Library / Solution chemistry, equilibria and kinetics / SCH-29
Solution chemistry, equilibria and kinetics
Solubility of a metal hydroxide at imposed pH
Dissolved metal at saturation for M(OH)ₙ in a solution held at hydronium concentration h, from the hydroxide concentration Kw/h.
- Ref
- SCH-29
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- s [mol/L]
For a metal hydroxide M(OH)ₙ in contact with solution at a fixed pH, Ksp = [M][OH⁻]ⁿ with [OH⁻] = Kw/h. So the dissolved metal at saturation is s = Ksp/(Kw/h)ⁿ. Solubility falls tenfold per pH unit for n = 1 and a hundredfold for n = 2, which is why metals are precipitated by raising the pH. Amphoteric metals redissolve at high pH through hydroxo complexes, which this does not include.
Dissolved metal at saturation for M(OH)ₙ in a solution held at hydronium concentration h, from the hydroxide concentration Kw/h. The solid is assumed present and all the dissolved metal is free M, with no complexes or amphoteric behaviour.
Calculator
- Hydroxide concentration, Kw/h1×10−5 mol/L
- pH, −log₁₀ h9 pH
- Solubility one pH unit higher, s/10ⁿ4×10−7 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.
- At pH 9 the saturated solution holds 4×10−5 mol/L of dissolved metal; raising the pH by one unit would cut it to 4×10−7 mol/L.
- To remove the metal to a limit, find the pH at which s drops to that value, and add a safety margin for complexes and for approach to equilibrium.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (mol/L) | Local step | Change in result |
|---|---|---|---|---|---|---|
| h Hydronium concentration | 1e-14 to 0.001 mol/L | 4e-15 | 4e7 | 4e7 | +10% | +21 % |
| n Hydroxide ions per metal ion | 1 to 4 | 4e-10 | 400,000 | 400,000 | +1 | +10,000,000 % |
| Ksp Solubility product | 1e-30 to 1e-5 | 1e-20 | 100,000 | 100,000 | +10% | +10 % |
| Kw Water ion product | 1e-15 to 1e-12 | 4e-9 | 0.004 | 0.004 | +10% | −17.4 % |
Sweep of Hydronium concentration
| Hydronium concentration (mol/L) | Dissolved metal (mol/L) |
|---|---|
| 1e-14 | 4e-15 |
| 2.371e-13 | 2.249e-12 |
| 5.623e-12 | 1.265e-9 |
| 1.334e-10 | 7.113e-7 |
| 3.162e-9 | 4e-4 |
| 7.499e-8 | 0.2249 |
| 1.778e-6 | 126.5 |
| 4.217e-5 | 71,130 |
| 0.001 | 4e7 |
Sweep one variable
Variables and how each one contributes
Dissolved metal
What the equation gives you. Everything else feeds it.
Solubility product
The solubility product of the hydroxide. Raises the dissolved metal in direct proportion. Raising it by 10 % (to 4.4×10−15) moves the result by +10 %, from 4×10−5 to 4.4×10−5 mol/L.
Water ion product
The water ion product. A larger Kw means more hydroxide at the same pH, so less metal remains dissolved. Raising it by 10 % (to 1.1×10−14) moves the result by −17.4 %, from 4×10−5 to 3.306×10−5 mol/L.
Hydronium concentration
The hydronium concentration, in mol/L. A higher h (lower pH) means less hydroxide, so more metal dissolves. Raising it by 10 % (to 1.1×10−9) moves the result by +21 %, from 4×10−5 to 4.84×10−5 mol/L.
Hydroxide ions per metal ion
The number of hydroxide ions per metal ion. A larger n makes the solubility fall more steeply with pH. Raising it by 10 % (to 2.2) moves the result by +900 %, from 4×10−5 to 4×10−4 mol/L.
Worked example with the values above
- Hydroxide: Kw/h = 1×10−14 / 1×10−9 = 1×10−5 mol/L.
- Raise to the power n = 2: 1×10−10.
- s = 4×10−15 / 1×10−10 = 4×10−5 mol/L.
Assumptions and limits
- Pure-water dissolution, or the stated common ion, with no complexation, hydrolysis or ion pairing unless stated.
- Concentration-based Ksp, with the solid present at equilibrium.
Common mistakes
- Using the formula-unit coefficients in the wrong places in the Ksp expression.
- Applying the approximation when the added solubility is not small compared with the common-ion concentration.
- Ignoring complexation, which can raise the solubility by orders of magnitude.
Statistics and uncertainty
Solubility products vary widely between sources, often by a factor of two or more, and activity effects at ionic strengths of 0.1 M change solubility by 20 % to 50 %.
Where it is used
- Predicting precipitation and the separation of ions.
- Water treatment, hydroxide precipitation and gravimetric analysis.
Maths you need
- Solubility product: Ksp, the product of ion concentrations at saturation
- Common-ion effect: adding a shared ion lowers solubility
- Ion product: Q, compared with Ksp to predict precipitation