Problem 18 - Chemistry

Question

The solubility of \(\mathrm{PbCl}_{2}\) increases with an increase in temperature. Is the dissolution of \(\mathrm{PbCl}_{2}(s)\) in water exothermic or endothermic? Explain.

Step-by-Step Solution

Answer

The dissolution of \(\mathrm{PbCl}_{2}(s)\) in water is endothermic. This is because the solubility of lead(II) chloride increases with an increase in temperature, which indicates that the process is absorbing heat.

Step 1: Recall the relationship between solubility, temperature, and heat of reaction

In a dissolution process, the solubility of a substance in a solvent is affected by temperature changes. The effect of temperature on solubility depends on the heat of reaction involved in the dissolution process. - If the dissolution process is exothermic (releases heat), increasing the temperature will decrease the solubility. - If the dissolution process is endothermic (absorbs heat), increasing the temperature will increase the solubility. This relationship is based on Le Chatelier's principle, which states that a system at equilibrium will shift to minimize the effects of a change in the system's conditions.

Step 2: Analyze the given information

According to the problem, the solubility of lead(II) chloride (\(\mathrm{PbCl}_{2}\)) in water increases with an increase in temperature. This implies that the dissolution process for \(\mathrm{PbCl}_{2}\) must be absorbing heat.

Step 3: Determine if the dissolution is exothermic or endothermic

Since the dissolution process of \(\mathrm{PbCl}_{2}\) in water is absorbing heat (temperature increase leads to an increase in solubility), the process is endothermic. Hence, the dissolution of \(\mathrm{PbCl}_{2}(s)\) in water is endothermic.

Key Concepts

Solubility

Solubility refers to the ability of a substance to dissolve in a solvent. In simpler terms, it describes how much of a solute can dissolve in a liquid. The resulting mixture is called a solution. Solubility can vary for every substance. Some materials might dissolve easily in water, while others do not. Factors affecting solubility include the nature of the solute and solvent, temperature, and pressure.

• **Nature of solute and solvent:** Polarity plays a significant role in solubility. "Like dissolves like" often applies, meaning polar solutes dissolve in polar solvents (like water), and non-polar solutes in non-polar solvents.
• **Temperature:** Generally, for solids and liquids, solubility increases with temperature. However, this isn't always the case for gases.
• **Pressure:** Mainly affects the solubility of gases; with increased pressure, gases are more soluble.

Understanding solubility is crucial in chemistry since it helps predict how substances interact in a solution. This forms the basis of many chemical reactions and processes.

Le Chatelier's principle

Le Chatelier's principle is a core concept in chemistry helping to predict how a system at equilibrium will respond to changes in its environment. Specifically, it states that if a dynamic equilibrium is disturbed by changing the conditions, the system shifts in a direction that tends to reduce that change.
Consider a chemical equilibrium affected by changes such as:

• **Concentration:** Increasing the concentration of one reactant shifts the equilibrium to form more products.
• **Pressure:** A change in pressure affects equilibria where gases are involved. An increase in pressure shifts equilibrium toward the fewer number of gas molecules.
• **Temperature:** Influences both exothermic and endothermic reactions. For endothermic processes (absorbing heat), an increase in temperature shifts equilibrium to the right (more products). For exothermic reactions, it shifts equilibrium to the left (more reactants).

By applying Le Chatelier's principle, predictions can be made about the direction of reaction shifts in response to environmental changes, ensuring reactions are controlled in industrial and laboratory settings.

Temperature effect on solubility

Temperature can have a profound impact on solubility, especially in reactions and dissolutions involving gases and solids in liquids. For solids like lead(II) chloride (\(\mathrm{PbCl}_{2}\)), solubility usually increases with temperature. This is primarily because higher temperatures provide more kinetic energy to the solute molecules, allowing them to overcome intermolecular forces more easily. In cases where solubility increases with temperature, the process is often endothermic, meaning it absorbs heat from the surroundings.
For gases, an increase in temperature often results in decreased solubility. This is because the molecules gain kinetic energy and are more likely to escape from the solvent to the gas phase.

• **Solids in liquids:** Often more soluble at higher temperatures.
• **Gases in liquids:** Typically less soluble at higher temperatures.

These trends help chemists and physicists to predict how different substances will behave under varying thermal conditions, thereby facilitating the planning of reactions and industrial carbonation or dissolution processes.