Chapter 15, Problem 1RQ

To what reaction does the solubility product constant, K_sp, refer? Table 15-1 lists K_sp values for several ionic solids. For any of these ionic compounds, you should be able to calculate the solubility. What is the solubility of a salt, and what procedures do you follow to calculate the solubility of a salt? How would you calculate the K_sp value for a salt given the solubility?

Interpretation Introduction

Interpretation:

The solubility product constant; solubility of a salt and the procedure to calculate the solubility of salt and the $K_{\text{sp}}$ of a salt whose solubility is given is to be stated.

Concept introduction:

The chemical laws of equilibrium for the dissolution of salt in a solvent. The dissolution of a salt depends on the type of salt whether it is completely soluble or partially soluble.

Answer to Problem 1RQ

The salts that do not dissolve completely in a solvent or they show the partial dissociation, for them solubility product that is $K_{\text{sp}}$ is used.

The solubility is defined as the amount of a particular salt that can dissolve in a given amount of a solvent at a particular temperature

The solubility product of a salt is equal to the product of concentration of each ion present in the salt and raised to the power equal to their stoichiometric coefficient.

Explanation of Solution

To determine:

The solubility product constant; solubility of a salt and the procedure to calculate the solubility of salt and the $K_{\text{sp}}$ of a salt whose solubility is given.

The salts that do not dissolve completely in a solvent or they show the partial dissociation, for them solubility product that is $K_{\text{sp}}$ is used.

The salts that do not dissolve completely in a solvent or they show the partial dissociation, for them solubility product that is $K_{\text{sp}}$ is used. The higher is the value of solubility product more is the solubility of the salt. The $K_{\text{sp}}$ value depends on temperature, therefore as the temperature changes, solubility product changes. Therefore, temperature must always be mentioned.

The solubility is defined as the amount of a particular salt that can dissolve in a given amount of a solvent at a particular temperature

The solubility is defined as the amount of a particular salt that can dissolve in a given amount of a solvent at a particular temperature. Therefore solubility of salt is also the amount of salt that can dissolve in the given amount of solvent. Solubility depends on the temperature conditions.

To determine the solubility of a salt its $K_{\text{sp}}$ value must be known. For example: Take a general salt ${\text{A}}_n{\text{B}}_{\text{m}}$, its solubility is calculated as,

${\text{A}}_n{\text{B}}_m\rightleftharpoons n{\text{A}}^{m+}+m{\text{B}}^{n-}$

Let the solubility of both the ions be $s\text{mol}/\text{L}$.

The concentration of A is $ns\text{M}$ and the concentration of B is $ms\text{M}$.

The value of solubility product $K_{\text{sp}}$ is given as,

$K_{\text{sp}}={\left[A\right]}^n{\left[B\right]}^m$

Substitute the value of concentration of each species in the above equation as,

$\begin{array}{c}{K}_{\text{sp}}={\left[A\right]}^n{\left[B\right]}^m\\ ={\left(ns\right)}^n{\left(ms\right)}^m\\ =n^n{s}^n{m}^m{s}^m\\ =n^n{m}^m{s}^{\left(n+m\right)}\end{array}$

Now if the value of $K_{\text{sp}}$ is known, then on rearrangement the value of solubility is calculated.

The solubility product of a salt is equal to the product of concentration of each ion present in the salt and raised to the power equal to their stoichiometric coefficient.

The solubility product of a salt is equal to the product of concentration of each ion present in the salt and raised to the power equal to their stoichiometric coefficient.

To determine the solubility of a salt its $K_{\text{sp}}$ value must be known. For example: Take a general salt ${\text{A}}_n{\text{B}}_{\text{m}}$, its solubility is calculated as,

${\text{A}}_n{\text{B}}_m\rightleftharpoons n{\text{A}}^{m+}+m{\text{B}}^{n-}$

Let the solubility of both the ions be $s\text{mol}/\text{L}$.

The concentration of A is $ns\text{M}$ and the concentration of B is $ms\text{M}$.

The value of solubility product $K_{\text{sp}}$ is given as,

$K_{\text{sp}}={\left[A\right]}^n{\left[B\right]}^m$

Substitute the value of concentration of each species in the above equation as,

$\begin{array}{c}{K}_{\text{sp}}={\left[A\right]}^n{\left[B\right]}^m\\ ={\left(ns\right)}^n{\left(ms\right)}^m\\ =n^n{s}^n{m}^m{s}^m\\ =n^n{m}^m{s}^{\left(n+m\right)}\end{array}$

This gives the solubility product of the salt.

Conclusion

The solubility of a sparingly soluble salt and its solubility product are related to each other and both are dependent on the temperature conditions.