If K_c = 7.5×10⁻⁹ at 1000 K for the reaction N₂(g) + O₂(g) → 2 NO(g), give the value of K_c at 1000 K for the reaction
(a) 2 NO(g) → N₂(g) + O₂(g)

검증된 단계별 안내

First, recognize that the second reaction is the reverse of the first reaction. In other words, the reactants and products have been swapped.

Next, recall that the equilibrium constant for the reverse reaction is the reciprocal of the equilibrium constant for the forward reaction. This is because the equilibrium constant is a ratio of the concentrations of the products to the reactants, so reversing the reaction swaps the numerator and denominator of this ratio.

Then, calculate the reciprocal of the given equilibrium constant, Kc, for the forward reaction. The reciprocal of a number is simply 1 divided by that number.

Finally, the reciprocal of Kc for the forward reaction is the value of Kc for the reverse reaction. This is the answer to the problem.

Remember, you don't need to calculate the exact value. The purpose of this problem is to understand the relationship between the equilibrium constants of forward and reverse reactions.

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주요 개념

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

Equilibrium Constant (Kc)

The equilibrium constant, Kc, quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is expressed as Kc = [products]^[coefficients] / [reactants]^[coefficients]. A small Kc value, like 7.5×10^−9, indicates that at equilibrium, the concentration of reactants is much greater than that of products.

Reversibility of Reactions

Chemical reactions are often reversible, meaning the products can react to form the original reactants. The equilibrium constant for the reverse reaction is the reciprocal of the forward reaction's Kc. For the reaction 2 NO(g) → N2(g) + O2(g), the Kc can be calculated as 1/(7.5×10^−9), reflecting the relationship between the forward and reverse reactions.

Temperature Dependence of Kc

The value of the equilibrium constant, Kc, is temperature-dependent. Changes in temperature can shift the position of equilibrium and alter the concentrations of reactants and products. Therefore, when calculating Kc for a reaction at a different temperature, it is essential to consider that Kc values are specific to the temperature at which they are measured.

If Kc = 7.5×10−9 at 1000 K for the reaction N2(g) + O2(g) → 2 NO(g), give the value of Kc at 1000 K for the reaction(a) 2 NO(g) → N2(g) + O2(g)