How to Calculate Molar Solubility From KSP?

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When a slightly soluble ionic compound is placed in water, there is an equilibrium between the solid state and the aqueous ions. This is found by the equilibrium constant for the reaction.

What Is Ksp?

Take a look at the reaction that occurs when silver (I) chloride dissolves in water:

When the solution is saturated, the dissolving of AgCl and formation of solid AgCl are occurring at the same time, or the reaction is at equilibrium:

The equilibrium constant can be written where the power on the components is the coefficient in the balanced equation:

Since there is no concentration for the solid AgCl, this can be removed from the equation. The resulting K value is called Ksp or the solubility product:

Ksp is a function of temperature. Say that the Ksp for AgCl is 1.7 x 10-10. With this information, you can find the molar solubility which is the number of moles that can be dissolved per liter solution until the solution becomes saturated. The units are given in moles per L, otherwise known as mol/L or M.

A saturated solution is a solution in which the maximum amount of solute has been dissolved at a given temperature.

An unsaturated solution is a solution in which all solute has completely dissolved in the solution.

Finding Molar Solubility From Ksp

Given that the Ksp for AgCl is 1.7 x 10-10, you can find the molar solubility, or the concentration of either ion in the solution:

Now what? There are two variables: [Ag+] and [Cl-], so how can you solve for the molar solubility? Since these ions come from the same solid, it is impossible that there is more of one than the other. This means that [Ag+] = [Cl-]. So:

or,

Taking the square root of both sides allows you to solve for the molar solubility:

Thus, the molar solubility of both Ag+ and Cl- is thus 1.3 x 10-5 M.

Finding Ksp From Molar Solubility

Given molar solubility for the ions in question and the balanced equation, you can find the Ksp.

Consider the following equation:

The solubility product is written as such:

Remember: The [F-] must be raised to the second power due to the coefficient in the balanced equation.

Now, given that the molar solubility is 2.2 x 10-3 M, you can plug this into the equation for both [F-] and [Ca2+]. Remember that the molar solubility must be the same for both since they come from the same compound.

So,

Factors Affecting Solubility

Solubility is affected by multiple factors.

  1. Solids becomes more soluble as temperature increases. 
  2. As pressure increases, gases become more soluble.
  3. The common-ion effect describes a decrease in solubility of an ionic compound when the solution already contains an ion that is the same as one from the compound.
  4. Solvent properties: A polar solvent will best dissolve a polar compound while a nonpolar solvent will best dissolve a nonpolar compound.

References

About the Author

Riti Gupta holds a Honors Bachelors degree in Biochemistry from the University of Oregon. She is currently working on her PhD in biology at Johns Hopkins University and has an interest in astrobiology and manned spaceflight. She has over 10 years of biology research experience in academia. She currently teaches classes in biochemistry, biology, biophysics, astrobiology, as well as high school AP Biology and Chemistry test prep.