Getting Started
A buffer solution is a chemical system designed to resist drastic changes in pH upon the addition of a strong acid or strong base. We can think of a buffer as a chemical "sponge" that soaks up added H⁺ or OH⁻ ions. This chapter explores the limits of that sponge: How much acid or base can a buffer absorb before it is overwhelmed and the pH changes dramatically? This quantitative limit is known as the buffer capacity.
What You Should Be Able to Do
After completing this section, you should be able to:
Differentiate between the pH of a buffer and its buffer capacity.
Explain how the absolute concentrations of the buffer components affect the buffer's capacity.
Predict whether a given buffer has a greater capacity to neutralize added acid or added base by analyzing the relative concentrations of its components.
Describe the chemical reactions responsible for a buffer's ability to neutralize acids and bases.
Key Concepts & Analysis
This section explores buffer capacity through the lens of Dynamics & Change, examining how a buffer system at equilibrium responds to the stress of an added acid or base.
Baseline Condition: The Buffer at Equilibrium
A buffer solution exists in a state of equilibrium, containing a significant amount of both a weak acid (HA) and its conjugate base (A⁻). The initial pH of the buffer is determined by the pKₐ of the weak acid and the ratio of the concentrations of the conjugate base to the weak acid, as described by the Henderson-Hasselbalch equation:
pH = pKₐ + log ([A⁻] / [HA])
For example, a solution with 1.0 M acetic acid (CH₃COOH, pKₐ = 4.74) and 1.0 M acetate (CH₃COO⁻) has a pH of 4.74. A solution with 0.1 M CH₃COOH and 0.1 M CH₃COO⁻ also has a pH of 4.74, because the ratio [A⁻]/[HA] is 1 in both cases. While their starting pH is identical, their ability to resist pH change is vastly different.
The Process or Stress: Adding Strong Acid or Base
The function of a buffer is to handle the stress of an influx of H₃O⁺ (from a strong acid) or OH⁻ (from a strong base). When this stress is applied, a neutralization reaction occurs.
Adding Strong Base (OH⁻): The weak acid component (HA) of the buffer neutralizes the added hydroxide ions.
HA(aq) + OH⁻(aq) → A⁻(aq) + H₂O(l)
This reaction consumes the buffer's acid component and produces more of its base component.
Adding Strong Acid (H₃O⁺): The conjugate base component (A⁻) of the buffer neutralizes the added hydronium ions.
A⁻(aq) + H₃O⁺(aq) → HA(aq) + H₂O(l)
This reaction consumes the buffer's base component and produces more of its acid component.
These are stoichiometric reactions; they go essentially to completion.
The Resulting Change: pH Shift and Capacity Limits
The neutralization reaction changes the absolute molar amounts of HA and A⁻, which in turn alters the [A⁻]/[HA] ratio and causes a small shift in pH. Buffer capacity is defined as the amount of acid or base a buffer can neutralize before the pH changes significantly.
The capacity is determined by the initial moles of the buffer components available for neutralization. A buffer with higher concentrations of HA and A⁻ has more "reservoirs" of these species to react with added stress. Once one of the components is nearly consumed, the buffer is said to be "broken" or exhausted, and the pH will change dramatically with any further addition of acid or base.
High Capacity: A buffer made with 1.0 M HA and 1.0 M A⁻ can neutralize a large amount of added acid or base before the [A⁻]/[HA] ratio is drastically altered.
Low Capacity: A buffer made with 0.1 M HA and 0.1 M A⁻ will be exhausted quickly, as it contains only one-tenth the moles of buffering agents.
Furthermore, the relative concentrations determine the capacity for either acid or base.
If [HA] > [A⁻], the buffer has a larger reservoir of the acid component and thus has a greater capacity to neutralize added base.
If [A⁻] > [HA], the buffer has a larger reservoir of the base component and thus has a greater capacity to neutralize added acid.
Key Models & Representations
The following matrix compares two buffer solutions with the same initial pH but different capacities. Both are 1.0 L solutions based on acetic acid (pKₐ = 4.74).
| Feature | Buffer A: Low Capacity | Buffer B: High Capacity | Analysis |
|---|---|---|---|
| Initial State | 0.10 mol CH₃COOH 0.10 mol CH₃COO⁻ | 1.0 mol CH₃COOH 1.0 mol CH₃COO⁻ | Both have an initial pH of 4.74 because the acid/base ratio is 1:1. |
| Stress Applied | Add 0.08 mol of strong base (OH⁻) | Add 0.08 mol of strong base (OH⁻) | The same amount of stress is applied to both systems. |
| Reaction | CH₃COOH + OH⁻ → CH₃COO⁻ + H₂O | CH₃COOH + OH⁻ → CH₃COO⁻ + H₂O | The weak acid component neutralizes the added base in both solutions. |
| Final State | 0.02 mol CH₃COOH 0.18 mol CH₃COO⁻ | 0.92 mol CH₃COOH 1.08 mol CH₃COO⁻ | Buffer A is nearly exhausted. Its ratio has changed dramatically (0.18/0.02 = 9). Buffer B's ratio has barely changed (1.08/0.92 = 1.17). |
| Resulting pH | pH = 4.74 + log(9) = 5.69 | pH = 4.74 + log(1.17) = 4.81 | The pH of Buffer A changed by nearly a full unit, a significant failure. The pH of Buffer B changed only slightly, demonstrating its high capacity. |
Key Terms, Quantities, & Concepts
Buffer: A solution containing a weak acid and its conjugate base (or a weak base and its conjugate acid) that resists changes in pH.
