Equilibrium Involving Dissolution of Solid or Gases

1.0Introduction 

Chemical equilibrium is a fundamental concept in chemistry, representing a state where the forward and reverse reactions occur at equal rates, leading to constant concentrations of reactants and products. In the context of dissolution, equilibrium pertains to the balance between the dissolution and precipitation (for solids) or dissolution and exsolution (for gases) processes. Understanding these equilibria is crucial for predicting solubility, designing chemical processes, and solving problems in competitive exams.

2.0Equilibrium Involving Dissolution of Solids in Liquids

Saturated Solutions and Dynamic Equilibrium

When a solid dissolves in a liquid, it disperses into its constituent ions or molecules, forming a solution. As more solute dissolves, the solution approaches saturation—a state where no additional solute can dissolve at a given temperature and pressure. At this point, a dynamic equilibrium is established between the dissolved ions/molecules and the undissolved solid:

$\text{Solid}\rightleftharpoons \text{Dissolved ions/molecules}$

In this equilibrium state, the dissolution rate equals the crystallisation rate, maintaining a constant concentration of dissolved solute.

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) quantifies the equilibrium between a sparingly soluble ionic compound and its ions in solution. For a generic salt ( AB ) that dissociates as:

$AB(s)\rightleftharpoons A^{+}(aq)+B_{(aq)}^{-}$

The solubility product expression is:

$K_{sp}=[A^{+}][B^{-}]$

For salts that dissociate into more ions, the expression adjusts accordingly. For example, for ( $A_{2}B$ ):

$A2B(s)\rightleftharpoons 2A^{+}(aq)+B^{2-}(aq)$

$K_{sp}=[A^{+}{]}^2[B^{2-}]$

Factors Affecting Solubility of Solids

Several factors influence the solubility of solids in liquids:

• Temperature: Generally, solubility increases with temperature for most solids due to endothermic dissolution processes. However, some salts exhibit decreased solubility with rising temperature.
• Nature of Solute and Solvent: The principle "like dissolves like" applies; polar solutes dissolve better in polar solvents, and non-polar solutes dissolve better in non-polar solvents.
• Common Ion Effect: The presence of a common ion in solution decreases the solubility of a salt due to Le Chatelier's principle.
• pH of the Solution: For salts of weak acids or bases, solubility can be pH-dependent. For instance, the solubility of calcium carbonate increases in acidic solutions due to the formation of soluble calcium bicarbonate.

3.0Equilibrium Involving Dissolution of Gases in Liquids

Henry's Law and Gas Solubility

Henry's Law states that the amount of gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the liquid, at constant temperature:

$C=k_H\times P$

Where:

• ( C ) = concentration of the dissolved gas
• ( $k_H$ ) = Henry's law constant (depends on the gas and solvent)
• ( P ) = partial pressure of the gas

This relationship explains why carbonated beverages are bottled under high CO₂ pressure to increase gas solubility.

Factors Affecting Solubility of Gases

• Pressure: Increasing the pressure of the gas above the liquid increases its solubility, as per Henry's Law.
• Temperature: Unlike solids, the solubility of gases typically decreases with increasing temperature because gas dissolution is exothermic.
• Nature of Gas and Solvent: Polar gases dissolve better in polar solvents due to stronger intermolecular interactions.

4.0Mathematical Expressions and Calculations

Calculating Solubility Product (Ksp)

For a salt ( AB ) with solubility ( S ) mol/L: $K_{sp}=S^2$

For ( $A_{2}B$ ): $K_{sp}=4S^3$

These expressions allow calculation of solubility from Ksp values and vice versa.

Applying Henry's Law in Calculations

To calculate the solubility of a gas using Henry's Law: $C=k_H\times P$

For example, if the partial pressure of CO₂ above a soft drink is 2 atm and ( $k_H$ ) for CO₂ is $(1.67\times 10^{-2})mol/(L\cdot atm)$:$C=1.67\times 10^{-2}\times 2=3.34\times 10^{-2}\text{ mol/L}$

5.0Real-life Applications and Significance

• Predicting Precipitation: Ksp values help determine whether a salt will precipitate from solution, essential in qualitative analysis.
• Carbonated Beverages: Understanding gas solubility under pressure explains the fizz in soft drinks.
• Scuba Diving: Knowledge of gas solubility under varying pressures is crucial to prevent decompression sickness.
• Environmental Chemistry: Predicting oxygen solubility in water bodies is vital to the sustainability of aquatic life.