Library / Solution chemistry, equilibria and kinetics / SCH-27
Solution chemistry, equilibria and kinetics
Onset of precipitation during selective addition
Free precipitant concentration at which the salt MₐXᵦ just starts to form, from the Ksp and the current free metal concentration.
- Ref
- SCH-27
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- [X]onset [mol/L]
For MₐXᵦ(s) the ion product Q = [M]ᵃ[X]ᵇ reaches Ksp when precipitation just starts, so the free precipitant concentration at onset is [X] = (Ksp/[M]ᵃ)^(1/b). A lower onset concentration means that salt precipitates first. In practice, nucleation can need some supersaturation, so use the actual diluted free concentrations at the moment considered.
Free precipitant concentration at which the salt MₐXᵦ just starts to form, from the Ksp and the current free metal concentration. Use diluted concentrations. In practice, nucleation may need some supersaturation.
Calculator
- pX at onset, −log₁₀[X]5
- Ratio Ksp/[M]^a (the required [X]^b)1×10−10 mol^b/L^b
- Metal that would precipitate at 0.01 mol/L of precipitant1×10−8 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.
- Precipitation of the salt begins when the free precipitant reaches 1×10−5 mol/L (pX 5) with 0.01 mol/L of metal present.
- For two metals competing for the same precipitant, the one with the lower onset concentration precipitates first, and the separation is clean only if the second onset is far higher.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (mol/L) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Ksp Solubility product | 1e-25 to 0.01 | 3.162e-12 | 1 | 1 | +10% | +4.88 % |
| a Metal ions per formula unit | 1 to 4 | 1e-5 | 0.01 | 0.00999 | +1 | +900 % |
| b Precipitant ions per formula unit | 1 to 4 | 1e-10 | 0.003162 | 0.003162 | +1 | +4,540 % |
| [M] Free metal concentration | 1e-6 to 1 mol/L | 1e-6 | 0.001 | 9.99e-4 | +10% | −4.65 % |
Sweep of Free metal concentration
| Free metal concentration (mol/L) | Precipitant at onset (mol/L) |
|---|---|
| 1e-6 | 0.001 |
| 5.623e-6 | 4.217e-4 |
| 3.162e-5 | 1.778e-4 |
| 1.778e-4 | 7.499e-5 |
| 0.001 | 3.162e-5 |
| 0.005623 | 1.334e-5 |
| 0.03162 | 5.623e-6 |
| 0.1778 | 2.371e-6 |
| 1 | 1e-6 |
Sweep one variable
Variables and how each one contributes
Precipitant at onset
What the equation gives you. Everything else feeds it.
Solubility product
The solubility product, on the concentration scale. Raises the onset concentration as the power 1/b. Raising it by 10 % (to 1.1×10−12) moves the result by +4.88 %, from 1×10−5 to 1.049×10−5 mol/L.
Free metal concentration
The free metal concentration, in mol/L. More metal means precipitation starts at a lower precipitant concentration. Raising it by 10 % (to 0.011) moves the result by −4.65 %, from 1×10−5 to 9.535×10−6 mol/L.
Metal ions per formula unit
The number of metal ions per formula unit. Steepens the dependence on the metal concentration. Raising it by 10 % (to 1.1) moves the result by +25.9 %, from 1×10−5 to 1.259×10−5 mol/L.
Precipitant ions per formula unit
The number of precipitant ions per formula unit. Flattens the dependence of the onset on Ksp and the metal concentration. Raising it by 10 % (to 2.2) moves the result by +185 %, from 1×10−5 to 2.848×10−5 mol/L.
Worked example with the values above
- Required [X]ᵇ: Ksp/[M]ᵃ = 1×10−12 / 0.01^1 = 1×10−10.
- Take the power 1/b = 1/2.
- [X]onset = 1×10−5 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