Library / Solution chemistry, equilibria and kinetics / SCH-14
Solution chemistry, equilibria and kinetics
pH of an amphiprotic intermediate salt
Approximate pH of a solution of the intermediate salt HA⁻ of a diprotic acid H₂A, such as hydrogencarbonate.
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- SCH-14
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- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- pH [pH]
The intermediate ion HA⁻ of a diprotic acid can both give and take a proton. When the acid steps are well separated, and the salt concentration is high, the pH is nearly the average of the two pKa values, pH ≈ ½(pKa1 + pKa2), independent of the concentration. It fails for very dilute solutions, where water matters, and for closely spaced pKa values, where the approximation breaks down.
Approximate pH of a solution of the intermediate salt HA⁻ of a diprotic acid H₂A, such as hydrogencarbonate. It is the average of the two pKa values and does not depend on the concentration.
Calculator
- Hydronium concentration, 10^(−pH)1×10−6 mol/L
- Gap between the pKa values4
- pH if the second pKa rises by one unit6.5 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.
- With pKa values of 4 and 8 the intermediate salt has a pH near 6, whatever its concentration within the valid range.
- This is how hydrogencarbonate (pKa 6.35 and 10.33) comes out near pH 8.3, the value used for the phenolphthalein endpoint.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (pH) | Local step | Change in result |
|---|---|---|---|---|---|---|
| pKa2 Second pKa | 2 to 14 | 3 | 9 | 6 | +10% | +6.67 % |
| pKa1 First pKa | 0 to 10 | 4 | 9 | 5 | +10% | +3.33 % |
Sweep of Second pKa
| Second pKa | pH of the salt (pH) |
|---|---|
| 2 | 3 |
| 3.5 | 3.75 |
| 5 | 4.5 |
| 6.5 | 5.25 |
| 8 | 6 |
| 9.5 | 6.75 |
| 11 | 7.5 |
| 12.5 | 8.25 |
| 14 | 9 |
Sweep one variable
Variables and how each one contributes
pH of the salt
What the equation gives you. Everything else feeds it.
First pKa
The pKa of the first dissociation of H₂A. Raises the pH by half of its change. Raising it by 10 % (to 4.4) moves the result by +3.33 %, from 6 to 6.2 pH.
Second pKa
The pKa of the second dissociation (of HA⁻). Raises the pH by half of its change. Raising it by 10 % (to 8.8) moves the result by +6.67 %, from 6 to 6.4 pH.
Worked example with the values above
- Add the pKa values: 4 + 8 = 12.
- Halve.
- pH ≈ 6.
Assumptions and limits
- Dilute solutions in which concentrations stand for activities, with constants on the concentration scale.
- No other acids, bases or dissolved gases such as CO₂ unless included.
Common mistakes
- Using pKa where Ka is needed, or the reverse.
- Using the Kw of 25 °C at other temperatures.
- Ignoring water autoionisation for acids below about 10⁻⁶ M.
Statistics and uncertainty
Acid constants change with ionic strength and temperature, so results are best to about 0.05 pH units even with accurate constants. Calibration of a pH electrode contributes about 0.02 pH.
Where it is used
- Calculating pH of dilute acids, salts and intermediate ions.
- Finding which species dominates at a given pH.
Maths you need
- pH: pH = −log₁₀ [H⁺]
- Acid dissociation constant: Ka = [H⁺][A⁻]/[HA]
- Water ion product: Kw = [H⁺][OH⁻]