Calculate the equilibrium concentrations of H2O(g), Cl2(g), HCl(g), and O2(g) at 298 K if the initial concentrations are [H2O] = 0.050 M and [Cl2] = 0.100 M. The equilibrium constant Kc for the reaction H2O(g) + Cl2(g) ⇌ 2 HCl(g) + O2(g) is 8.96 × 10^-9 at 298 K.

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Write the balanced chemical equation for the reaction: H2O(g) + Cl2(g) ⇌ 2 HCl(g) + O2(g).

Set up an ICE (Initial, Change, Equilibrium) table to track the concentrations of each species. Initially, [H2O] = 0.050 M, [Cl2] = 0.100 M, and [HCl] and [O2] are 0 M.

Define the change in concentration for the reactants and products in terms of x, where x is the amount of H2O and Cl2 that reacts. The changes will be: -x for H2O and Cl2, +2x for HCl, and +x for O2.

Express the equilibrium concentrations in terms of x: [H2O] = 0.050 - x, [Cl2] = 0.100 - x, [HCl] = 2x, and [O2] = x.

Substitute these expressions into the equilibrium constant expression Kc = ([HCl]^2[O2])/([H2O][Cl2]) and solve for x using the given Kc value of 8.96 × 10^-9.

Key Concepts

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

Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. In this state, the system is dynamic, meaning that reactions continue to occur, but there is no net change in concentration. Understanding this concept is crucial for calculating equilibrium concentrations, as it allows us to apply the equilibrium constant (Kc) to the reaction.

Equilibrium Constant (Kc)

The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their coefficients in the balanced equation. For the reaction H2O(g) + Cl2(g) ⇌ 2 HCl(g) + O2(g), Kc = [HCl]^2[O2] / [H2O][Cl2]. This constant provides insight into the position of equilibrium and is essential for calculating the equilibrium concentrations from initial concentrations.

ICE Table (Initial, Change, Equilibrium)

An ICE table is a tool used to organize the initial concentrations, the changes in concentrations as the reaction proceeds, and the equilibrium concentrations of all species involved in a chemical reaction. By setting up an ICE table for the given reaction, one can systematically determine how the initial concentrations of H2O and Cl2 change to reach equilibrium, allowing for the calculation of the final concentrations of all species.

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Textbook Question

The reaction of fumarate with water to form L-malate is catalyzed by the enzyme fumarase; Kc = 3.3 at 37°C. When a reaction mixture with [fumarate] = 1.56 * 10-3 M and [l -malate] = 2.27 * 10-3 M comes to equilibrium in the presence of fumarase at 37 °C, what are the equilibrium concentrations of fumarate and L-malate? (Water can be omit- ted from the equilibrium equation because its concentration in dilute solutions is essentially the same as that in pure water.)

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Textbook Question

Consider the following equilibrium: Ag⁺ (aq) + Cl^-(aq) → AgCl(s) Use Le Châtelier's principle to predict how the amount of solid silver chloride will change when the equilibrium is disturbed by: (a) Adding NaCl (b) Adding AgNO₃

Textbook Question

Consider the following equilibrium: Ag⁺(aq) + Cl^-(aq) ⇌ AgCl(s) Use Le Châtelier's principle to predict how the amount of solid silver chloride will change when the equilibrium is disturbed by: (d) Removing Cl^-; also account for the change using the reaction quotient Q_c