Answer
(a) $$K_c = 0.50$$
(b)
$ [ CO_2 ] = 0.48 \space M $
$ [ H_2 ] = 0.020 \space M $
$ [ CO ] = 0.075 \space M $
$ [ H_2O ] = 0.065 \space M $
Work Step by Step
(a)
1. Write the equilibrium constant expression:
- The exponent of each concentration is equal to its balance coefficient.
$$K_C = \frac{[Products]}{[Reactants]} = \frac{[ CO ][ H_2O ]}{[ CO_2 ][ H_2 ]}$$
2. Substitute the values and calculate the constant value:
$$K_c = \frac{( 0.050 )( 0.040 )}{( 0.086 )( 0.045 )} = 0.50$$
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(b)
3. At equilibrium, these are the concentrations of each compound:
$ [ CO_2 ] = 0.50 \space M - x$
$ [ H_2 ] = 0.045 \space M - x$
$ [ CO ] = 0.050 \space M + x$
$ [ H_2O ] = 0.040 \space M + x$
$$0.50 = \frac{(0.050 + x)(0.040 + x)}{(0.50 - x)(0.045 - x)}$$
x = 0.025
$ [ CO_2 ] = 0.48 \space M $
$ [ H_2 ] = 0.020 \space M $
$ [ CO ] = 0.075 \space M $
$ [ H_2O ] = 0.065 \space M $
