparing pH differences among buffer solutions, handling of the pH meter greatly affects the results.

Example Discussion:
Possible causes of deviation in the pH measurement include insufficient calibration of the pH meter and insufficient cleaning of the electrode.
If the pH meter is not correctly calibrated, the measured pH may be systematically shifted from the theoretical pH.
In addition, if residue from the previous sample remains on the electrode, it may affect the pH measurement of the buffer solution, so the electrode must be thoroughly cleaned between measurements.

Effect of Temperature on pH

pH and pKa may change with temperature.
If the temperature at which the buffer solution was prepared differs from the measurement temperature, the theoretical pH and measured pH may differ.
In addition, the response of the pH-meter electrode is affected by temperature, making temperature compensation important.

In biochemical experiments, the pH of a buffer solution must be considered according to the temperature conditions of enzyme reactions and similar experiments.
A pH adjusted at room temperature may have a different value at the reaction temperature.

Example Discussion:
A possible cause of the difference between the measured pH and the theoretical value is the difference in measurement temperature.
Because the pKa of a weak acid and the response of the pH meter change with temperature, differences between the preparation temperature and measurement temperature may cause differences in pH.
Therefore, for accurate pH evaluation, it is important to record the measurement temperature and perform temperature compensation when necessary.

When a Buffer Solution Does Not Work Properly

If a buffer solution does not work properly, possible causes include a pH that is far from the pKa, a low concentration of buffer components, an excessive amount of acid or base added, preparation errors, or selection of a buffer that is unsuitable for the desired pH.
Components in the sample may also act as acids or bases and change the pH beyond the buffer capacity.

Buffering action has limits.
No matter how effective a buffer is, if enough acid or base is added to consume the buffer components, the pH will change greatly.
In a report, it is useful to explain that a buffer solution does not completely prevent pH changes but rather reduces them.

Example Discussion:
A possible reason the pH changed greatly after adding acid or base is that the amount added exceeded the buffer capacity of the solution.
A buffer solution suppresses pH changes caused by small amounts of acid or base, but its buffering action becomes weaker as the buffer components are consumed.
Therefore, even a buffer solution may show a large pH change when a large amount of acid or base is added.

Errors in Buffer Preparation

In buffer preparation, reagent weighing, solution concentration, volume measurement, mixing ratio, and pH adjustment affect the results.
If the ratio of the weak acid to the conjugate base deviates, the pH calculated from the Henderson-Hasselbalch equation also changes.
Operation of volumetric flasks and pipettes, alignment with calibration marks, and reagent purity can also be sources of error.

If the pH is finely adjusted with acid or base, adding too much may cause the target pH to be overshot.
In addition, if the solution is not mixed thoroughly after pH adjustment, the pH may differ depending on the location of measurement.

Example Discussion:
A possible reason the measured pH of the buffer differed from the theoretical value is that the mixing ratio of the weak acid and conjugate base deviated from the set value.
Because the concentration ratio determines the pH in the Henderson-Hasselbalch equation, errors in pipetting or aligning the volumetric flask with the calibration mark also change the pH.
Insufficient mixing after pH adjustment may also have caused the measured value to remain unstable.

Discussion When Too Much Acid or Base Is Added

A buffer solution can respond to small amounts of acid or base, but if too much is added, the buffer components are consumed and the pH changes greatly.
When a large amount of acid is added, the conjugate base becomes insufficient and can no longer accept all of the H+.
When a large amount of base is added, the weak acid becomes insufficient and can no longer neutralize all of the OH−.

In such cases, even if the pH of the buffer solution changes greatly, this does not mean that there was no buffering action at all.
Rather, the buffering limit was reached because an amount of acid or base exceeding the buffer capacity was added.

Example Discussion:
The large decrease in pH under conditions where a large amount of acid was added is considered to have occurred because the conjugate base was consumed and could no longer accept sufficient H+.
A buffer solution suppresses pH changes, but its capacity is limited.
Therefore, when an amount of acid or base exceeding the amount of buffer components is added, the pH changes greatly.

When the pH of a Buffer Solution Changes Over Time

The pH of a buffer solution may change over time.
Possible causes include dissolution of carbon dioxide from the air, microbial contamination, loss of volatile components, temperature changes, and contamination from the container.
Particularly in weakly basic buffer solutions, dissolved carbon dioxide may form carbonic acid and lower the pH.

When using a buffer solution that has been stored for a long period, it is important to recheck the pH before use.
In biochemical experiments, contamination and pH changes during storage may affect enzyme activity and protein stability.

Example Discussion:
Possible causes of the difference in pH between immediately after preparation and the time of measurement include dissolution of carbon dioxide from the air and temperature changes.
When carbon dioxide dissolves in water, carbonic acid is formed and may lower the pH of the solution.
Therefore, when using a stored buffer solution, it is important to recheck the pH before use.

When the Results Can Be Considered Good

Results in a buffer-solution experiment can be considered good when the measured pH of the prepared buffer is close to the theoretical value and the pH change after adding acid or base is clearly smaller than in pure water.
Results are also reasonable when trends consistent with theory are observed, such as a smaller pH change at higher buffer concentrations and stronger buffering action near the pKa.

Example Discussion:
The measured pH of the prepared buffer was close to the theoretical pH, and the pH change remained small even after acid or base was added.
In addition, compared with the addition of the same amount of acid or base to pure water, the pH change in the buffer solution was clearly suppressed.
From these results, the buffer prepared in this experiment is considered to have shown appropriate buffering action.

Example Discussion When the Experiment Did Not Go Well

If a buffer-solution experiment does not go well, causes are considered from results such as a measured pH that differs greatly from the theoretical value, a large pH change after adding acid or base, no difference caused by concentration, or unstable pH-meter readings.
It is easier to organize the discussion by separating preparation errors, pH-meter effects, temperature, amount of acid or base added, and buffering range.

