Question

Write equilibrium constant expressions for these equilibria. $$ \begin{array}{l}{\text { a. } \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{g})} \\ {\text { b. } 2 \mathrm{H}_{2} \mathrm{S}(\mathrm{g}) \rightleftharpoons 2 \mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{S}_{2}(\mathrm{g})} \\\ {\text { c. } \mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CH}_{4}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})} \\ {\text { d. } 4 \mathrm{NH}_{3}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 4 \mathrm{NO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})} \\ {\text { e. } \mathrm{CH}_{4}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{S}(\mathrm{g}) \rightleftharpoons \mathrm{CS}_{2}(\mathrm{g})+4 \mathrm{H}_{2}(\mathrm{g})}\end{array} $$

Short answer

The equilibrium constant expressions for the given reactions are: a. \( K_a = \frac{[NO_2]^2}{[N_2O_4]} \) b. \( K_b = \frac{[H_2]^2[S_2]}{[H_2S]^2} \) c. \( K_c = \frac{[CH_4][H_2O]}{[CO][H_2]^3} \) d. \( K_d = \frac{[NO]^4[H_2O]^6}{[NH_3]^4[O_2]^5} \) e. \( K_e = \frac{[CS_2][H_2]^4}{[CH_4][H_2S]^2} \)

Step-by-step solution

Equilibrium expression for reaction a.

We are given the following reaction involving gases: \( N_2O_4(g) \rightleftharpoons 2NO_2(g) \) To write the equilibrium constant expression, we have: \( K_a = \frac{[NO_2]^2}{[N_2O_4]} \)

Equilibrium expression for reaction b.

We are given the following reaction involving gases: \( 2H_2S(g) \rightleftharpoons 2H_2(g) + S_2(g) \) To write the equilibrium constant expression, we have: \( K_b = \frac{[H_2]^2[S_2]}{[H_2S]^2} \)

Equilibrium expression for reaction c.

We are given the following reaction involving gases: \( CO(g) + 3H_2(g) \rightleftharpoons CH_4(g) + H_2O(g) \) To write the equilibrium constant expression, we have: \( K_c = \frac{[CH_4][H_2O]}{[CO][H_2]^3} \)

Equilibrium expression for reaction d.

We are given the following reaction involving gases: \( 4NH_3(g) + 5O_2(g) \rightleftharpoons 4NO(g) + 6H_2O(g) \) To write the equilibrium constant expression, we have: \( K_d = \frac{[NO]^4[H_2O]^6}{[NH_3]^4[O_2]^5} \)

Equilibrium expression for reaction e.

We are given the following reaction involving gases: \( CH_4(g) + 2H_2S(g) \rightleftharpoons CS_2(g) + 4H_2(g) \) To write the equilibrium constant expression, we have: \( K_e = \frac{[CS_2][H_2]^4}{[CH_4][H_2S]^2} \)

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction. This results in the concentrations of reactants and products remaining constant over time, not zero. Understanding this concept is crucial for students because it allows them to predict how a system will react when conditions change.

For example, if we look at the equilibrium involving nitrogen dioxide and dinitrogen tetroxide:
\[ N_2O_4(g) \rightleftharpoons 2NO_2(g) \]
The point at which the rate of the forward reaction, where \( N_2O_4 \) decomposes into \( NO_2 \), is equal to the rate at which \( NO_2 \) recombines to form \( N_2O_4 \) is known as chemical equilibrium. It's essential to note that achieving equilibrium does not mean the reactants and products are in equal concentrations, but rather that their concentrations have stabilized and will not change without external influence.

Reaction Quotient

The reaction quotient, \( Q \), is a measure of the relative amounts of products and reactants present during a reaction at a given moment. It is calculated using the same formula as the equilibrium constant \( K \), but \( Q \) can be used at any point during the reaction, not just at equilibrium. Comparing \( Q \) to \( K \) tells us in which direction the reaction will proceed to reach equilibrium.

For instance, for the reaction:
\[ CO(g) + 3H_2(g) \rightleftharpoons CH_4(g) + H_2O(g) \]
The reaction quotient would be expressed as:
\[ Q_c = \frac{[CH_4][H_2O]}{[CO][H_2]^3} \]
If \( Q_c < K_c \), it means the reaction will proceed forward to produce more products. If \( Q_c > K_c \), it will shift backward, producing more reactants. If \( Q_c = K_c \), the system is at equilibrium. Students should practice calculating the reaction quotient as it is instrumental in predicting the behavior of the system when conditions change.

Le Chatelier's Principle

Le Chatelier's principle states that if an external stress is applied to a system at equilibrium, the system adjusts to minimize the stress and re-establish equilibrium. The 'stress' can include changes in concentration, pressure, volume, or temperature. Understanding this principle helps predict the effects of changes and is crucial in industrial applications where conditions are often manipulated to increase product yield.

For example, let's examine the reaction:
\[ 4NH_3(g) + 5O_2(g) \rightleftharpoons 4NO(g) + 6H_2O(g) \]
If the concentration of \( NH_3 \) is increased, Le Chatelier's principle tells us that the system will shift to the right, favoring the formation of more products \( NO \) and \( H_2O \) to counteract the added stress. Similarly, an increase in temperature for an exothermic reaction will shift the equilibrium towards the reactants, as the system seeks to absorb the excess heat. Grasping the nuances of Le Chatelier's principle is critical, as it enables students to manipulate reactions to their advantage.