Question

For the reaction \[ N_2 + O_2 \rightleftharpoons 2NO \] the equilibrium concentrations are given as \[ [N_2]=0.5\,M,\qquad [O_2]=0.7\,M,\qquad [NO]=0.4\,M \] Calculate the value of \(K_c\).

• A. 0.58
• B. 0.48
• C. 1.15
• D. 2014

Hint:

Always write the balanced chemical equation first and then construct the equilibrium constant expression using stoichiometric coefficients as powers.

Answer 1

The Correct Option is B

Concept: The equilibrium constant in terms of concentration, denoted by \(K_c\), is defined as the ratio of the product of molar concentrations of products to the product of molar concentrations of reactants, each raised to the power of their stoichiometric coefficients. For a general reaction \[ aA+bB \rightleftharpoons cC+dD \] the equilibrium constant is \[ K_c=\frac{[C]^c[D]^d}{[A]^a[B]^b} \] The value of \(K_c\) indicates the extent to which reactants are converted into products at equilibrium.

Step 1: Write the equilibrium constant expression. For the reaction \[ N_2+O_2 \rightleftharpoons 2NO \] the equilibrium constant expression is \[ K_c=\frac{[NO]^2}{[N_2][O_2]} \]

Step 2: Substitute the equilibrium concentrations. Given: \[ [N_2]=0.5\,M \] \[ [O_2]=0.7\,M \] \[ [NO]=0.4\,M \] Substituting: \[ K_c=\frac{(0.4)^2}{(0.5)(0.7)} \] \[ K_c=\frac{0.16}{0.35} \]

Step 3: Perform the calculation. \[ K_c=0.457 \] \[ K_c \approx 0.46 \] Among the given options, the closest value is \[ \boxed{0.48} \] Hence, the correct option is \[ \boxed{(2)} \]