Unit 8 · Topic 8.7 Beta

pH and pKa

Comparing pH with pKa tells you which form of an acid is in the majority: protonated below pKa, deprotonated above it, equal at pKa, with a tenfold change in ratio for every pH unit.

Practice 4: Model AnalysisPractice 6: Argumentation

Question set for this topic

Part 1 · Hook

Why this matters

Red cabbage juice turns red in lemon juice and green in baking soda water. The pigment is a weak acid whose protonated and deprotonated forms have different colors, and which one wins depends only on how the pH compares with its pKa. That one comparison also picks the indicator for a titration.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. What is pKa if Ka = 1 × 10⁻⁶?

  1. 6
  2. −6
  3. 1 × 10⁶
  4. 8
Show the answer

pKa = −log Ka = −log(10⁻⁶) = 6.

  • Correct: 6:
  • −6:
  • 1 × 10⁶:
  • 8:

2. At the half-equivalence point of a weak acid titration, what is true?

  1. pH = pKa
  2. pH = 7
  3. All the acid has reacted
  4. pH = pKb
Show the answer

[HA] = [A⁻] there, so pH = pKa.

  • Correct: pH = pKa:
  • pH = 7:
  • All the acid has reacted:
  • pH = pKb:

3. What does an indicator mark in a titration?

  1. The end point, ideally at the equivalence point
  2. The start of the titration
  3. The half-equivalence point
  4. The volume of the buret
Show the answer

The indicator's color change is the end point, which should coincide with equivalence.

  • Correct: The end point, ideally at the equivalence point:
  • The start of the titration:
  • The half-equivalence point:
  • The volume of the buret:

Part 4 · See it

See it first

A pH axis for an acid with pKa 4.7: below pH 4.7 the protonated form HA predominates, above it the deprotonated form A⁻ predominates, and at pH 4.7 they are equal. The ratio [A⁻]:[HA] is 1:10 one unit below pKa and 10:1 one unit above. An indicator with pKa 9.3 changes color from about pH 8.3 to 10.3.
Below pKa the protonated form wins; above it, the deprotonated form. An indicator changes color over about pKa ± 1. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. Ka = [H₃O⁺][A⁻]/[HA] holds at any pH[A⁻]/[HA] = Ka/[H₃O⁺] = 10^(pH − pKa)
  2. When pH is below pKa, [H₃O⁺] is larger than Kathe ratio is below 1: the protonated form HA predominates
  3. When pH is above pKathe deprotonated form A⁻ predominates; at pH = pKa they are equal
  4. An indicator is a weak acid with two colored formsits color switches over about pKa ± 1, where neither form outnumbers the other more than tenfold
  5. The end point should land on the steep part of the curvechoose an indicator whose pKa is close to the equivalence-point pH

Part 6 · Key ideas

Key ideas

  • pH < pKa: protonated form (HA, or BH⁺) predominates. pH > pKa: deprotonated form (A⁻, or B). pH = pKa: equal.
  • Every pH unit away from pKa is a factor of 10 in [A⁻]/[HA]: ratio = 10^(pH − pKa).
  • An indicator HIn changes color over about pKa ± 1.
  • Pick the indicator whose pKa is near the equivalence-point pH: phenolphthalein for weak acid + strong base, a pKa near 5 for weak base + strong acid.

Part 7 · Misconception

A common mistake

The wrong idea: Any indicator that changes color somewhere during the titration will mark the equivalence point.

What actually happens: An indicator changes color at a pH near its own pKa. If that pH is reached in the buffer region, the color changes too early; its pKa has to match the equivalence-point pH.

Part 8 · Check yourself

Check yourself

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

Data table

Four acid-base indicators

Each indicator is a weak acid, HIn, whose protonated and deprotonated forms have different colors.

Indicator pKa and colors
IndicatorpKa of HInColor of HInColor of In⁻
Methyl orange3.5redyellow
Bromocresol green4.7yellowblue
Bromothymol blue7.1yellowblue
Phenolphthalein9.3colorlesspink

1. Acetic acid is titrated with NaOH; the equivalence point is at pH 8.72. Which indicator is the best choice?

  1. Phenolphthalein
  2. Bromothymol blue
  3. Bromocresol green
  4. Methyl orange
Show the answer

An indicator changes color over about pKa ± 1. Phenolphthalein (pKa 9.3) changes between about 8.3 and 10.3, which brackets the equivalence pH of 8.72 on the steep part of the curve.

  • Correct: Phenolphthalein: Right: its color change falls on the steep rise around pH 8.7.
  • Bromothymol blue: Its range (about 6.1 to 8.1) sits just below the equivalence pH; it would change a little early, though on a steep curve the error is small. Phenolphthalein matches better.
  • Bromocresol green: Its range (about 3.7 to 5.7) is in the buffer region; it would change color long before equivalence.
  • Methyl orange: It changes near pH 3.5, at the very start of the titration.

