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How can I find solubility product?

Published in Solubility Chemistry 4 mins read

Finding the solubility product (Ksp) typically involves either determining it experimentally from the solubility of a salt or calculating it from known equilibrium concentrations. Here's a breakdown of how to do both:

1. Determining Ksp Experimentally from Solubility:

  • Measure the Solubility: The first step is to experimentally determine the solubility of the sparingly soluble salt in pure water at a specific temperature. Solubility is usually expressed as grams of solute per liter of solution (g/L) or moles of solute per liter of solution (mol/L, also known as molar solubility, s).

  • Convert Solubility to Molar Solubility (if needed): If the solubility is given in g/L, convert it to mol/L by dividing by the salt's molar mass.

  • Write the Dissolution Equilibrium: Write the balanced equilibrium equation for the dissolution of the solid in water. For example, for silver chloride (AgCl):

    AgCl(s) ⇌ Ag+(aq) + Cl-(aq)

  • Relate Solubility to Ion Concentrations: Determine the relationship between the molar solubility (s) and the equilibrium concentrations of the ions. For AgCl, the concentration of Ag+ is equal to s, and the concentration of Cl- is also equal to s.

  • Calculate Ksp: Write the Ksp expression and substitute the ion concentrations in terms of s. For AgCl:

    Ksp = [Ag+][Cl-] = (s)(s) = s^2

    Solve for Ksp by substituting the numerical value of s.

Example:

Suppose the solubility of AgCl is found to be 1.3 x 10^-5 mol/L at 25°C. Then:

Ksp = (1.3 x 10^-5)^2 = 1.69 x 10^-10

2. Calculating Ksp from Equilibrium Concentrations:

  • Determine Equilibrium Concentrations: If you are given the equilibrium concentrations of the ions in a saturated solution, you can directly calculate Ksp.

  • Write the Dissolution Equilibrium: Same as above, write the balanced equilibrium equation.

  • Write the Ksp Expression: Same as above, write the Ksp expression based on the equilibrium.

  • Substitute and Solve: Substitute the given equilibrium concentrations into the Ksp expression and calculate the value of Ksp.

Example:

A saturated solution of lead(II) iodide (PbI2) has [Pb2+] = 1.3 x 10^-3 M and [I-] = 2.6 x 10^-3 M. Calculate the Ksp.

  • Dissolution equilibrium: PbI2(s) ⇌ Pb2+(aq) + 2I-(aq)
  • Ksp expression: Ksp = [Pb2+][I-]^2
  • Ksp = (1.3 x 10^-3)(2.6 x 10^-3)^2 = 8.788 x 10^-9

3. Using ICE Tables and the Common Ion Effect:

When a sparingly soluble salt is dissolved in a solution already containing one of its ions (the common ion), the solubility of the salt decreases. To calculate the solubility in the presence of a common ion and then calculate Ksp (if the solubility in the common ion solution is given), use an ICE (Initial, Change, Equilibrium) table:

Example: Estimate the solubility of barium sulfate (BaSO4) in a 0.020 M sodium sulfate (Na2SO4) solution. The solubility product constant for barium sulfate is 1.1 x 10^-10.

  • Dissolution equilibrium: BaSO4(s) ⇌ Ba2+(aq) + SO42-(aq)
  • Ksp = [Ba2+][SO42-] = 1.1 x 10^-10
Ba2+ SO42-
Initial 0 0.020
Change +s +s
Equilibrium s 0.020 + s

Ksp = (s)(0.020 + s) = 1.1 x 10^-10

Since Ksp is very small, assume s is negligible compared to 0.020.

(s)(0.020) ≈ 1.1 x 10^-10

s ≈ 5.5 x 10^-9 M

The solubility of BaSO4 in the 0.020 M Na2SO4 solution is approximately 5.5 x 10^-9 M. If the solubility in the common ion solution was given, you could then calculate the Ksp by solving for it using a similar ICE table setup.

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