Question

In a \(K_{\mathrm{sp}}\) expression, the concentration of solid salt is not included. Why?

Short answer

The concentration of solid salt is not included in the \(K_{\mathrm{sp}}\) expression because it remains constant in a saturated solution and does not affect the equilibrium.

Step-by-step solution

Understanding Solubility Product Constant (\(K_{\text{sp}}\_{}))

The solubility product constant, or \(K_{\text{sp}}\), is an expression that describes the equilibrium between a solid and its constituent ions in a saturated solution. It includes only the concentrations of the dissolved ions and not the solid, because the concentration of the solid is constant as long as some undissolved solid is present.

Concept of Solid's Concentration in Equilibrium Expression

In a saturated solution at equilibrium, the undissolved solid has a constant concentration because it's in a fixed state, not dependent on the amount present. Since it is constant, it doesn't change the position of equilibrium and is therefore not included in the equilibrium expression.

Equilibrium Expression Without Solid

The equilibrium constant expression for a saturated solution (in this case, \(K_{\text{sp}}\)) reflects only the concentrations of the soluble ionic species. The concentration of the solid salt doesn't appear because it neither changes nor impacts the value of \(K_{\text{sp}}\).

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in a chemical system where the rates of the forward and reverse reactions are equal, resulting in no net change in the concentrations of the reactants and products over time. It's important to understand that reaching equilibrium doesn't mean the reactants and products are present in equal amounts, but rather that their ratios stay constant.

At the macroscopic level, the system appears static; however, at the microscopic level, reactions continue to occur. These ongoing processes are what maintain the equilibrium state. In the context of solubility, a solid ionic compound in contact with a solvent may dissolve until the maximum amount of dissolved ions is reached, at which point the solution becomes saturated. From this point on, the rate at which the solid dissolves to form ionized particles is equal to the rate at which these particles come together to form the solid—this is the point of equilibrium for the dissolution process.

Saturated Solution

A saturated solution represents a condition where the solution contains the maximum concentration of solute that can be dissolved at a given temperature and pressure. Any additional solute will remain undissolved, establishing a dynamic equilibrium with its dissolved ions.

When a solution reaches this saturated state, it’s important to realize that the undissolved solute is in constant contact with the solution, and its concentration is consistent due to its vast excess compared to the dissolved ions. As such, the amount of solid has no direct effect on the solubility equilibrium and, by extension, on the solubility product constant (Ksp). This is why, in the Ksp expression, the solid's concentration does not factor in—it remains stable and won't vary under constant conditions.

Equilibrium Constant Expression

The equilibrium constant expression is a mathematical way of representing a chemical equilibrium. It is derived from the concentration of the ionic products of a reaction, raised to the power of their respective stoichiometric coefficients in the balanced equation.

For the dissolution of salts, the equilibrium constant is known as the solubility product constant, or Ksp. This expression includes only the ions that are in the saturated solution and omits the solid phase for the reasons we've discussed. The Ksp is a fundamental principle in chemistry that tells us about the solubility of compounds. It helps us understand how likely a salt is to dissolve in a solution and, remarkably, even allows us to predict precipitate formation if solutions of two soluble salts are mixed.