Question

You are browsing through the Handbook of Hypothetical Chemistry when you come across a solid that is reported to have a \(K_{s p}\) value of zero in water at \(25^{\circ} \mathrm{C}\) . What does this mean?

Short answer

A solid with a \(K_{sp}\) value of zero in water at 25°C means that the solid is completely insoluble at this temperature, as the equilibrium constant for the dissolution process is equal to zero. This implies the solid does not dissolve in water, and its constituent ions are not present in the solution.

Step-by-step solution

Understand the dissolution process

When an ionic solid dissolves in water, it breaks into its constituent ions. For example, consider a generic solid, AB, dissolving in water: \[ AB(s) \rightleftharpoons A^{(+) } (aq) + B^{(-) } (aq) \] Here, AB is the solid and A^+ and B^- are its ions in aqueous solution. The process reaches an equilibrium in which both the solid and its ions exist together in solution.

Write the equilibrium constant expression

To determine the solubility product constant, we need to write the equilibrium constant expression for the dissolution process. Since \(K_{sp}\) represents the mathematical product of the dissociated ions' concentrations raised to the power of their respective stoichiometric coefficients, we have: \[ K_{sp}=[A^+][B^-] \] Keep in mind that the concentration of the solid is not included in the expression, as it is constant throughout the dissolution process.

Understand the meaning of a \(K_{sp}\) value of zero

A \(K_{sp}\) value of zero for solid AB means that the equilibrium constant for the dissolution process is equal to zero, which implies that the dissolution process does not occur to any appreciable extent. In other words, solid AB does not dissolve in water at 25°C, and its ions do not exist in the solution.

Conclude the result

A solid with a \(K_{sp}\) value of zero means that the solid is completely insoluble in water at 25°C, and the equilibrium condition for its dissolution is such that the solid does not dissociate into its constituent ions in solution.

Key concepts

Ksp value

The solubility product constant, abbreviated as \(K_{sp}\), is a crucial parameter in understanding the behavior of sparingly soluble ionic compounds in water. It provides insight into the extent to which a solid can dissolve in a solvent. Simply put, \(K_{sp}\) is the equilibrium constant for the dissolution of a solid into its ions in a saturated solution.
When you encounter a \(K_{sp}\) value, it refers to the mathematical expression that captures the product of the molar concentrations of the dissolved ions, each raised to the power of its stoichiometric coefficient from the balanced chemical equation. For instance, if a salt AB dissociates into ions A\(^+\) and B\(^-\), then \(K_{sp} = [A^+][B^-]\).
It's vital to grasp that a higher \(K_{sp}\) value often suggests a greater solubility, meaning that the solid can dissolve more significantly in the solution. Conversely, a \(K_{sp}\) value of zero holds particular significance, indicating that the solid does not dissolve at all under standard conditions.

dissolution process

The dissolution process is an essential chemical process by which a solid substance dissolves in a solvent, forming a homogeneous mixture or solution. It involves breaking and forming of bonds when a compound interacts with a solvent like water.
This process can be represented by a balanced chemical equation. For example, consider a generic ionic compound AB, which when added to water, dissociates into its ions as follows:

• AB(s) \( \rightleftharpoons \) A\(^{+} \)(aq) + B\(^{-} \)(aq)

Here, \(AB\) represents the solid form of the compound, and \(A^+\) and \(B^-\) are its ions in the aqueous state.
The dissolution process is dynamic and achieves a state of dynamic equilibrium when the rate of dissolution equals the rate of precipitation, meaning the amounts of the dissolved ions and the undissolved solid become constant. Understanding this balance is critical to mastering solubility concepts in chemistry.

equilibrium constant

An equilibrium constant is a numerical value that expresses the ratio of the concentrations of products to reactants for a reversible chemical reaction at equilibrium. In dissolution processes, the equilibrium constant is represented by the \(K_{sp}\), or solubility product constant.
This constant indicates the extent to which a solute dissolves in a solvent to form a saturated solution. What makes \(K_{sp}\) unique is that it only incorporates the concentrations of the ions in the solution, excluding the concentration of the undissolved solid.
This is because the concentration of the solid is considered constant. For instance, for the dissolution of AB:

• \(K_{sp} = [A^+][B^-]\)

The equilibrium constant simplifies the analysis of solubility, offering insights into how shifts in ion concentration can influence the dissolution process or the formation of precipitates. Understanding equilibrium constants like \(K_{sp}\) is fundamental to predicting solubility and the behavior of electrolytes in water.

insolubility

Insolubility refers to the inability of a substance to dissolve in a solvent. A material described as insoluble does not dissolve to a significant degree, even when introduced to a solvent under standard conditions.
The concept of insolubility is directly linked to extremely low or zero \(K_{sp}\) values. When a substance's \(K_{sp}\) is zero, as noted in the original exercise, it indicates that the equilibrium conditions do not favor any dissolution. No ions are released into the solution, and therefore, the solid remains intact.

Considerations for insolubility include:
• Chemical nature of the solute and solvent: Similar substances tend to dissolve each other.
• Temperature and pressure: Conditions that can sometimes enhance solubility.

Understanding insolubility is vital for predicting compound behavior in solutions, assessing reaction feasibility, and in processes like crystallization and precipitation.