Answer
$$K_P = 0.127$$
Work Step by Step
- Convert all pressures to atm: 1 atm = 760 mmHg
$P_A (initial)$ = 0.336
$P_A (equilibrium)$ = 0.0724
1. Write the equilibrium constant expression:
- The exponent of each concentration is equal to its balance coefficient.
$$K_P = \frac{[Products]}{[Reactants]} = \frac{P_{ B }P_{ C } ^{ 2 }}{P_{ A } ^{ 2 }}$$
2. At equilibrium, these are the concentrations of each compound:
$ P_{ A } = 0.336 \space atm - 2x$
$ P_{ B } = 0 \space atm + x$
$ P_{ C } = 0 \space atm + 2x$
- We know that, at equilibrium, $P_A = 0.0724 \space atm$, thus:
$0.0724 = 0.336 -2x$
$x = 0.132 \space atm$
$P_B =x = 0.132$
$P_c = 2x = 2(0.132) = 0.264$
$$K_P = \frac{(0.132)(0.264)^2}{0.0724} = 0.127 $$
