Answer
$$K_c = 1.8 \times 10^-2$$
Work Step by Step
1. Write the equilibrium constant expression:
- The exponent of each concentration is equal to its balance coefficient.
$$K_C = \frac{[Products]}{[Reactants]} = \frac{[ SO_2 ][ Cl_2 ]}{[ SO_2Cl_2 ]}$$
2. 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$
As we know, at equilibrium: $[Cl_2 ] = 1.2 \times 10^{-2} \space M$
Thus, $x = 1.2 \times 10^{-2}$. Substituting:
$ [ SO_2 ] = 1.2 \times 10^{-2} \space M$
$ [ SO_2Cl_2 ] = 8.0 \times 10^{-3} \space M$
$$K_c = \frac{(1.2 \times 10^{-2}) (1.2 \times 10^{-2} )}{( 8.0 \times 10^{-3})} = 1.8 \times 10^{-2}$$
