Question

Write the equilibrium expression for each of the following reactions. a. \(2 \mathrm{O}_{3}(g) \rightleftharpoons 3 \mathrm{O}_{2}(g)\) b. \(\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\) c. \(C_{2} H_{4}(g)+C l_{2}(g) \rightleftharpoons C_{2} H_{4} C l_{2}(g)\).

Short answer

a. \(K = \frac{[O_2]^3}{[O_3]^2}\) b. \(K = \frac{[CO_2][H_2O]^2}{[CH_4][O_2]^2}\) c. \(K = \frac{[C_2H_4Cl_2]}{[C_2H_4][Cl_2]}\)

Step-by-step solution

Write the equilibrium expression

Start by identifying the reactants and products in the equation: Reactants: O3 Products: O2 The equilibrium expression (K) for this reaction will be: K = \(\frac{[O_2]^3}{[O_3]^2}\) #b. For reaction CH4(g) + 2 O2(g) ⇌ CO2(g) + 2 H2O(g)#

Write the equilibrium expression

Identify the reactants and products in the equation: Reactants: CH4, O2 Products: CO2, H2O The equilibrium expression (K) for this reaction will be: K = \(\frac{[CO_2][H_2O]^2}{[CH_4][O_2]^2}\) #c. For reaction C2H4(g) + Cl2(g) ⇌ C2H4Cl2(g)#

Write the equilibrium expression

Identify the reactants and products in the equation: Reactants: C2H4, Cl2 Products: C2H4Cl2 The equilibrium expression (K) for this reaction will be: K = \(\frac{[C_2H_4Cl_2]}{[C_2H_4][Cl_2]}\)

Key concepts

Equilibrium Expression

Chemical equilibrium is an important concept in chemistry, describing the balance between reactants and products in a reversible reaction. To understand this, let's explore the equilibrium expression.
The equilibrium expression is a mathematical representation describing the ratio of the concentrations of products to reactants at equilibrium. It uses the formula known as the equilibrium constant, denoted by \( K \).
In a chemical reaction, at equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. This means the concentrations of reactants and products remain constant over time, but not necessarily equal.

• The general form of an equilibrium expression is \( K = \frac{[\text{Products}]}{[\text{Reactants}]} \).
• Each concentration is raised to the power of its coefficient in the balanced chemical equation.

Using the solution for the reactions:
For example, for the reaction \(2\, \text{O}_3(g) \rightleftharpoons 3\, \text{O}_2(g)\), the expression becomes: \( K = \frac{[\text{O}_2]^3}{[\text{O}_3]^2} \). This ratio provides insight into how far the reaction proceeds before reaching equilibrium.

Reactants and Products

Understanding the role of reactants and products is crucial when writing an equilibrium expression. Reactants are the starting substances in a chemical reaction, while products are the substances formed as a result of the reaction.
In reversible reactions, as seen in the exercises, reactants and products can transform into each other until equilibrium is achieved. The characteristics of each are:

• Reactants: These are on the left side of the chemical equation. Their concentrations decrease as the reaction proceeds forward.
• Products: Found on the right side of the equation. Their concentrations increase as the forward reaction proceeds.

The balance between the concentration of reactants and products is captured in the equilibrium expression. For example, in the reaction \( \text{CH}_4(g) + 2\, \text{O}_2(g) \rightleftharpoons \text{CO}_2(g) + 2\, \text{H}_2\text{O}(g) \), the equilibrium expression involves the concentrations of \( \text{CH}_4 \), \( \text{O}_2 \), \( \text{CO}_2 \), and \( \text{H}_2\text{O} \), capturing the dynamic equilibrium between the consumption of reactants and formation of products.

Chemical Reactions

Chemical reactions are processes that transform substances into different substances by breaking and forming chemical bonds. They are often categorized into reactants converting into products.
Reversible reactions, like those given in the exercise, can proceed in both forward and reverse directions. Such reactions lead to a state of equilibrium, where the rates of the forward and reverse reactions are equal. Key characteristics include:

• Dynamic nature: At equilibrium, the reaction does not stop; instead, products continue to form from reactants and vice versa.
• Equilibrium state: Represented by a double-headed arrow (⇌) in the chemical equation.

For instance, in the reaction \( \text{C}_2\text{H}_4(g) + \text{Cl}_2(g) \rightleftharpoons \text{C}_2\text{H}_4\text{Cl}_2(g) \), reaching equilibrium involves a balance between the rate at which \( \text{C}_2\text{H}_4 \) and \( \text{Cl}_2 \) form \( \text{C}_2\text{H}_4\text{Cl}_2 \) and the reverse process. Understanding how to write equilibrium expressions helps in predicting and explaining this balance.