Answer
$$0.0176 \space torr$$
Work Step by Step
- Convert the pressures to atm:
$$ 137 \space torr \times \frac{1 \space atm}{760 \space torr} = 0.180 \space atm$$
$$ 285 \space torr \times \frac{1 \space atm}{760 \space torr} = 0.375 \space atm$$
1. The exponent of each concentration is equal to its balance coefficient.
$$K_P = \frac{[Products]}{[Reactants]} = \frac{P_{ SO_2 }P_{ Cl_2 }}{P_{ SO_2Cl_2 }}$$
2. Solve for the missing concentration:
$$ P_{SO_2Cl_2} = \frac{P_{ SO_2 } P_{ Cl_2 } }{ K_P}$$
3. Evaluate the expression:
$$ P_{SO_2Cl_2} = \frac{( 0.18 )( 0.375 )}{(2.91 \times 10^3)} $$
$$[SO_2Cl_2] = 2.32 \times 10^{-5} \space atm \times \frac{760 \space torr}{1 \space atm} = 0.0176 \space torr$$
