Question

State in words the meaning of the solubility product equation for \(\mathrm{PbI}_{2}\) : $$ K_{\mathrm{xp}}=\left[\mathrm{Pb}^{2+}\right]\left[\mathrm{I}^{-}\right]^{2} $$

Short answer

The solubility product equation for PbI₂, \( K_{\mathrm{xp}}=\left[\mathrm{Pb}^{2+}\right]\left[\mathrm{I}^{-}\right]^{2} \), represents the relationship between the concentrations of lead (II) cations (Pb²⁺) and iodide anions (I⁻) in a saturated solution of PbI₂. It signifies the equilibrium constant for the solubility of PbI₂ in water, with higher values indicating greater solubility.

Step-by-step solution

Dissociation of lead (II) iodide (PbI₂)

When lead (II) iodide is placed in water, it begins to dissociate into its individual ions. This dissolution can be represented by the following equilibrium chemical equation: $$ \mathrm{PbI_{2}\rightleftharpoons Pb^{2+} + 2I^{-}} $$

Understanding the solubility product (Kₓₚ)

The solubility product (Kₓₚ) is an equilibrium constant that represents the degree to which a solute will dissolve in a solvent (in this case, water). It is the product of the equilibrium concentrations of the ions, each raised to the power of their stoichiometric coefficients. For the PbI₂ system, the solubility product equation is: $$ K_{\mathrm{xp}}=\left[\mathrm{Pb}^{2+}\right]\left[\mathrm{I}^{-}\right]^{2} $$

Relation between Kₓₚ and ion concentrations

The equilibrium constant Kₓₚ provides information about the solubility of a solute in a solvent. For a given solute, a larger Kₓₚ value indicates a higher level of solubility. In the case of PbI₂, the concentration of Pb²⁺ ions and I⁻ ions in the solution can be represented by [Pb²⁺] and [I⁻] respectively. The Kₓₚ equation then allows us to relate these concentrations to the solubility of PbI₂: $$ K_{\mathrm{xp}}=\left[\mathrm{Pb}^{2+}\right]\left[\mathrm{I}^{-}\right]^{2} $$ To summarize, the solubility product equation for PbI₂ represents the relationship between the concentrations of the lead (II) cations (Pb²⁺) and iodide anions (I⁻) in a saturated solution of PbI₂. The equilibrium constant, Kₓₚ, indicates the solubility of PbI₂ in water, with higher values signifying greater solubility.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in a reversible reaction where the rate of the forward reaction equals the rate of the backward reaction, resulting in no overall change in the concentrations of reactants and products over time. It is essential to understand that this doesn't mean the reactants and products are at equal concentrations, but that their rates of formation are stable.

For the dissolution of lead (II) iodide, chemical equilibrium is achieved when the rate at which the solid PbI₂ turns into its ions is the same as the rate at which the ions combine to form the solid. The solubility product equation comes into play to quantify this particular equilibrium state.

Dissolution of Lead (II) Iodide

The dissolution of lead (II) iodide (PbI₂) in water is an interesting process that involves the solid salt dividing into its constituent ions. This occurs as PbI₂ interacts with water molecules, leading to the separation of lead (II) cations (Pb²⁺) and iodide anions (I⁻).

The dissolution can be described by a simple chemical equation: \[\mathrm{PbI_{2}\rightleftharpoons Pb^{2+} + 2I^{-}}\] Each molecule of PbI₂ separates into one Pb²⁺ ion and two I⁻ ions. This reaction reaches a state of equilibrium, where the rate of dissolution equals the rate of precipitation, meaning solid formation.

Equilibrium Constant Calculation

The equilibrium constant calculation for the dissolution of a salt like PbI₂ is represented by the solubility product constant (Kₓₚ). It describes the level at which the salt can dissolve in a solvent at a particular temperature.

To calculate the equilibrium constant, you look at the concentrations of the dissolved ions at equilibrium. For lead (II) iodide, the equation is: \[K_{\mathrm{xp}}=\left[\mathrm{Pb}^{2+}\right]\left[\mathrm{I}^{-}\right]^{2}\] The exponents correspond to the stoichiometric coefficients of the ions in the dissolution equation. Understanding this relationship helps predict the behavior of the salt in solution and calculate concentrations effectively.

Ion Concentration and Solubility

The ion concentration in a solution is paramount to determining the solubility of a substance. Ion concentration refers to the molarity, or the number of moles of an ion per liter of solution. Solubility is a measure of how much of a particular substance can be dissolved in a solvent, and it's directly influenced by the ion concentration in the solution at equilibrium.

For PbI₂, understanding the solubility product equation allows you to calculate the solubility of the salt. A high Kₓₚ value signifies that more lead (II) iodide can dissolve in the water, indicating a higher solubility. Conversely, a lower Kₓₚ implies lesser solubility. Thus, the equilibrium constant serves as a valuable tool in predicting the extent of a substance's solubility in various conditions.