2. Ammonia is titrated with HCl; the equivalence point is at pH 5.28. Which indicator is the best choice?

  1. Bromocresol green
  2. Phenolphthalein
  3. Bromothymol blue
  4. Methyl orange
Show the answer

Bromocresol green (pKa 4.7) changes between about 3.7 and 5.7, which brackets the acidic equivalence pH of 5.28.

  • Correct: Bromocresol green: Right: pKa close to the equivalence pH.
  • Phenolphthalein: Phenolphthalein changes near pH 9, in the buffer region of this titration, long before equivalence.
  • Bromothymol blue: It changes near pH 7, before equivalence in this titration of a weak base.
  • Methyl orange: Its pKa (3.5) is below the equivalence pH, so it changes near the bottom of the steep drop, slightly after equivalence. Bromocresol green's pKa is closer to 5.28.

3. What color is bromothymol blue in a solution at pH 9.5?

  1. Blue
  2. Yellow
  3. Green
  4. Colorless
Show the answer

pH 9.5 is well above its pKa of 7.1, so the deprotonated form, In⁻ (blue), predominates.

  • Correct: Blue: Right: pH > pKa, the deprotonated form.
  • Yellow: Yellow is the HIn form, which predominates below pH 7.1.
  • Green: Green, a mix of both forms, appears only near pH 7.1.
  • Colorless: Neither form of bromothymol blue is colorless.

Particle view

One acid in three buffers

Box 1HAHAHAHAHAHAHAHAHAA⁻Box 2HAHAHAHAHAA⁻A⁻A⁻A⁻A⁻Box 3HAA⁻A⁻A⁻A⁻A⁻A⁻A⁻A⁻A⁻

Key: HA the protonated form of a weak acid with pKa 6.0; A⁻ the deprotonated form. The three boxes are at pH 5.0, 6.0 and 7.0, in some order. Water and buffer ions are not drawn.

4. Which box is at pH 7.0?

  1. Box 3
  2. Box 1
  3. Box 2
  4. The volume of each box is needed to tell
Show the answer

At pH 7.0, one unit above pKa, [A⁻]/[HA] = 10^(7.0 − 6.0) = 10, which matches 9 A⁻ to 1 HA (about 10 : 1).

  • Correct: Box 3: Right: pH > pKa, mostly deprotonated.
  • Box 1: Box 1 is mostly HA, which fits pH 5.0, below pKa.
  • Box 2: Box 2 has equal amounts, which fits pH = pKa = 6.0.
  • The volume of each box is needed to tell: The ratio [A⁻]/[HA] needs no volume: it is set by pH − pKa, and 9 : 1 fits pH 7.0.

5. Box 1 is brought to pH 3.0 by adding a strong acid. How does the ratio [A⁻]/[HA] change?

  1. It falls to about 1/1000
  2. It rises to about 1000
  3. It stays about 1/10
  4. It falls to about 1/3
Show the answer

[A⁻]/[HA] = 10^(pH − pKa) = 10^(3.0 − 6.0) = 10⁻³: nearly all the acid is protonated.

  • Correct: It falls to about 1/1000: Right: three units below pKa.
  • It rises to about 1000: Lower pH means more H₃O⁺, which protonates A⁻; the ratio falls.
  • It stays about 1/10: The ratio depends on pH; it changes as the pH changes.
  • It falls to about 1/3: The ratio changes by a factor of ten per pH unit, not in proportion to the pH value.

6. Put these steps for choosing an indicator in order.

  1. Decide what is in the flask at the equivalence point
  2. Estimate the equivalence-point pH (7, above 7 or below 7)
  3. Find an indicator whose pKa is close to that pH
  4. Check that its range (pKa ± 1) falls on the steep part of the curve
Show the answer

The species at equivalence set its pH; the indicator's pKa must match that pH so the color change coincides with the steep rise.

  • Correct order: 1. Decide what is in the flask at the equivalence point 2. Estimate the equivalence-point pH (7, above 7 or below 7) 3. Find an indicator whose pKa is close to that pH 4. Check that its range (pKa ± 1) falls on the steep part of the curve

7. Methylammonium, CH₃NH₃⁺, has pKa 10.64. What fraction of methylamine is in the protonated form at pH 9.64? Give your answer as a decimal.

Type a number.

Show the answer

[B]/[BH⁺] = 10^(pH − pKa) = 10^(9.64 − 10.64) = 0.10, so 10 BH⁺ for each B. Protonated fraction = 10/(10 + 1) = 0.91.

  • Answer: 0.91

Part 9 · Summary

Summary

Comparing pH with pKa tells you which form of an acid is in the majority: protonated below pKa, deprotonated above it, equal at pKa, with a tenfold change in ratio for every pH unit. An indicator is a weak acid whose two forms have different colors, so it changes over about pKa ± 1; choose one whose pKa matches the equivalence-point pH.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections