Answer
$$[N_2O_4] = 0.54 \space M$$
Work Step by Step
1. Write the equilibrium constant expression:
$$K_c = \frac{[Products]}{[Reactants]} = \frac{[ NO_2 ]^{ 2 }}{[ N_2O_4 ]}$$
2. Solve for the missing concentration:
$$ [N_2O_4] = \frac{[ NO_2 ]^{ 2 }}{K_c}$$
3. Evaluate the expression:
$$ [N_2O_4] = \frac{( 0.050 )^{ 2 }}{(4.6 \times 10^{-3})} $$
$$[N_2O_4] = 0.54 \space M$$
