At 2000°C, the equilibrium constant for the reaction 2 NO(𝑔) ⇌ N₂(𝑔) + O₂(𝑔) is 𝐾_𝑐= 2.4×10³. If the initial concentration of NO is 0.175 M, what are the equilibrium concentrations of NO, N₂, and O₂?

검증된 단계별 안내

Write the balanced chemical equation: 2 \(\text{NO}\)(g) \(\rightleftharpoons\) \(\text{N}\)_2(g) + \(\text{O}\)_2(g).

Set up an ICE (Initial, Change, Equilibrium) table to track the concentrations of each species. Initially, [NO] = 0.175 \(\text{ M}\), and [N_2] = [O_2] = 0 \(\text{ M}\).

Define the change in concentration for NO as -2x, for N_2 as +x, and for O_2 as +x, where x is the change in concentration at equilibrium.

Express the equilibrium concentrations in terms of x: [NO] = 0.175 - 2x, [N_2] = x, [O_2] = x.

Substitute these expressions into the equilibrium constant expression: K_c = \(\frac{[N_2][O_2]}{[NO]^2}\) = \(\frac{x \cdot x}{(0.175 - 2x)^2}\) = 2.4 \(\times\) 10^3, and solve for x.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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. For the reaction 2 NO(g) ⇌ N2(g) + O2(g), Kc = [N2][O2]/[NO]^2. A larger Kc value indicates that products are favored at equilibrium, while a smaller Kc suggests that reactants are favored.

ICE Table

An ICE table (Initial, Change, Equilibrium) is a tool used to organize the concentrations of reactants and products in a chemical reaction at different stages. It helps in calculating the changes in concentration as the system reaches equilibrium. By filling in the initial concentrations, the changes that occur, and the equilibrium concentrations, one can systematically determine the equilibrium state of the reaction.

Stoichiometry

Stoichiometry involves the quantitative relationships between the amounts of reactants and products in a chemical reaction, based on the balanced chemical equation. In the reaction 2 NO(g) ⇌ N2(g) + O2(g), stoichiometry allows us to relate the change in concentration of NO to the formation of N2 and O2, using the coefficients from the balanced equation to determine how much of each species is present at equilibrium.

At 2000°C, the equilibrium constant for the reaction 2 NO(𝑔) ⇌ N2(𝑔) + O2(𝑔) is 𝐾𝑐 = 2.4×103. If the initial concentration of NO is 0.175 M, what are the equilibrium concentrations of NO, N2, and O2?