Question

For a reaction, \(A_{x} B_{y} \rightleftharpoons x A^{y+}+y B^{x-}, K_{s p}\) can be represented as (a) \(\left[A^{y+}\right]^{x}\left[B^{x-}\right]^{y}\) (b) \([A]^{y}[B]^{x}\) (c) \([A]^{x}[B]^{y}\) (d) \([A]^{x+y}[B]^{x-y}\)

Short answer

The correct expression for the solubility product constant (Ksp) is option (a): \(\left[A^{y+}\right]^{x}\left[B^{x-}\right]^{y}\).

Step-by-step solution

Write the expression for the solubility product constant (Ksp)

The solubility product constant, Ksp, for a reaction of the type, \(A_{x} B_{y} \rightleftharpoons x A^{y+} + y B^{x-}\), is the product of the molar concentrations of the ions, each raised to the power of its stoichiometric coefficient in the balanced equation. So for this reaction, the expression is \(Ksp = [A^{y+}]^x[B^{x-}]^y\).

Identify the correct Ksp expression from the given options

Compare the derived expression \(Ksp = [A^{y+}]^x[B^{x-}]^y\) with each option to see which one matches. The correct representation is reflected directly in the derived expression from Step 1.

Select the correct option

The correct option that represents the Ksp expression for the given reaction is (a) \(\left[A^{y+}\right]^{x}\left[B^{x-}\right]^{y}\), as it precisely matches the derived expression.

Key concepts

Ksp Expression

The solubility product constant, abbreviated as Ksp, is a crucial concept in chemistry, particularly in the context of solutions and precipitates. It provides invaluable information about the solubility of compounds, particularly ionic compounds in a solution. The Ksp expression reveals the extent to which a compound will dissociate into its ions in a saturated solution at a specific temperature.

The general form for the Ksp expression of a sparingly soluble salt, represented as \(A_{x}B_{y}\), decomposes in water to yield \(x A^{y+}\) ions and \(y B^{x-}\) ions as per this equilibrium: \[A_{x}B_{y} \rightleftharpoons x A^{y+} + y B^{x-}\]. Using this reaction, the Ksp expression can be written as: \[K_{sp} = [A^{y+}]^{x}[B^{x-}]^{y}\].

Each ion concentration is raised to a power equal to its stoichiometric coefficient from the balanced chemical equation, reflecting the number of times each ion appears in the dissociation equation. This expression does not include the concentrations of solid substances because their concentration is a constant under a given set of conditions and is incorporated into the value of Ksp itself.

The precise understanding of the Ksp expression allows chemists to predict whether a precipitate will form in a particular solution. If the 'ionic product' or the actual ionic concentrations in the solution exceed Ksp, the solution is supersaturated and precipitation is likely to occur. Understanding and calculating Ksp is crucial in fields ranging from industrial chemistry to environmental science, and plays a role in pharmaceutical product formulation as well.

Chemical Equilibrium

Chemical equilibrium is a state in which a chemical reaction proceeds at the same rate in both the forward and reverse directions. This means that the concentrations of reactants and products reach a certain balance and remain constant over time, although they may not necessarily be equal. In the context of solubility, equilibrium is achieved when the rate at which the compound dissolves is equal to the rate at which it precipitates.

In the Ksp context, this equilibrium does not imply that the ions are static; rather, it signifies a dynamic equilibrium where ions continue to dissolve and precipitate at equal rates. Therefore, the concept of equilibrium emphasizes a point of balance in terms of reaction rates, not the cessation of movement or change in concentrations.

Ionic Product

The ionic product, often used interchangeably with the term 'ion product', refers to the product of the concentrations of the ions present in solution at any given moment, with each raised to the power of its coefficient in the balanced equation, expressed as \[\text{Ionic Product} = [A^{y+}]^{x}[B^{x-}]^{y}\].

This ionic product is a pivotal factor in determining the level of saturation of a solution. If the ionic product is less than Ksp, the solution is unsaturated, indicating that more solid can dissolve. When the ionic product equals Ksp, the solution is saturated, and any additional solid will not dissolve. A solution where the ionic product exceeds Ksp is supersaturated, and the excess dissolved ions will start to form a solid precipitate to restore equilibrium.

Monitoring the ionic product is essential in pharmaceuticals, water treatment, metallurgy, and many other applications where solubility control is essential. For instance, in kidney stone prevention, understanding the ion product of calcium and oxalate can aid in diet adjustments or medication to maintain a solution state where stones are less likely to form.