A mixture of 0.10 mol of NO, 0.050 mol of H2, and 0.10 mol of H2O is placed in a 1.0-L vessel at 300 K. The following equilibrium is established: 2 NO(g) + 2 H2(g) ⇌ N2(g) + 2 H2O(g). At equilibrium [NO] = 0.062 M. (a) Calculate the equilibrium concentrations of H2, N2, and H2O.

Verified step by step guidance

Identify the initial concentrations of each species in the reaction. Since the volume of the vessel is 1.0 L, the initial concentrations are: [NO] = 0.10 M, [H2] = 0.050 M, and [H2O] = 0.10 M.

Write the balanced chemical equation for the reaction: 2 NO(g) + 2 H2(g) ⇌ N2(g) + 2 H2O(g).

Set up an ICE (Initial, Change, Equilibrium) table to track the changes in concentrations of each species as the system reaches equilibrium. Use 'x' to represent the change in concentration for the reactants and products.

Use the given equilibrium concentration of NO, [NO] = 0.062 M, to determine the change in concentration, 'x'. Since the initial concentration of NO was 0.10 M, the change is 0.10 M - 0.062 M.

Apply the stoichiometry of the balanced equation to find the changes in concentrations of H2, N2, and H2O. Use these changes to calculate their equilibrium concentrations.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equilibrium Constant Expression

The equilibrium constant expression (K) relates the concentrations of reactants and products at equilibrium for a given reaction. For the reaction 2 NO(g) + 2 H2(g) ⇌ N2(g) + 2 H2O(g), K is calculated using the formula K = [N2][H2O]^2 / [NO]^2[H2]^2. Understanding how to set up and manipulate this expression is crucial for determining the concentrations of all species at equilibrium.

Stoichiometry of the Reaction

Stoichiometry involves the quantitative relationships between the reactants and products in a chemical reaction. In this case, the stoichiometric coefficients indicate that 2 moles of NO react with 2 moles of H2 to produce 1 mole of N2 and 2 moles of H2O. This relationship is essential for calculating the changes in concentration as the system reaches equilibrium.

Initial and Equilibrium Concentrations

To solve for equilibrium concentrations, one must understand the initial concentrations of the reactants and how they change as the reaction progresses to equilibrium. The initial concentrations are given, and the change in concentration can be represented using 'x' to denote the amount reacted. By applying these changes to the initial concentrations, one can derive the equilibrium concentrations for all species involved.

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Textbook Question

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.

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