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
(b) NO(g) → 1/2 N₂(g) + 1/2 O₂(g)

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Identify the given equilibrium constant \( K_c = 7.5 \times 10^{-9} \) for the reaction \( \text{N}_2(g) + \text{O}_2(g) \rightarrow 2 \text{NO}(g) \).

Recognize that the reaction in part (b) is the reverse of the given reaction, but with coefficients halved: \( \text{NO}(g) \rightarrow \frac{1}{2} \text{N}_2(g) + \frac{1}{2} \text{O}_2(g) \).

Recall that when a reaction is reversed, the equilibrium constant for the reverse reaction is the reciprocal of the original reaction's equilibrium constant.

Understand that when the coefficients of a balanced equation are multiplied by a factor, the equilibrium constant is raised to the power of that factor.

Calculate the new equilibrium constant by taking the reciprocal of \( K_c \) and then raising it to the power of \( \frac{1}{2} \) to account for the change in coefficients.

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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. It is calculated using the formula Kc = [products]^[coefficients] / [reactants]^[coefficients]. A small Kc value, like 7.5×10^−9, indicates that at equilibrium, the reaction favors the reactants over the products.

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Equilibrium Constant Expressions

Reaction Quotient (Q)

The reaction quotient (Q) is a measure of the relative concentrations of products and reactants at any point in time during a reaction. It is calculated in the same way as Kc but does not require the system to be at equilibrium. Comparing Q to Kc helps predict the direction in which a reaction will proceed to reach equilibrium.

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Reaction Quotient Q

Reverse Reaction and Kc Relationship

For a given reaction, the equilibrium constant for the reverse reaction is the reciprocal of the equilibrium constant for the forward reaction. If Kc for the forward reaction is known, Kc for the reverse reaction can be calculated as Kc(reverse) = 1/Kc(forward). This relationship is crucial for determining Kc for the reaction given in the question, which is the reverse of the original reaction.

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