Question

The following reaction $$ 2 \mathrm{H}_{2} \mathrm{~S}(\mathrm{~g}) \rightleftarrows 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{S}_{2}(\mathrm{~g}) $$ was allowed to proceed to equilibrium. The contents of the two-liter reaction vessel were then subjected to analysis and found to contain \(1.0\) mole \(\mathrm{H}_{2} \mathrm{~S}, 0.20\) mole \(\mathrm{H}_{2}\), and \(0.80\) mole \(\mathrm{S}_{2}\). What is the equilibrium constant \(\mathrm{K}\) for this reaction?

Short answer

The equilibrium constant K for the reaction $$ 2 \mathrm{H}_{2} \mathrm{~S}(\mathrm{~g}) \rightleftarrows 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{S}_{2}(\mathrm{~g}) $$ is 0.016.

Step-by-step solution

Calculate the equilibrium concentrations of the reactants and products

Divide the moles of each compound by the volume of the reaction vessel (2 liters) to get the equilibrium concentration. For H2S: \[ \frac{1.0\, \text{mole}}{2\, \text{L}} = 0.50\, \text{M} \] For H2: \[ \frac{0.20\, \text{mole}}{2\, \text{L}} = 0.10\, \text{M} \] For S2: \[ \frac{0.80\, \text{mole}}{2\, \text{L}} = 0.40\, \text{M} \]

Set up the expression for the equilibrium constant K

The equilibrium constant expression for the given reaction is: \[ K = \frac{[\text{H}_2]^2[\text{S}_2]}{[\text{H}_2\text{S}]^2} \]

Plug in the equilibrium concentrations into the K expression

Substitute the equilibrium concentrations calculated in Step 1 into the K expression: \[ K = \frac{(0.10\, \text{M})^2(0.40\, \text{M})}{(0.50\, \text{M})^2} \]

Calculate K

Perform the calculations to get the value of K: \[ K = \frac{(0.01\, \text{M}^2)(0.40\, \text{M})}{(0.25\, \text{M}^2)} = \frac{0.004\, \text{M}^2}{0.25\, \text{M}^2} = 0.016 \] The equilibrium constant K for the reaction is 0.016.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in a reversible chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction. Consequently, the concentrations of reactants and products remain constant over time, not because the reactions have stopped, but because they proceed at the same rate in both directions.

It's vital to understand that equilibrium does not imply that the reactants and products are present in equal amounts. Instead, it depends on the particular reaction's dynamics, which is quantified by the equilibrium constant. For the reaction \( 2 H_2S(g) \rightleftarrows 2 H_2(g) + S_2(g) \), the equilibrium state would mean that the decomposition rate of \( H_2S \) into \( H_2 \) and \( S_2 \) is balanced by the rate at which \( H_2 \) and \( S_2 \) combine to form \( H_2S \).

Reaction Quotient

The reaction quotient, Q, helps determine the direction in which a reaction mixture will proceed to reach equilibrium. It has the same form as the equilibrium constant expression but uses initial concentrations instead of equilibrium concentrations.

Calculating Reaction Quotient

The reaction quotient is calculated by plugging the initial concentrations of the reactants and products into the equilibrium constant expression. For the discussed reaction, the reaction quotient would be:\[ Q = \frac{[H_2]^2[S_2]}{[H_2S]^2} \]If Q is less than the equilibrium constant \( K \), the forward reaction is favored, and the system will proceed in the direction that converts reactants to products. Conversely, if Q is greater than \( K \), the system will favor the reverse reaction.

Le Chatelier's Principle

Le Chatelier's principle provides a qualitative prediction of how a system at equilibrium reacts to external changes. According to this principle, if a dynamic equilibrium is disturbed by changing the conditions (such as concentration, temperature, or pressure), the position of equilibrium moves to counteract the change.

For instance, if the concentration of \( H_2 \) in the given reaction equilibrium is increased, the system would respond by consuming more \( H_2 \) (and \( S_2 \)) to form more \( H_2S \), thereby shifting the equilibrium to the left. This principle assists in understanding and predicting the effects of different stresses on a system at equilibrium.

Equilibrium Concentration

Equilibrium concentration refers to the concentration of a reactant or product in a reaction mixture when the system has reached equilibrium. At this point, as discussed earlier, the concentrations will remain constant as long as external conditions are unchanged.

Importance of Equilibrium Concentrations

Knowing the equilibrium concentrations is crucial for calculating the equilibrium constant, which is a measure of the extent of the reaction and helps predict the yield of the products. As demonstrated in the exercise, the equilibrium concentrations were used to calculate the equilibrium constant: