Home >> Science & Nature >> Science

How to Calculate Molar Solubility With Ksp in .26m CuCl2

The water solubility of many poorly soluble salts can often be described in terms of their solubility product constant, or Ksp, a number that represents the equilibrium between solute and solid at a given temperature. Adding a second salt that supplies more of the same ions as the poorly soluble salt will decrease the solubility of the latter further still because the Ksp remains constant. This phenomenon is known as the common-ion effect. You can make use of the common ion effect and the Ksp to calculate the molar solubility of salts like silver chloride in a solution of 0.26 molar copper (II) chloride.

Instructions

- 1
  Determine the Ksp value for your chlorine- or copper-containing salt. If your salt is silver chloride, for example, the Ksp is 1.8 x 10^-10. See Resources for a link to a list of solubility product constants.
- 2
  Write out the chemical equation for the process that takes place when your salt dissolves. When ionic compounds dissolve, they dissociate or split up into their component ions. Silver chloride, for example, dissociates into silver and chloride ions, so the chemical equation for it would be as follows:
  
  AgCl ---> Ag+ + Cl-
- 3
  Write out the equation for the Ksp based on the chemical equation you formulated. Remember that the equation for Ksp is just the product of the concentrations of the two ions formed when the salt dissolves. Each concentration is raised to the power of the coefficient in the chemical equation. For silver chloride, this is very simple because the silver and chloride ions in the chemical equation just have a coefficient of 1. The Ksp equation for silver chloride would therefore be as follows:
  
  Ksp = [Ag+] [Cl-]
  
  where [ ] indicate the concentration of the species inside the brackets.
- 4
  Determine the solubility of each species in terms of the variable x, the number of moles of silver chloride that dissolve. To continue the example, if x is the number of moles of silver chloride that dissolve, the final concentration of silver ions at equilibrium will be x, while the concentration of chloride ions will be 0.52 + x, since the solution has a 0.26 molar concentration of CuCl2 and each mole of copper (II) chloride that dissolves releases 2 moles of chloride ions.
- 5
  Substitute the values from the previous step into your equation. To continue the example, the Ksp equation for silver chloride would be as follows:
  
  Ksp = 1.8 x 10^-10 = [x] [0.52 + x]
- 6
  Notice that in most cases, the 0.52 molar concentration of chloride ions contributed by the copper (II) chloride will be far greater than the contribution of the poorly soluble salt. Consequently, you can simplify this expression by assuming the concentration of chloride ions is 0.52 molar -- a convenient approximation.
- 7
  Plug in the numbers and calculate x. Your result for x will be the molar solubility of your compound. To continue the example, if Ksp = 1.8 x 10^-10 = [x] [0.52], divide both sides by 0.52 to obtain x = 3.46 x 10^-10 -- meaning you obtain a mere 3.46 x 10^-10 moles per liter of silver ions in solution.

Science