Example Discussion:
In this experiment, the pH change after adding acid to the buffer solution was larger than expected.
One possible cause is that the total concentration of the buffer was low and the amount of conjugate base was insufficient relative to the amount of acid added.
Errors in preparing the mixing ratio of the weak acid and conjugate base and insufficient calibration of the pH meter may also have caused the measured pH to differ from the theoretical value.

How to Write Points for Improvement

In a discussion of buffer solutions, including not only sources of error but also points for improvement makes the report easier to organize.
Improvements are easier to organize when divided into buffer preparation, pH measurement, acid/base addition, and temperature control.

Improvements to Buffer Preparation

Prepare the concentrations of the weak acid and conjugate base accurately
Use volumetric flasks and volumetric pipettes correctly
Keep the mixing ratio accurate
Select a buffer system with a pKa close to the desired pH
Mix thoroughly after pH adjustment

Improvements to pH Measurement

Calibrate the pH meter with standard solutions
Clean the electrode between measurements
Read the value after it has stabilized
Record the measurement temperature
Recheck the pH of stored buffer solutions before use

Improvements to Acid/Base Addition Experiments

Measure the amount of acid or base added accurately
Mix thoroughly after addition
Do not add an amount exceeding the buffer capacity
Keep the comparison conditions with pure water the same
Perform multiple measurements to confirm reproducibility

Example of How to Write Points for Improvement:
To bring the pH of the buffer solution closer to the theoretical value, the concentrations and mixing ratio of the weak acid and conjugate base must be prepared accurately.
In addition, it is important to calibrate the pH meter with standard solutions and thoroughly clean the electrode before measurement.
In experiments involving the addition of acid or base, the added amount should be kept accurate and the pH should be measured after thorough mixing so that the buffering action can be evaluated more accurately.

Difference Between a Superficial Discussion and a Good Discussion

In a discussion of buffer solutions, simply writing that “the pH did not change much” or “there was buffering action” results in a superficial discussion.
Relating the weak acid, conjugate base, neutralization of H+ and OH−, pKa, concentration, buffer capacity, and sources of error produces a more persuasive discussion.

Superficial Discussion	Good Discussion
The pH did not change much even after acid was added.	When acid is added, H+ increases, but the conjugate base A− in the buffer accepts H+ and becomes HA, so the increase in H+ concentration is suppressed and the decrease in pH is considered to have remained small.
The pH did not change much even after base was added.	When base is added, OH− increases, but the weak acid HA supplies H+ and neutralizes OH−, so the increase in pH is considered to have been suppressed.
The theoretical and measured values differed.	Possible causes of the difference between theoretical and measured pH include errors in the mixing ratio of the weak acid and conjugate base, insufficient calibration of the pH meter, temperature differences, and effects of ionic strength.

Examples of Expressions That Can Be Used in Reports

The following expressions can be used when writing the results and discussion of a buffer-solution experiment.
Adjust the necessary parts according to your own experimental results.

A buffer solution suppresses pH changes through the coexistence of a weak acid and its conjugate base.
When acid is added, the conjugate base accepts H+, so the decrease in pH is small.
When base is added, the weak acid supplies H+ and neutralizes OH−, so the increase in pH is small.
According to the Henderson-Hasselbalch equation, the pH of a buffer solution is determined by the concentration ratio of the weak acid and conjugate base.
When [A−] = [HA], the pH is equal to the pKa.
A buffer solution shows its strongest buffering action near the pKa.
The higher the total concentration of buffer components, the smaller the pH change when acid or base is added.
If the concentration ratio is maintained during dilution, the pH does not change greatly, but the buffer capacity decreases.
Possible causes of a difference between the measured pH and theoretical value include preparation errors and calibration errors of the pH meter.
Buffer solutions also have limits, and the pH changes greatly when an amount of acid or base exceeding the buffer capacity is added.

Points to Check When Discussing Buffer Solutions

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

Have you written the components of the buffer solution?
Have you explained the combination of weak acid and conjugate base?
Have you explained the reaction when acid is added?
Have you explained the reaction when base is added?
Have you compared the difference in pH changes with pure water?
Have you used the Henderson-Hasselbalch equation in the discussion?
Have you explained the relationship between pKa and the buffering range?
Have you considered the relationship between buffer concentration and buffer capacity?
Have you distinguished between changes in pH and changes in buffer capacity caused by dilution?
Have you discussed the difference between theoretical and measured pH?
Have you considered errors caused by the pH meter and temperature?
Do the points for improvement correspond to the sources of error?

Summary

A buffer solution is a solution that suppresses pH changes even when a small amount of acid or base is added.
The coexistence of a weak acid and its conjugate base, or a weak base and its conjugate acid, neutralizes added H+ or OH− and stabilizes the pH.
When acid is added, the conjugate base accepts H+, and when base is added, the weak acid supplies H+.

According to the Henderson-Hasselbalch equation, the pH of a buffer solution is determined by the concentration ratio of the weak acid and conjugate base.
When the pH is near the pKa, both the weak acid and conjugate base are present in sufficient amounts, so the buffering action becomes strong.
In addition, the higher the total concentration of buffer components, the larger the buffer capacity becomes, whereas dilution decreases buffer capacity even if the pH does not change greatly.

In a report, rather than simply writing that “the pH did not change much,” discuss the functions of the weak acid and conjugate base, the reactions after acid and base addition, pKa, the Henderson-Hasselbalch equation, buffer capacity, and differences between theoretical and measured values in relation to one another.
A buffer solution does not completely prevent pH changes; explaining that it reduces changes within the range of its buffer capacity produces a more persuasive discussion.