At 1000 K, the value of Kc for the reaction C1s2 + H2O1g2 ∆ CO1g2 + H21g2 is 3.0 * 10-2. Calculate the equilibrium concentrations of H2O, CO2, and H2 in a reac- tion mixture obtained by heating 6.00 mol of steam and an excess of solid carbon in a 5.00-L container. What is the molar composition of the equilibrium mixture?

Verified step by step guidance

1. Identify the balanced chemical equation: \( \text{C(s)} + \text{H}_2\text{O(g)} \rightleftharpoons \text{CO(g)} + \text{H}_2\text{(g)} \).
2. Write the expression for the equilibrium constant \( K_c \): \( K_c = \frac{[\text{CO}][\text{H}_2]}{[\text{H}_2\text{O}]} \).
3. Determine the initial concentrations: \([\text{H}_2\text{O}]_0 = \frac{6.00 \text{ mol}}{5.00 \text{ L}} = 1.20 \text{ M}\), \([\text{CO}]_0 = 0\), \([\text{H}_2]_0 = 0\).
4. Set up an ICE table (Initial, Change, Equilibrium) to express the changes in concentration in terms of \( x \), where \( x \) is the change in concentration of \( \text{CO} \) and \( \text{H}_2 \).
5. Substitute the equilibrium concentrations into the \( K_c \) expression and solve for \( x \) to find the equilibrium concentrations of \( \text{H}_2\text{O} \), \( \text{CO} \), and \( \text{H}_2 \).

Key Concepts

Equilibrium Constant (Kc)

The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is calculated using the formula Kc = [products]^[coefficients] / [reactants]^[coefficients]. A Kc value less than 1 indicates that at equilibrium, reactants are favored, while a value greater than 1 suggests that products are favored.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows us to determine the relationships between the amounts of substances consumed and produced. In this case, understanding the stoichiometric coefficients of the reaction is essential for calculating the equilibrium concentrations of H2O, CO2, and H2.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure, volume, temperature, and number of moles of a gas. In this scenario, it is important for converting between moles and concentrations, especially since the reaction involves gases. Knowing the volume of the container and the number of moles allows us to calculate the molarity of the gases at equilibrium, which is necessary for determining the equilibrium concentrations.