Library / Solution chemistry, equilibria and kinetics / SCH-18
Solution chemistry, equilibria and kinetics
Strong acid dose to reach a lower buffer pH
Moles of strong acid that must react with the conjugate base A⁻ to bring a buffer down to a target pH.
- Ref
- SCH-18
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- x [mol]
To lower a buffer’s pH, strong acid converts some A⁻ into HA. If x moles of H⁺ are added, the new ratio must equal r = 10^(pHt − pKa), so (nA − x)/(nHA + x) = r, giving x = (nA − r nHA)/(1 + r). A negative x means the target is above the present pH (use base instead), and x must stay below nA, so that some base remains.
Moles of strong acid that must react with the conjugate base A⁻ to bring a buffer down to a target pH. Needs both buffer components present, and 0 ≤ x < nA.
Calculator
- Amount of base after the dose, nA − x0.02 mol
- Amount of acid after the dose, nHA + x0.02 mol
- Starting pH, pKa + log₁₀(nA/nHA)5.477 pH
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 strong acid (10 mmol) takes the buffer to pH 5, leaving 0.02 mol of base and 0.02 mol of acid.
- Add it slowly while stirring, and check with a calibrated pH meter, since real buffers deviate from the ideal ratio at higher ionic strength.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (mol) | Local step | Change in result |
|---|---|---|---|---|---|---|
| nA Starting amount of conjugate base A⁻ | 0.03 to 1 mol | 0.01 | 0.495 | 0.485 | +10% | +15 % |
| pKa pKa of the weak acid | 5 to 8 | 0.01 | 0.02996 | 0.01996 | +10% | +104 % |
| pHt Target pH | 3 to 5 | 0.01 | 0.0296 | 0.0196 | +10% | — |
| nHA Starting amount of weak acid HA | 0.001 to 0.03 mol | 0 | 0.0145 | 0.0145 | +10% | −5 % |
Sweep of Target pH
| Target pH | Acid dose (mol) |
|---|---|
| 3 | 0.0296 |
| 3.25 | 0.0293 |
| 3.5 | 0.02877 |
| 3.75 | 0.02787 |
| 4 | 0.02636 |
| 4.25 | 0.02396 |
| 4.5 | 0.02039 |
| 4.75 | 0.0156 |
| 5 | 0.01 |
Sweep one variable
Variables and how each one contributes
Acid dose
What the equation gives you. Everything else feeds it.
Starting amount of conjugate base A⁻
The starting amount of conjugate base, in mol. More base needs more acid to reach the same target, so x rises. Raising it by 10 % (to 0.033) moves the result by +15 %, from 0.01 to 0.0115 mol.
Starting amount of weak acid HA
The starting amount of weak acid, in mol. More acid already present means less acid is needed, so x falls. Raising it by 10 % (to 0.011) moves the result by −5 %, from 0.01 to 0.0095 mol.
Target pH
The target pH. A lower target needs more acid, so x falls as the target rises. Raising it by 10 % (to 5.5) gives no valid result at the other default values.
pKa of the weak acid
The pKa of the weak acid. A higher pKa lowers r for the same target, so more acid is needed. Raising it by 10 % (to 5.5) moves the result by +104 %, from 0.01 to 0.02039 mol.
Worked example with the values above
- Target ratio: r = 10^(5 − 5) = 1.
- Numerator: nA − r nHA = 0.03 − 1 × 0.01 = 0.02; denominator 1 + r = 2.
- x = 0.01 mol.
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