The equilibrium expression, K_sp, is a ratio of products over reactants and can be written as K_sp = [products]/[reactants]. This expression represents the equilibrium between an ionic solid and its ions in solution.

In a reaction where a chemical is dissolved into separate components in a solution (such as water), there is a natural tendency for the reaction to reach equilibrium, which is a state in which the products and reactants are in balance with each other. The tendency for a compound to reach equilibrium in solution is represented by the equilibrium expression, K_sp. The expression can be written out as the concentration of the products of the reaction over the concentration of reactants in the reaction:

K_sp = [products]/[reactants]

This expression uses the molarity (M), or concentration, of the products and reactants. Concentrations, in this case, are noted by the use of brackets. For example, let us say we have a compound, Ag₂CrO₄(s), and we completely dissolve it in water. This can be represented by the following equilibrium reaction:

Ag₂CrO₄(s) –> 2 Ag⁺(aq) + CrO₄-(aq)

We are given the concentration of Ag₂CrO₄(s), which is 7.8*10^-5 M. Some important notes to remember when solving for K_sp:

• Pure solids (s) and liquids (aq) are not included in equilibrium expressions. Aqueous (aq) and gas (g) species are included.
• When a species has a coefficient, the concentration of that species is both raised to the power of the coefficient value and multiplied by the coefficient value.
• If there are multiple products or reactants, multiply them by each other in the expression. See the example below.
• If it is explicitly stated that the species fully dissociates in solution, you can assume that is concentration is also the concentration of the individual species.

With these points in mind, we can write an expression for the K_spof Ag₂CrO₄(s):

K_sp = (2*[Ag⁺])² [CrO₄^–]

There is nothing in the denominator (bottom of the fraction) of the expression because the reactant of the reaction, Ag₂CrO₄(s), is solid. Plugging in the given molarity we are given the following equation to solve:

K_sp = (2*7.8*10^-5 M)²*(7.8*10^-5 M)

K_sp = 1.90*10^-12

The final value for K_sp is unitless. Because the value of K_sp is small, we can assume Ag₂CrO₄(s) has a low solubility value.

 

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Key Points

• The expression for the solubility constant in equilibrium is K_sp = [products]/[reactants].

• Pure solids (s) and liquids (aq) are not included in equilibrium expressions. Aqueous (aq) and gas (g) species are included.

• When a species has a coefficient, the concentration of that species is both raised to the power of the coefficient value and multiplied by the coefficient value.

• If there are multiple products or reactants, multiply them by each other in the expression.

• K_sp  is unitless.

• If it is explicitly stated that the species fully dissociates in solution, you can assume that is concentration is also the concentration of the individual species.

Key Terms

Equilibrium/equilibria: the state in which products and reactants are in balance in each other

Molarity: concentration of a substance, denoted with brackets and represented by moles/Liters or M

Concentration: a measure of the concentration of a chemical species in terms of the amount of substance per unit volume of solution

Product: end result of a reaction; the ride side of an equilibrium equation

Reactant: combined with other reactants to form the product; the left side of an equilibrium equation