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 2 N2(g) + 2 O2(g) ⇌ 4 NO(g)

Verified step by step guidance

1. Step 1: Understand that the equilibrium constant \( K_c \) is dependent on the stoichiometry of the reaction. When the coefficients of a balanced chemical equation are multiplied by a factor, the equilibrium constant is raised to the power of that factor.
2. Step 2: Identify the original reaction: \( \text{N}_2(g) + \text{O}_2(g) \rightleftharpoons 2 \text{NO}(g) \) with \( K_c = 7.5 \times 10^{-9} \).
3. Step 3: Recognize that the new reaction is \( 2 \text{N}_2(g) + 2 \text{O}_2(g) \rightleftharpoons 4 \text{NO}(g) \), which is the original reaction multiplied by 2.
4. Step 4: Apply the rule for modifying \( K_c \): Since the reaction is multiplied by 2, raise the original \( K_c \) to the power of 2. This means \( K_{c, \text{new}} = (K_c)^2 \).
5. Step 5: Substitute the given \( K_c \) value into the equation: \( K_{c, \text{new}} = (7.5 \times 10^{-9})^2 \). This will give you the new equilibrium constant for the modified reaction.