Library / Solution chemistry, equilibria and kinetics / SCH-17
Solution chemistry, equilibria and kinetics
Buffer pH after a strong-base addition
pH of a buffer after x moles of strong base are added, from the starting moles of acid nHA and conjugate base nA.
- Ref
- SCH-17
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- pH [pH]
Strong base added to a buffer first reacts completely with HA, converting it to A⁻: nHA falls by x and nA rises by x. The new pH comes from the Henderson–Hasselbalch equation with the new amounts, pH = pKa + log₁₀[(nA + x)/(nHA − x)]. It needs 0 ≤ x < nHA, so that some acid remains, and both components in a common final volume.
pH of a buffer after x moles of strong base are added, from the starting moles of acid nHA and conjugate base nA. The base first converts HA to A⁻, then the new ratio sets the pH. Needs 0 ≤ x < nHA.
Calculator
- Starting pH, before the addition4.523 pH
- pH change caused by the addition0.4771 pH
- Acid remaining, nHA − x0.02 mol
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Adding 0.01 mol of base moves the pH from 4.523 to 5, a change of 0.477 units.
- The same addition to unbuffered water of this size would raise the pH by several units, which shows what the buffer does.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (pH) | Local step | Change in result |
|---|---|---|---|---|---|---|
| pKa pKa of the weak acid | 0 to 14 | 9.643e-17 | 14 | 14 | +10% | +10 % |
| nHA Starting amount of weak acid HA | 0.02 to 1 mol | 3.305 | 5.301 | 1.996 | +10% | −1.21 % |
| nA Starting amount of conjugate base A⁻ | 5e-4 to 1 mol | 4.72 | 6.703 | 1.983 | +10% | +0.424 % |
| x Amount of OH⁻ added | 0 to 0.019 mol | 4.523 | 5.421 | 0.8981 | +10% | +0.869 % |
Sweep of Amount of OH⁻ added
| Amount of OH⁻ added (mol) | pH after addition (pH) |
|---|---|
| 0 | 4.523 |
| 0.002375 | 4.651 |
| 0.00475 | 4.767 |
| 0.007125 | 4.874 |
| 0.0095 | 4.978 |
| 0.01188 | 5.082 |
| 0.01425 | 5.187 |
| 0.01663 | 5.299 |
| 0.019 | 5.421 |
Sweep one variable
Variables and how each one contributes
pH after addition
What the equation gives you. Everything else feeds it.
pKa of the weak acid
The pKa of the weak acid. Raises the pH one for one. Raising it by 10 % (to 5.5) moves the result by +10 %, from 5 to 5.5 pH.
Starting amount of conjugate base A⁻
The starting amount of conjugate base, in mol. Raises the pH by increasing the base-to-acid ratio. Raising it by 10 % (to 0.011) moves the result by +0.424 %, from 5 to 5.021 pH.
Starting amount of weak acid HA
The starting amount of weak acid, in mol. More acid lowers the pH and gives more resistance to added base. Raising it by 10 % (to 0.033) moves the result by −1.21 %, from 5 to 4.939 pH.
Amount of OH⁻ added
The amount of strong base added, in mol. Raises the pH, slowly at first and steeply as the acid runs out. Raising it by 10 % (to 0.011) moves the result by +0.869 %, from 5 to 5.043 pH.
Worked example with the values above
- After reaction: nA + x = 0.01 + 0.01 = 0.02 mol; nHA − x = 0.03 − 0.01 = 0.02 mol.
- Log of the ratio: log₁₀(1) = 9.6433×10−17.
- pH = 5 + 9.6433×10−17 = 5.
Assumptions and limits
- A monoprotic weak acid and its conjugate base, both at appreciable concentration, in dilute solution.
- Constant volume, with concentration-based constants and negligible activity effects.
Common mistakes
- Adding the strong acid or base to the wrong component.
- Using a buffer more than about one pH unit from its pKa.
- Forgetting that the buffer ratio is of amounts in the same final volume.
Statistics and uncertainty
Buffer pH shifts with temperature, ionic strength and dilution, typically by 0.01 to 0.05 pH units, and the pKa itself carries an uncertainty of about 0.02 to 0.05.
Where it is used
- Preparing buffers and predicting their response to added acid or base.
- Choosing an indicator for a given pH range.
Maths you need
- Henderson–Hasselbalch equation: pH = pKa + log₁₀([A⁻]/[HA])
- Conjugate pair: a weak acid and its base
- Buffer capacity: the base needed per unit pH change