Answer
K = $4.0\times10^{6}$
Work Step by Step
According to the law of mass action, a general formula of the form
jA + kB ⇌ lC + mD
is represented by the following equilibrium expression:
K = $\frac{[C]^{l}[D]^{m}}{[A]^{j}[B]^{k}}$
where A, B, C, and D represent the chemical species and j, k, l, and m are their coefficients in the balanced equation.
Therefore,
K = $\frac{[N_{2}][H_{2}O]^{2}}{[NO]^{2}[H_{2}]^{2}}$
K = $\frac{(5.3\times10^{-2})(2.9\times10^{-3})^{2}}{(8.1\times10^{-3})^{2}(4.1\times10^{-5})^{2}}$
K = $4.04\times10^{6}$ (carried one extra significant digits)
K = $4.0\times10^{6}$
