AP® Chemistry review sheet from Aim for Five (aimforfive.com/chem/units/8/8-7)
Unit 8 · Topic 8.7
8.7 pH and pKa
Comparing a solution's pH with an acid's pKa tells you which form of the acid dominates: below the pKa the protonated form (HA) is the main form, and above it the deprotonated form (A⁻) is. Acid–base indicators are weak acids whose two forms have different colors, so you choose one whose pKa is close to the pH at the equivalence point.
Key terms
- pKa
- protonated form
- deprotonated form
- acid-base indicator
- end point
Which form dominates?
For a weak acid HA in any solution, the ratio of its two forms depends only on the solution's pH and the acid's pKa. From the Henderson–Hasselbalch equation, log([A⁻]/[HA]) = pH − pKa.
| Comparison | Ratio [A⁻]/[HA] | Main form |
|---|---|---|
| pH < pKa | Less than 1 | Protonated, HA |
| pH = pKa | Exactly 1 | Equal amounts |
| pH > pKa | Greater than 1 | Deprotonated, A⁻ |
How lopsided it gets
Each pH unit away from the pKa changes the ratio by a factor of 10. At one unit below the pKa, [A⁻]/[HA] = 1/10, so about 91% of the acid is HA. At two units below, the ratio is 1/100. At one unit above, the ratio is 10, so A⁻ is about 91%.
This matters in biology. Blood has a pH of about 7.4. Acetic acid's pKa is 4.74, about 2.7 units lower, so in blood almost all of it exists as acetate ions.
For a weak base, apply the same reasoning to its conjugate acid: compare the pH with the pKa of HB⁺. Below that pKa, the protonated form HB⁺ dominates.
How indicators work
An acid–base indicator is a weak acid, HIn, whose protonated form and deprotonated form have different colors. At a pH below its pKa, the HIn color shows. At a pH above its pKa, the In⁻ color shows. The color changes over a range of roughly pKa ± 1, where both forms are present in noticeable amounts.
Common examples: phenolphthalein is colorless in its acid form and pink in its base form, and changes color at a fairly high pH (roughly 8 to 10). Methyl red changes at a much lower pH, from red to yellow, and bromothymol blue changes near neutral, from yellow to blue.
Choosing an indicator for a titration
The endpoint is when the indicator changes color; the equivalence point is when the moles have exactly reacted. For accurate results, the endpoint must land on the steep jump at the equivalence point. So choose an indicator whose pKa is close to the pH at the equivalence point.
Strong acid with strong base: equivalence at pH 7, and the jump is so steep that several indicators work. Weak acid with strong base: equivalence above 7, so pick one with a higher pKa. Weak base with strong acid: equivalence below 7, so pick one with a lower pKa.
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
Predominant form at a given pH
Acetic acid has pKa = 4.74. In a solution buffered at pH 7.40, which form is predominant, and what is the ratio [CH₃COO⁻]/[CH₃COOH]? What about at pH 3.74?
Show the solutionHide the solution
- Step 1: At pH 7.40: pH > pKa, so the deprotonated form, CH₃COO⁻, dominates.
- Step 2: Ratio = 10^(pH − pKa) = 10^(7.40 − 4.74) = 10^2.66 ≈ 460. There are about 460 acetate ions for every acetic acid molecule.
- Step 3: At pH 3.74: pH is one unit below pKa, so ratio = 10^(−1.00) = 0.10. CH₃COOH dominates, making up about 91% of the total.
Answer: pH 7.40: CH₃COO⁻ dominates, ratio ≈ 460; pH 3.74: CH₃COOH dominates, ratio = 0.10
- Example 2
Trap: picking the indicator
A weak acid is titrated with NaOH, and the pH at the equivalence point is 8.7. Which indicator is best: methyl red (pKa ≈ 5.0), bromothymol blue (pKa ≈ 7.1) or phenolphthalein (pKa ≈ 9.3)? Explain why the others would give poor results.
Show the solutionHide the solution
- Step 1: Choose the indicator whose pKa is closest to the equivalence pH of 8.7. That's phenolphthalein.
- Step 2: Methyl red would change color around pH 5, which happens well before the equivalence point, while lots of acid is still unreacted. The endpoint volume would be too small.
- Step 3: Bromothymol blue changes near pH 7. That's also before equivalence for this titration. The trap is choosing it because 'neutral is 7', but a weak acid's equivalence point is basic.
Answer: Phenolphthalein; the other two change color before the equivalence point, giving too small a titrant volume.
Common mistakes
- Flipping the rule: when pH is below pKa, the protonated (acid) form dominates, not the base form.
- Choosing an indicator by its pKa being 7 instead of matching the equivalence-point pH.
- Thinking the endpoint and equivalence point are the same thing. A poorly chosen indicator makes them different.
On the exam
- Expect questions asking which form of an acid predominates at a given pH, or which indicator suits a titration curve. Justify with pH versus pKa.
- Lab questions may ask how choosing the wrong indicator would change the calculated concentration of the analyte: an early endpoint gives too little titrant and too low a concentration.
Connected topics
Videos
Check yourself
4 questions on 8.7 pH and pKa. Pick an answer to see if you got it, and why.
Acetic acid has a pKa of 4.76. In blood, which has a pH of about 7.4, which of the following best describes the acetic acid present?
The indicator bromocresol green, HIn, has a pKa of about 4.7. Its HIn form is yellow and its In⁻ form is blue. What color is the indicator in a solution with a pH of 2.5?
A weak acid, HA, has a pKa of 6.0. A solution of the acid is adjusted to pH 8.0. What is the ratio [A⁻]/[HA] in the solution?
A drug molecule contains an amine group whose protonated form, BH⁺, has a pKa of 9.5. In the stomach, where the pH is about 2, which form of the drug is present in the greater amount?
0 of 4 answered