Unit 8 · Topic 8.10 Beta

Buffer Capacity

Buffer capacity is how much strong acid or base a buffer can absorb before its pH changes sharply.

Practice 4: Model AnalysisPractice 6: Argumentation

Question set for this topic

Part 1 · Hook

Why this matters

A swimming pool and a test tube can hold buffers with the same pH, but drop a cup of acid into each and only the pool barely notices. Pool owners top up the buffer, not the pH, because a buffer can only absorb as much acid or base as it has particles to react with.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. A buffer has [A⁻]/[HA] = 1. What is its pH?

  1. pKa
  2. 7.00
  3. pKa + 1
  4. 0
Show the answer

pH = pKa + log 1 = pKa.

  • Correct: pKa:
  • 7.00:
  • pKa + 1:
  • 0:

2. Which species in a buffer reacts with added OH⁻?

  1. The weak acid HA
  2. The conjugate base A⁻
  3. Water
  4. The spectator ion
Show the answer

OH⁻ + HA → A⁻ + H₂O.

  • Correct: The weak acid HA:
  • The conjugate base A⁻:
  • Water:
  • The spectator ion:

Part 4 · See it

See it first

pH against moles of NaOH added to two 1.00 L buffers with pKa 4.74, both starting at pH 4.74. The dilute buffer (0.0200 mol each of HA and A⁻, dashed) fails after about 0.02 mol of base; the concentrated buffer (0.100 mol each, solid) holds until about 0.10 mol.
Two buffers at the same pH: the one with five times the material absorbs five times the base before it fails. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. Each mole of added OH⁻ uses up one mole of HA, and each mole of H₃O⁺ one mole of A⁻the moles of the components set how much acid or base the buffer can absorb
  2. A buffer with more moles of both componentshas a larger capacity, even at the same pH
  3. When the components are equal, the ratio is furthest from both endscapacity for acid and for base is balanced, at pH = pKa
  4. Once one component is used upthe next addition stays free and the pH jumps, as in the steep part of a titration curve

Part 6 · Key ideas

Key ideas

  • Buffer capacity grows with the moles of HA and A⁻. Same ratio, more material: same pH, bigger capacity.
  • Capacity for added base depends on HA; capacity for added acid depends on A⁻.
  • A buffer works best within pKa ± 1, where neither component is less than a tenth of the other.
  • Once a component is used up, find the pH from the excess strong acid or base, not from Henderson-Hasselbalch.

Part 7 · Misconception

A common mistake

The wrong idea: A buffer at the right pH can absorb any amount of added acid.

What actually happens: Each mole of added acid uses up a mole of conjugate base. Once A⁻ runs out, the next acid stays free and the pH falls sharply.

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

Data table

Four acetate buffers

Four 1.00 L buffers are made from acetic acid (pKa 4.74) and sodium acetate.

Moles of each component in 1.00 L
BufferCH₃COOH (mol)CH₃COO⁻ (mol)pH
P0.500.504.74
Q0.0500.0504.74
R0.900.103.79
S0.100.905.69

1. Which buffer has the largest capacity for both added strong acid and added strong base?

  1. P
  2. Q
  3. R
  4. S
Show the answer

Capacity for acid depends on the moles of CH₃COO⁻ and capacity for base on the moles of CH₃COOH. P has 0.50 mol of each, so it can take up to 0.50 mol of either.

  • Correct: P: Right: large and equal amounts of both components.
  • Q: Q has the same ratio but a tenth of the amounts, so a tenth of the capacity.
  • R: R can absorb up to 0.90 mol of base but only 0.10 mol of acid.
  • S: S can absorb up to 0.90 mol of acid but only 0.10 mol of base.

2. What is the pH of Buffer Q after 0.010 mol HCl is added?

Type a number.

Show the answer

Acetate 0.050 − 0.010 = 0.040 mol; acid 0.050 + 0.010 = 0.060 mol. pH = 4.74 + log(0.040/0.060) = 4.56, a drop of 0.18. The same acid would lower P by only 0.02.

  • Answer: 4.56

3. Buffer R is much better at handling one kind of addition than the other. Which, and why?

  1. Added base, because it has 0.90 mol CH₃COOH to react with OH⁻
  2. Added acid, because its pH is below pKa
  3. Added acid, because it has 0.90 mol CH₃COOH to react with H₃O⁺
  4. Both equally, because a buffer resists acid and base the same
Show the answer

OH⁻ is consumed by CH₃COOH, which R has plenty of. H₃O⁺ is consumed by CH₃COO⁻, which R has only 0.10 mol of, so 0.10 mol of acid would use it up.

  • Correct: Added base, because it has 0.90 mol CH₃COOH to react with OH⁻: Right: the large acid component handles base.
  • Added acid, because its pH is below pKa: A low pH says nothing about how much acetate is left to take up added acid.
  • Added acid, because it has 0.90 mol CH₃COOH to react with H₃O⁺: H₃O⁺ reacts with acetate, not with acetic acid.
  • Both equally, because a buffer resists acid and base the same: A buffer with unequal components resists one direction much better than the other.

4. What is the pH of Buffer R after 0.15 mol HCl is added? (The buffer is overwhelmed: find the excess first.)

Type a number.

Show the answer

0.10 mol CH₃COO⁻ reacts with 0.10 mol H₃O⁺; 0.05 mol H₃O⁺ is left over in 1.00 L. The H₃O⁺ from 1.00 M acetic acid is negligible beside 0.050 M of strong acid. pH = −log(0.050) = 1.30.

  • Answer: 1.30

Graph

Adding base to two buffers

Solid NaOH is added in portions to two 1.00 L buffers, each made from the same weak acid HA and NaA, and the pH is measured after each addition.

246810121400.020.040.060.080.10.12NaOH added (mol)pH

Buffer 1Buffer 2

Data table
NaOH added (mol)Buffer 1Buffer 2
04.744.74
0.014.835.22
0.024.928.67
0.035.0112
0.045.1112.3
0.065.3412.6
0.085.6912.78
0.096.0212.85
0.19.0212.9
0.111212.95
0.1212.313

5. Which statement does the graph support?

  1. Buffer 1 has the larger capacity: its pH stays nearly flat until about 0.10 mol NaOH
  2. Buffer 2 has the larger capacity, because its pH rises sooner
  3. The buffers have different pKa values, because they start at different pH
  4. The capacities are equal, because both start at pH 4.74
Show the answer

Buffer 1 holds its pH until roughly 0.10 mol of base; Buffer 2 fails after about 0.02 mol. The longer flat stretch means more HA available to react with OH⁻.

  • Correct: Buffer 1 has the larger capacity: its pH stays nearly flat until about 0.10 mol NaOH: Right: capacity is how much it can absorb before the pH shoots up.
  • Buffer 2 has the larger capacity, because its pH rises sooner: A buffer that fails sooner has the smaller capacity.
  • The buffers have different pKa values, because they start at different pH: Both start at pH 4.74, the same pKa and the same 1 : 1 ratio.
  • The capacities are equal, because both start at pH 4.74: Equal starting pH means equal ratios, not equal amounts.

6. The pH of each buffer rises sharply once its HA is used up. How many moles of HA did Buffer 2 contain at the start? (Read where its steep rise is centered.)

Type a number in mol.

Show the answer

OH⁻ + HA → A⁻ + H₂O. The steep rise is centered where the base added equals the HA present: about 0.020 mol for Buffer 2.

  • Answer: 0.020 mol

7. How do the compositions of the two buffers most likely differ?

  1. Buffer 1 has about five times the moles of both HA and A⁻
  2. Buffer 1 has five times as much HA but the same A⁻
  3. Buffer 1 has a larger ratio [A⁻]/[HA]
  4. Buffer 1 uses a stronger weak acid
Show the answer

Same starting pH means the same ratio (and the same acid). Buffer 1 resists five times as much base (0.10 vs 0.02 mol), so it has five times the amounts of both.

  • Correct: Buffer 1 has about five times the moles of both HA and A⁻: Right: same ratio, five times the amounts.
  • Buffer 1 has five times as much HA but the same A⁻: More HA with the same A⁻ would make Buffer 1 start at a lower pH.
  • Buffer 1 has a larger ratio [A⁻]/[HA]: A larger ratio would start at a higher pH.
  • Buffer 1 uses a stronger weak acid: A different acid would show a different pKa, so a different starting pH.

Part 9 · Summary

Summary

Buffer capacity is how much strong acid or base a buffer can absorb before its pH changes sharply. It depends on the moles of the components, not the pH: more of each, more capacity, with capacity for base set by HA and for acid by A⁻. Capacity is balanced at pH = pKa, and the buffer fails once one component is used up.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections