Library / Solution chemistry, equilibria and kinetics / SCH-26
Solution chemistry, equilibria and kinetics
Molar solubility of a binary salt in pure water
Solubility of the salt AₐBᵦ in pure water, which gives a cations and b anions per formula unit.
- Ref
- SCH-26
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- s [mol/L]
A salt AₐBᵦ(s) ⇌ aAᵇ⁺ + bBᵃ⁻ gives [A] = a s and [B] = b s in pure water, so Ksp = (a s)ᵃ(b s)ᵇ = aᵃbᵇ s^(a+b). The solubility is s = [Ksp/(aᵃbᵇ)]^(1/(a+b)). It neglects common ions, hydrolysis and complex formation, which raise the solubility, and activity effects, which also raise it. Use positive whole-number coefficients.
Solubility of the salt AₐBᵦ in pure water, which gives a cations and b anions per formula unit. No common ions, hydrolysis or complexation, and concentration-based Ksp.
Calculator
- Cation concentration, a s0.001 mol/L
- Anion concentration, b s0.002 mol/L
- Ion product check, [A]^a [B]^b4×10−9
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 Ksp = 4×10−9 the salt dissolves to 0.001 mol/L, giving 0.001 mol/L of cation and 0.002 mol/L of anion.
- Salts with different formulas cannot be ranked by Ksp alone: a 1:2 salt with a smaller Ksp can still be more soluble than a 1:1 salt.
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-20 to 0.01 | 1.357e-7 | 0.1357 | 0.1357 | +10% | +3.23 % |
| a Cations per formula unit | 1 to 4 | 0.001 | 0.01255 | 0.01155 | +1 | +298 % |
| b Anions per formula unit | 1 to 4 | 6.325e-5 | 0.006899 | 0.006835 | +1 | +249 % |
Sweep of Solubility product
| Solubility product | Molar solubility (mol/L) |
|---|---|
| 1e-20 | 1.357e-7 |
| 1.778e-18 | 7.632e-7 |
| 3.162e-16 | 4.292e-6 |
| 5.623e-14 | 2.413e-5 |
| 1e-11 | 1.357e-4 |
| 1.778e-9 | 7.632e-4 |
| 3.162e-7 | 0.004292 |
| 5.623e-5 | 0.02413 |
| 0.01 | 0.1357 |
Sweep one variable
Variables and how each one contributes
Molar solubility
What the equation gives you. Everything else feeds it.
Solubility product
The solubility product, on the concentration scale. Raises the solubility as the power 1/(a + b). Raising it by 10 % (to 4.4×10−9) moves the result by +3.23 %, from 0.001 to 0.001032 mol/L.
Cations per formula unit
The number of cations per formula unit. Changes the exponent and the aᵃ factor, so the solubility changes in a non-obvious way. Raising it by 10 % (to 1.1) moves the result by +20.8 %, from 0.001 to 0.001208 mol/L.
Anions per formula unit
The number of anions per formula unit. Changes the exponent and the bᵇ factor, so the solubility changes in a non-obvious way. Raising it by 10 % (to 2.2) moves the result by +38.1 %, from 0.001 to 0.001381 mol/L.
Worked example with the values above
- Coefficient factor: aᵃ bᵇ = 4.
- Ratio: Ksp/(aᵃ bᵇ) = 1×10−9; exponent 1/(a + b) = 1/3.
- s = 0.001 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