Let's solve this problem step-by-step.
First, we need to write the balanced chemical equation for the reaction:
[tex]\[ N_2(g) + O_2(g) \rightleftarrows 2 NO(g) \][/tex]
Next, we write the equilibrium expression for this reaction. This is based on the concentrations of the reactants and products at equilibrium:
[tex]\[ K_c = \frac{[\text{NO}]^2}{[\text{N}_2][\text{O}_2]} \][/tex]
We are given the equilibrium concentrations:
[tex]\[
[N_2] = 0.86 \, \text{M}, \quad [O_2] = 0.88 \, \text{M}, \quad [NO] = 0.018 \, \text{M}
\][/tex]
Now, substitute these concentrations into the equilibrium expression:
[tex]\[ K_c = \frac{(0.018)^2}{(0.86)(0.88)} \][/tex]
Calculate the numerator:
[tex]\[ (0.018)^2 = 0.000324 \][/tex]
Calculate the denominator:
[tex]\[ (0.86)(0.88) = 0.7568 \][/tex]
Now, divide the numerator by the denominator to find [tex]\( K_c \)[/tex]:
[tex]\[ K_c = \frac{0.000324}{0.7568} \approx 0.0004281183932346722 \][/tex]
Thus, the equilibrium constant [tex]\( K_c \)[/tex] is approximately [tex]\( 4.28 \times 10^{-4} \)[/tex].
Comparing this with the given choices, the correct answer is:
[tex]\[ B. \, 4.2 \times 10^{-4} \][/tex]
