How to use the ksp solubility calculator
- Choose Molar solubility to find how much of a salt dissolves, or Precipitation test to check a mixture.
- Enter Ksp as a number such as 1.8e-10. Use the value for your temperature from your own table.
- Enter how many cations and anions are in one formula unit. For Ca(OH)2 that is 1 and 2.
- Enter any ion that is already in the solution, and optionally the molar mass, then read the solubility and the ion concentrations.
Formula
For a salt with x cations and y anions: Ksp = [cation]^x [anion]^y
Dissolving s mol/L gives [cation] = x s and [anion] = y s, so Ksp = x^x y^y s^(x+y) and s = (Ksp / (x^x y^y))^(1/(x+y))
With a common ion already present, solve (x s + cation)^x (y s + anion)^y = Ksp for s
Precipitation: the ion product Q = [cation]^x [anion]^y. If Q is above Ksp, solid forms.
With no common ion the solubility has a closed form. With a common ion the page solves the equation numerically, to full double precision.
Silver chloride and calcium hydroxide
For AgCl, Ksp is 1.8e-10 with 1 cation and 1 anion. The solubility is the square root of 1.8e-10, which is 1.3416e-5 mol/L, or about 0.0019 g/L with a molar mass of 143.32. With 0.1 M chloride already present, the solubility drops to 1.8e-9 mol/L, a fall of a factor of about 7,500.
For Ca(OH)2, Ksp is 5.0e-6 with 1 cation and 2 anions, so s = (5.0e-6 / 4)^(1/3) = 0.010772 mol/L. For the precipitation test, mixing solutions that give 0.01 M lead and 0.01 M iodide in PbI2 (Ksp 9.8e-9) makes Q = 0.01 x 0.01^2 = 1.0e-6, which is about 100 times Ksp, so a precipitate forms.
The common ion effect
A salt dissolves less in a solution that already holds one of its ions. The ion product still has to equal Ksp, so adding chloride to a saturated silver chloride solution pushes silver out as a solid. The page treats the concentration you enter as the amount of that ion already present before the salt dissolves.
For equilibria that involve acids, bases and several species, use the ICE table equilibrium calculator. To turn the molar solubility into grams per liter, you can also use the moles to grams calculator.
What this simple model leaves out
Real solubility also depends on activities (see the ionic strength calculator), on complex ions that hold metals in solution, and on the pH for hydroxides and for salts of weak acids. A salt such as a carbonate or a phosphate can dissolve far more in acid than the simple calculation says.
The precipitation test compares concentrations after mixing. Mixing two solutions dilutes both, so work out the concentrations in the combined volume before you enter them.
Assumptions and limits
- Ksp is for the temperature you care about and for the formula as written.
- Ions behave ideally, so activity coefficients are 1. Complex ions and pH effects are not included.
- The salt dissolves completely into the ions counted in the formula.
- Concentrations in the precipitation test are the values after mixing.
Frequently asked questions
How do I find solubility from Ksp?
For a 1:1 salt take the square root of Ksp. In general use s = (Ksp / (x^x y^y))^(1/(x+y)), where x and y are the numbers of ions in the formula.
What does the common ion effect do?
It lowers solubility. The ion already in solution counts toward the ion product, so less salt can dissolve before the product reaches Ksp.
How do I know if a precipitate will form?
Compare the ion product Q with Ksp. A Q above Ksp means the solution is supersaturated and solid forms.
Why is my measured solubility different?
Activities, ion pairs, complex ions and pH all change real solubility, and the simple Ksp calculation includes none of them.