For the reaction N_2(g) + 3H_2(g) ightleftharpoons 2NH_3(g), the equilibrium concentrations at a certain temperature are [N_2] = 0.50 M, [H_2] = 1.50 M, and [NH_3] = 2.00 M. What is the value of the equilibrium constant K_c for this reaction?

• A. K_c = 23.7
• B. K_c = 8.0
• C. K_c = 0.042
• D. K_c = 0.67

Answer: (A)

Verified step by step guidance

1. Write the balanced chemical equation: \(\mathrm{N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)}\).
2. Recall the expression for the equilibrium constant \(K_c\) in terms of concentrations: \(K_c = \frac{[\mathrm{NH_3}]^2}{[\mathrm{N_2}][\mathrm{H_2}]^3}\).
3. Substitute the given equilibrium concentrations into the expression: \(K_c = \frac{(2.00)^2}{(0.50)(1.50)^3}\).
4. Calculate the powers and products in the denominator and numerator separately, keeping track of each step carefully.
5. Divide the numerator by the denominator to find the numerical value of \(K_c\).