Solubility product constants \(\left(\mathrm{K}_{\mathrm{sp}}\right)\) of salts of types \(\mathrm{MX}, \mathrm{MX}_{2}\) and \(\mathrm{M}_{3} \mathrm{X}\) at temperature 'T' are \(4.0 \times 10^{-8}, 3.2 \times 10^{-14}\) and \(2.7 \times 10^{-15}\), respectively. Solubilities \(\left(\mathrm{mol} \mathrm{dm}^{-3}\right)\) of the salts at temperature 'T' are in the order (A) \(\mathrm{MX}>\mathrm{MX}_{2}>\mathrm{M}_{3} \mathrm{X}\) (B) \(\mathrm{M}_{3} \mathrm{X}>\mathrm{MX}_{2}>\mathrm{MX}\) (C) \(\mathrm{MX}_{2}>\mathrm{M}_{3} \mathrm{X}>\mathrm{MX}\) (D) \(\mathrm{MX}>\mathrm{M}_{3} \mathrm{X}>\mathrm{MX}_{2}\)

In the context of solubility, chemical equilibrium refers to the dynamic balance between the solid phase of a sparingly soluble salt and its dissociated ions in solution. At equilibrium, the rate at which the solid dissolves to form its constituent ions is equal to the rate at which these ions recombine to form the solid. This state is crucial because it describes how much of a compound will dissolve in water under specific conditions, which is essential for predicting the behavior of ionic compounds in various chemical environments.

For a salt represented as MX, the equilibrium can be illustrated by the equation:
MX(s) ⇌ M⁺(aq) + X^–(aq)

When the system reaches equilibrium, the concentrations of the ions in solution remain constant, assuming no external changes such as temperature or pressure fluctuations. The solubility product constant, K_sp, captures this state, providing a quantitative measure of how much the salt can dissolve at a given temperature. The value of K_sp remains constant for a particular salt at a specific temperature.

Understanding chemical equilibrium is fundamental in predicting and calculating the solubility of salts, which can have a broad range of applications including in medicinal chemistry, environmental science, and materials engineering.

Dissociation reactions are processes in which ionic compounds separate into their individual ions when they dissolve in water. These reactions are pivotal in understanding the solubility of compounds. For example, the salt MX dissociates in water to form M⁺ and X^– ions. Each type of salt, such as MX, MX₂, or M₃X, has a characteristic dissociation reaction.

The extent of the dissociation is governed by the solubility product constant (K_sp). A higher K_sp usually indicates that the salt is more soluble, leading to more significant dissociation into ions. For instance, a salt with the formula MX₂ dissociates according to the reaction: MX₂(s) ⇌ M²⁺(aq) + 2X^–(aq).

As students of chemistry, it is crucial to write accurate dissociation equations since these are the foundation for deriving the expressions for K_sp and understanding the solubility of different compounds. Moreover, appreciating the nuances of these reactions aids in predicting the outcomes of various chemical processes, such as precipitation reactions, and is essential for a deep understanding of aqueous chemistry.

K_sp calculations are essential for evaluating the solubility of sparingly soluble salts. K_sp, or the solubility product constant, represents the maximum product of the ion concentrations of a salt that can exist in solution at equilibrium. It is derived from the dissociation reactions of the salts.

To calculate the solubility product constant, the following steps are typically taken:

• Write down the balanced dissociation equation for the salt.
• Create the expression for K_sp by multiplying the concentrations of the resulting ions, each raised to the power of their stoichiometric coefficients.
• Solve for the solubility (s) using the K_sp value and the expression from the previous step.

For a simple salt like MX, the calculation of K_sp would be performed using the equation K_sp = [M⁺][X^–] = s². More complex salts such as MX₂ or M₃X have higher powers of s in their expressions due to the stoichiometry of their dissociation reactions, leading to different mathematical relations between K_sp and solubility. In the case of the exercise, these calculations help us determine the solubilities of salts, which then allows us to establish their order based on their solubility at a given temperature. This understanding is not only critical to solving chemistry problems but also applies to practical scenarios such as drug delivery, where the solubility of a drug can affect its bioavailability.