Answer
When the mixture reaches equilibrium, the total pressure is less than the sum of the initial pressures.
Work Step by Step
1. Write the equilibrium constant expression:
- The exponent of each concentration is equal to its balance coefficient.
$$K_p = \frac{[Products]}{[Reactants]} = \frac{[ SO_3 ]^{ 2 }}{[ SO_2 ]^{ 2 }[ O_2 ]}$$
2. At equilibrium, these are the concentrations of each compound:
$[ SO_2 ] = 0.350 \space - 2x$
$[ O_2 ] = 0.762 \space - x$
$[ SO_3 ] = 2x$
$$5.60 \times 10^{4} = \frac{(2x)^2}{(0.350-2x)^2(0.350-2x)}$$
x = 0.169
$[ SO_2 ] = 0.350 \space - 2(0.169) = 0.012$
$[ O_2 ] = 0.762 \space - 0.169 = 0.059 $
$[ SO_3 ] = 2(0.169) = 0.338$
3. Total initial pressure = 0.350 + 0.762 + 0 = 1.112 atm
4. Total equilibrium pressure = 0.012 + 0.059 + 0.338 = 0.409 atm
