Answer
$K_c = 0.018$
Work Step by Step
1. At equilibrium, these are the concentrations of each compound:
$ [ SO_2Cl_2 ] = 0.020 \space M - x$
$ [ SO_2 ] = 0 \space M + x$
$ [ Cl_2 ] = 0 \space M + x$
2. Using the concentration of $ Cl_2 $ at equilibrium, find x:
$ 0 + x = 1.2 \times 10^{-2} $
$x = 0.012 $
$ [ SO_2Cl_2 ] = 0.020 \space M - 0.012 =8.0 \times 10^{-3} $
$ [ SO_2 ] = 0 \space M + 0.012 =0.012 $
$ [ Cl_2 ] = 0 \space M + 0.012 =0.012 $
- The exponent of each concentration is equal to its balance coefficient.
$$K_C = \frac{[Products]}{[Reactants]} = \frac{[ SO_2 ][ Cl_2 ]}{[ SO_2Cl_2 ]}$$
3. Substitute the values and calculate the constant value:
$$K_C = \frac{( 0.012 )( 0.012 )}{( 8.0 \times 10^{-3} )} = 0.018$$
