Consider the equilibrium that exists for a saturated aqueous solution of PbCl₂. Which expression gives the solubility product constant K_sp for PbCl₂ if the [Pb²⁺] = n mol/L?

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11ecba2d_123f_d366_a3bf_7fde73f34e8e_MD0008_00 For an ionic compound Z, which dissociates into ions X and Y when placed in water, an equilibrium will be established in which the rate of dissolution (forward reaction) equals the rate of precipitation (reverse reaction). 11ecba2d_123f_d367_a3bf_1bf65fb77cf3_MD0008_00 This equilibrium position is indicated by the solubility product constant K_sp, which provides a measure of the solubility of a compound at a given temperature. The general K_sp expression is written as: 11ecba2d_123f_d368_a3bf_1b637a67e0f1_MD0008_00 where [X] and [Y] are the molar concentrations of the X and Y ions, and b and c are the respective coefficients of the balanced dissolution reaction. The K_sp is the product of the maximum possible concentrations of each ion in the solution under the given conditions. As a result, the K_sp represents the limit of solubility for the compound (a saturated solution). Applying these concepts to the solubility equilibrium of PbCl₂, the K_sp for the compound is: 11ecba2d_123f_d369_a3bf_21e9672ddfb6_MD0008_00 The equilibrium shows that 2 moles of Cl⁻ are present for every 1 mole of Pb²⁺. As a result, if [Pb²⁺] = n mol/L, then [Cl⁻] = 2n mol/L. Substituting these values into the K_sp expression for PbCl₂ gives: 11ecba2d_123f_d36a_a3bf_db01124b4063_MD0008_00 (Choices A, B, and C) These expressions result from one or both of the following calculation errors: using [Cl⁻] = n mol/L, or failing to square the [Cl⁻] term. Educational objective: The solubility product constant K_sp represents the limit of solubility for a compound, and it is defined as the product of the molar concentrations of the dissolved species each raised to the power of their respective coefficients from the balanced dissolution reaction.

Consider the Equilibrium That Exists for a Saturated Aqueous Solution