Buffer Capacity: The amount of acid or base that can be added to a buffer solution before a significant change in pH occurs. It is determined by the molar concentrations of the buffer components.
Conjugate Acid-Base Pair: Two species that differ by a single proton (H⁺). For example, acetic acid (CH₃COOH) is the conjugate acid of the acetate ion (CH₃COO⁻).
Henderson-Hasselbalch Equation: An equation (pH = pKₐ + log([A⁻]/[HA])) used to calculate the pH of a buffer solution. It shows that pH is dependent on the pKₐ and the ratio of the conjugate base to the weak acid.
Neutralization: A chemical reaction in which an acid and a base react quantitatively with each other. In a buffer, this involves a strong acid/base reacting with a weak base/acid component.
Stoichiometry: The quantitative relationship between reactants and products in a chemical reaction. It is used to calculate the change in moles of buffer components after neutralization.
Skill Snapshots
Causation
Cause: Increasing the concentrations of both the weak acid and conjugate base while keeping their ratio constant.
Effect: The buffer capacity increases, but the initial pH of the buffer does not change.
Cause: Adding a strong base (OH⁻) to a buffer.
Effect: The weak acid component (HA) is converted into its conjugate base (A⁻), causing the [A⁻]/[HA] ratio to increase.
Cause: The moles of added acid exceed the initial moles of the conjugate base component in the buffer.
Effect: The buffer capacity is exceeded, the buffer is "broken," and the pH plummets.
Comparison
Buffer Capacity vs. Buffer pH: Capacity depends on the absolute molar amounts of the buffer components, while pH depends on their ratio. Two buffers can have the same pH but vastly different capacities.
High [HA] Buffer vs. High [A⁻] Buffer: A buffer with more weak acid than conjugate base ([HA] > [A⁻]) has a greater capacity for added base. A buffer with more conjugate base than weak acid ([A⁻] > [HA]) has a greater capacity for added acid.
Concentrated Buffer vs. Dilute Buffer: A 1.0 M buffer can neutralize significantly more added acid/base than a 0.1 M buffer of the same volume and component ratio.
Continuity, Change, Over Time (CCOT)
Baseline: A buffer solution is prepared with equal moles of HA and A⁻, establishing an initial pH equal to the pKₐ.
Change 1: As small amounts of strong base are added over time, the concentration of HA decreases and A⁻ increases, causing a gradual, slow rise in pH.
Change 2: Once the amount of added base exceeds the initial amount of HA, the buffer is exhausted. The system is no longer a buffer, and the pH rises sharply as excess OH⁻ accumulates.
Continuity: Throughout the effective buffering range, the solution continuously contains significant amounts of both the weak acid and its conjugate base, which are responsible for its pH-stabilizing properties.
Common Misconceptions & Clarifications
Misconception: A buffer with a pH of 5.0 and a buffer with a pH of 9.0 have the same capacity if their component concentrations are the same.
- Clarification: This is incorrect. Buffer capacity is maximized when pH = pKₐ (i.e., when [HA] = [A⁻]). As the pH moves further from the pKₐ, the concentration of one component becomes very low, drastically reducing the capacity to neutralize either added acid or base. An effective buffer range is generally considered to be pKₐ ± 1.
Misconception: Buffer pH and buffer capacity are the same thing.
- Clarification: pH is a measure of the solution's acidity at a single point in time, determined by the ratio of [A⁻]/[HA]. Capacity is a measure of the buffer's ability to resist a change in pH, determined by the absolute concentrations of A⁻ and HA. A 0.01 M buffer and a 1.0 M buffer can have the exact same pH, but the 1.0 M buffer has 100 times the capacity.
Misconception: Diluting a buffer with water will change its pH.
- Clarification: Adding water will not change the pH of the buffer, because it decreases the concentrations of both HA and A⁻ equally, leaving their ratio unchanged. However, dilution does decrease the buffer capacity because there are now fewer moles of the buffering components in any given volume of the solution.
One-Paragraph Summary
Buffer capacity quantifies a buffer's ability to resist pH changes and is distinct from the buffer's pH itself. While pH is governed by the ratio of the conjugate base to the weak acid, capacity is determined by their absolute concentrations. Increasing the moles of the buffer components directly increases the buffer's capacity to neutralize added acid or base without altering the initial pH. A buffer with a higher concentration of weak acid has a greater capacity for added base, while one with a higher concentration of conjugate base has a greater capacity for added acid. When the moles of added strong acid or base exceed the moles of the corresponding buffer component, the buffer is exhausted, and the pH changes dramatically.