Library / Solution chemistry, equilibria and kinetics / SCH-13
Solution chemistry, equilibria and kinetics
Hydroxide from a salt of a weak monoprotic acid
Hydroxide concentration of a solution of the sodium-type salt of a weak acid, where A⁻ + H₂O ⇌ HA + OH⁻.
- Ref
- SCH-13
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- [OH⁻] [mol/L]
A salt of a weak acid, such as sodium acetate, acts as a weak base: A⁻ + H₂O ⇌ HA + OH⁻, with Kb = Kw/Ka. With x = [OH⁻], Kb = x²/(C − x), and the positive root is x = 2C/[1 + √(1 + 4C/Kb)]. It avoids the approximation x ≪ C. It neglects hydroxide from pure water, so it fails when x approaches 10⁻⁷ M.
Hydroxide concentration of a solution of the sodium-type salt of a weak acid, where A⁻ + H₂O ⇌ HA + OH⁻. C is the formal concentration of A⁻ and Kb = Kw/Ka. Valid when the hydroxide from the salt greatly exceeds that of pure water.
Calculator
- pOH, −log₁₀[OH⁻]3.002
- Degree of hydrolysis, [OH⁻]/C0.00995
- Simple approximation, √(Kb C)0.001 mol/L
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.
- A 0.1 mol/L solution has [OH⁻] = 9.95×10−4 mol/L, pOH 3.002, with only 0.995 % of the base hydrolysed.
- The simple √(Kb C) = 0.001 mol/L is 0.501 % off here, so the exact form matters only for stronger or more dilute bases.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (mol/L) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Kb Base constant of A⁻ (Kw/Ka) | 1e-12 to 0.01 | 3.162e-7 | 0.02702 | 0.02702 | +10% | +4.86 % |
| C Formal concentration of the weak base A⁻ | 1e-4 to 2 mol/L | 2.702e-5 | 0.004467 | 0.00444 | +10% | +4.91 % |
Sweep of Formal concentration of the weak base A⁻
| Formal concentration of the weak base A⁻ (mol/L) | Hydroxide concentration (mol/L) |
|---|---|
| 1e-4 | 2.702e-5 |
| 3.448e-4 | 5.394e-5 |
| 0.001189 | 1.042e-4 |
| 0.004101 | 1.976e-4 |
| 0.01414 | 3.711e-4 |
| 0.04877 | 6.934e-4 |
| 0.1682 | 0.001292 |
| 0.58 | 0.002403 |
| 2 | 0.004467 |
Sweep one variable
Variables and how each one contributes
Hydroxide concentration
What the equation gives you. Everything else feeds it.
Formal concentration of the weak base A⁻
The formal concentration of the salt (as A⁻), in mol/L. Raises the hydroxide, roughly with its square root for a weak base. Raising it by 10 % (to 0.11) moves the result by +4.91 %, from 9.95×10−4 to 0.001044 mol/L.
Base constant of A⁻ (Kw/Ka)
The base constant of A⁻, equal to Kw/Ka. A larger Kb makes a stronger base, so the hydroxide rises roughly with its square root. Raising it by 10 % (to 1.1×10−5) moves the result by +4.86 %, from 9.95×10−4 to 0.001043 mol/L.
Worked example with the values above
- Group: 4C/Kb = 4 × 0.1 / 1×10−5 = 40,000; root of (1 + that) = 200.
- Denominator: 1 + 200 = 201.
- [OH⁻] = 2 × 0.1 / 201 = 9.9501×10−4 mol/L.
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⁻]