Library / Solution chemistry, equilibria and kinetics / SCH-16
Solution chemistry, equilibria and kinetics
Amounts required for a target buffer
Moles of weak acid HA needed in a buffer of total amount nt to give a target pH, from the pKa.
- Ref
- SCH-16
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- nHA [mol]
The Henderson–Hasselbalch equation gives the base-to-acid ratio of a buffer, r = [A⁻]/[HA] = 10^(pH − pKa). With a total of nt moles, nHA = nt/(1 + r) and nA = nt r/(1 + r). This calculator returns the acid, and the base is in the derived rows. Choose a weak acid whose pKa lies within one unit of the target pH, so r stays between 0.1 and 10.
Moles of weak acid HA needed in a buffer of total amount nt to give a target pH, from the pKa. The conjugate base amount nA = nt − nHA is in the derived rows. Assumes dilute solution and both forms appreciable.
Calculator
- Amount of conjugate base, nt r/(1 + r)0.1 mol
- Base-to-acid ratio, 10^(pH − pKa)10
- Fraction of the buffer as acid, 1/(1 + r)0.09091
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.
- For pH 6 with a pKa of 5, use 0.01 mol of acid and 0.1 mol of base, a base-to-acid ratio of 10.
- Dissolve both in a common final volume; the concentration sets the capacity, the ratio sets the pH.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (mol) | Local step | Change in result |
|---|---|---|---|---|---|---|
| nt Total buffer amount | 1e-4 to 10 mol | 9.091e-6 | 0.9091 | 0.9091 | +10% | +10 % |
| pKa pKa of the weak acid | 0 to 14 | 1.1e-7 | 0.11 | 0.11 | +10% | +164 % |
| pH Target pH | 0 to 14 | 1.1e-10 | 0.11 | 0.11 | +10% | −73 % |
Sweep of Target pH
| Target pH | Amount of weak acid HA (mol) |
|---|---|
| 0 | 0.11 |
| 1.75 | 0.1099 |
| 3.5 | 0.1066 |
| 5.25 | 0.03959 |
| 7 | 0.001089 |
| 8.75 | 1.956e-5 |
| 10.5 | 3.478e-7 |
| 12.25 | 6.186e-9 |
| 14 | 1.1e-10 |
Sweep one variable
Variables and how each one contributes
Amount of weak acid HA
What the equation gives you. Everything else feeds it.
Total buffer amount
The total amount of buffer (acid plus base), in mol. Raises the amount of acid in direct proportion. Raising it by 10 % (to 0.121) moves the result by +10 %, from 0.01 to 0.011 mol.
Target pH
The target pH. A higher target pH needs more base and less acid, so the acid amount falls. Raising it by 10 % (to 6.6) moves the result by −73 %, from 0.01 to 0.002695 mol.
pKa of the weak acid
The pKa of the weak acid. A higher pKa means more acid is needed for the same target pH, so the acid amount rises. Raising it by 10 % (to 5.5) moves the result by +164 %, from 0.01 to 0.02643 mol.
Worked example with the values above
- Ratio: r = 10^(6 − 5) = 10.
- Acid fraction: 1/(1 + r) = 0.090909.
- nHA = 0.11 × 0.090909 = 0.01 mol; nA = 0.1 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