Problem 20 - Chemistry The Molecular Science

Question

Write the equilibrium constant expression for each of these heterogeneous systems. (a) \(\mathrm{CaSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \rightleftharpoons \mathrm{CaSO}_{4} \cdot 3 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (b) \(\mathrm{SiF}_{4}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{SiO}_{2}(\mathrm{~s})+4 \mathrm{HF}(\mathrm{g})\) (c) \(\mathrm{LaCl}_{3}(\mathrm{~s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{LaClO}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{g})\)

Step-by-Step Solution

Answer

(a) \(K = [\mathrm{H}_{2} \mathrm{O}]^2\); (b) \(K = \frac{[\mathrm{HF}]^4}{[\mathrm{SiF}_4][\mathrm{H}_2\mathrm{O}]^2}\); (c) \(K = [\mathrm{HCl}]^2\).

Step 1: Identify Phases in the Reaction

For each reaction, determine which components are in the solid phase (s) and which are in the gaseous phase (g). In heterogeneous equilibria, only gases and aqueous solutions are included in the expression for the equilibrium constant.

Step 2: Equilibrium Expression for Reaction (a)

The reaction is: \(\mathrm{CaSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \rightleftharpoons \mathrm{CaSO}_{4} \cdot 3 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\). Solids are not included in the equilibrium expression. Thus, \(K = [\mathrm{H}_{2} \mathrm{O}]^2\).

Step 3: Equilibrium Expression for Reaction (b)

The reaction is: \(\mathrm{SiF}_{4}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{SiO}_{2}(\mathrm{~s})+4 \mathrm{HF}(\mathrm{g})\). Omit the solid \(\mathrm{SiO}_{2}\) in the expression. So, \(K = \frac{[\mathrm{HF}]^4}{[\mathrm{SiF}_4][\mathrm{H}_2\mathrm{O}]^2}\).

Step 4: Equilibrium Expression for Reaction (c)

The reaction is: \(\mathrm{LaCl}_{3}(\mathrm{~s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{LaClO}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{g})\). Ignore solids in the expression, so \(K = [\mathrm{HCl}]^2\).

Key Concepts

Heterogeneous Equilibria

In chemistry, heterogeneous equilibria involve reactions that include more than one phase of matter, such as solid, liquid, and gas. These types of systems are essential because they demonstrate how different states of matter interact.
Understanding heterogeneous equilibria is crucial for writing equilibrium constant expressions. Only substances in the gas and aqueous (dissolved in water) phases are included in these mathematical expressions. Solids and pure liquids are left out because their concentrations remain constant throughout the reaction.
Consider the first reaction from our exercise:

• CaSO \( _4 \cdot \) 5H\(_2\)O(s) \( \rightleftharpoons \) CaSO\(_4\cdot\) 3H\(_2\)O(s) + 2H\(_2\)O(g)

The equilibrium expression is written as \( K = [H_2O]^2 \). Here, water vapor (gas) is included, but the solids are ignored. This omission simplifies the math since solids have a fixed concentration based on density and molar mass.

Phases in Reactions

Phases in reactions refer to the different states (solid, liquid, gas, or aqueous) that reactants and products can occupy. In multi-phase systems, it's key to identify these phases to properly analyze and solve chemistry problems. Each phase behaves differently:

• **Solids** typically do not change significantly in concentration.
• **Liquids** are usually in pure form unless specified as a solution.
• **Gases** have concentrations affected by volume, pressure, and temperature.
• **Aqueous solutions** include dissolved substances and can vary in concentration.

For instance, in the given reaction of SiF\(_4\)(g) \( + \) 2 H\(_2\)O(g) \( \rightleftharpoons \) SiO\(_2\)(s) + 4 HF(g), the equilibrium constant expression includes gases only: \( K = \frac{[HF]^4}{[SiF_4][H_2O]^2} \). Recognizing each phase enables us to focus on changing components that influence equilibrium.

Chemistry Problem Solving

When solving chemistry problems involving equilibrium, start by identifying all reactants and products, noting their phases. This step helps define which components will be involved in writing the equilibrium constant expression.
The equilibrium constant \( K \) gives an insight into the state of the system. A large \( K \) suggests that products predominate, whereas a small \( K \) indicates prevalent reactants. To solve these problems effectively:

• Write a balanced chemical equation.
• Identify the phases to know which substances to include in the equilibrium expression.
• Omit solids and liquids from the expression, focusing on gases and aqueous solutions.
• Use concentrations to express component quantities.

For example, in LaCl\(_3\)(s) + H\(_2\)O(g) \( \rightleftharpoons \) LaClO(s) + 2 HCl(g), the expression becomes \( K = [HCl]^2 \). By actively solving such problems, you gain a deeper understanding of equilibrium dynamics and improve your chemistry proficiency.