A mixture of 0.2000 mol of CO₂, 0.1000 mol of H₂, and 0.1600 mol of H₂O is placed in a 2.000-L vessel. The following equilibrium is established at 500 K: CO₂(𝑔) + H₂(𝑔) ⇌ CO(𝑔) + H₂O (𝑔) (d) Calculate 𝐾_𝑐 for the reaction.

Verified step by step guidance

1. Write the balanced chemical equation for the reaction: CO₂(g) + H₂(g) ⇌ CO(g) + H₂O(g).
2. Calculate the initial concentrations of the reactants and products. Use the formula concentration = moles/volume. For CO₂, H₂, and H₂O, use their given moles and the volume of the vessel (2.000 L). Assume the initial concentration of CO(g) is 0 since it is not mentioned in the problem statement.
3. Set up the expression for the equilibrium constant, K_c, based on the balanced equation. K_c = [CO][H₂O] / [CO₂][H₂].
4. Determine the changes in concentration for each species at equilibrium. Let 'x' be the change in concentration of CO₂ and H₂ that react. Then, the change in concentration of CO and H₂O will also be 'x' since they are produced in a 1:1 ratio with the reactants.
5. Substitute the equilibrium concentrations (initial concentration ± x) into the K_c expression and solve for K_c.

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 chemical reaction. It is calculated using the formula Kc = [products]^[coefficients] / [reactants]^[coefficients], where the brackets denote molarity. A larger Kc indicates a greater concentration of products at equilibrium, while a smaller Kc suggests that reactants are favored.

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution (mol/L). In the context of gas reactions, it can also be applied to gaseous reactants and products in a container. To calculate molarity, you divide the number of moles of each substance by the volume of the container in liters, which is essential for determining the concentrations needed to compute Kc.

Stoichiometry

Stoichiometry is the area of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It involves using balanced chemical equations to determine the amounts of substances consumed and produced. Understanding stoichiometry is crucial for calculating the equilibrium constant, as it allows for the correct interpretation of the molar ratios of the reactants and products involved in the reaction.