## What is K_{sp}?

, or the solubility product constant, is a unitless measure of how well a solid dissolves in an aqueous solution. To be precise, is an equilibrium constant, which tells how much a solid dissociates when the dissolution has reached equilibrium. Solubility is a specific case of acid or base dissociation, so solubility is calculated similarly to or .

The more soluble a salt is, the higher the value will be. This is because the salt will dissolve into more product ions, making the concentration of each product higher. According to the solubility constant expression, greater product = greater . A slightly soluble salt, as a result, will have a relatively low value.

## How to Calculate K_{sp}

As mentioned above, solubility is a specific case of acid or base dissociation, in which the original reactant is a solid. Given the generic formula for the equilibrium constant:

In the case of acid dissociation,

Thus,

However, only aqueous substances are included in equilibrium expressions. Solids, liquids, and gases are not included. In the case of solubility, where the reactant is a solid, the equilibrium product should only include the aqueous products.

Thus,

## How to Calculate Molar Solubility

Using the equation, you can calculate solubility given the balanced dissolution equation and the .

In the dissolution equation:

Each of the lowercase letters symbolizes the coefficients of the corresponding substance, A is the solid reactant, and B and C are aqueous products.

The solubility constant expression for this reaction would be

Since all products come from the same reactant, they will always be produced in proportion to each other. Thus, you can replace B and C with x and add the coefficients into the equation.

If the value of is given, the molar solubility of A can be found by solving for x.

For any questions, you will likely not need to memorize the or molar solubility values for any compounds – they should be given in the problem!

## Solubility Product Constant Practice Problems

**Problem 1**

You dissolve of salt with a molecular formula of one cation and two cations () into . This salt dissolves according to the following reaction:

You measure the concentration of to be once the solution reaches equilibrium. Calculate the solubility product constant.

**Problem 2**

Under standard conditions in water, the salt has the solubility product . You dissolve into aqueous solution. Assume has completely solubilized. Calculate the final equilibrium concentration of . (Hint: you will need to use the quadratic formula)

## Solubility Product Constant Practice Problem Solutions

1:

2: