Answer
$$P_{SO_2Cl_2} = 2.32 \times 10^{-5} \space atm = 1.76 \times 10^{-2} \space torr$$
Work Step by Step
- Convert all the pressures to atm: 1 atm = 760 torr.
$P_{SO_2} = 0.180 \space atm$
$P_{Cl_2} = 0.375 \space atm$
1. Write the equilibrium constant expression:
- 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:
$$ P_{SO_2Cl_2} = \frac{( 0.180 )( 0.375 )}{(2.91 \times 10^3)} $$
$$P_{SO_2Cl_2} = 2.32 \times 10^{-5} \space atm = 1.76 \times 10^{-2} \space torr$$
