b. smaller, decrease
c. higher, increase
d. smaller, increase
B. smaller, decrease
First calculate the equilibrium constant:
Kc = [CO] [H2O] / [CO2] [H2] = (0.050) (0.040) / (0.086) (0.045) = 0.517.
By adding more CO2, the equilibrium will shift to the right, so both CO2 and H2 will lose x, and both CO and H2O will gain x. The new equilibrium expression is:
0.517 = (0.050+x) (0.040+x) / (0.25-x) (0.045-x)
Now rearrange to quadratic form (this takes some work):
0.483x² + 0.242x - 0.00381 = 0
Solving, using the quadratic formula, x = 0.0153 is the only positive root. Now we can calculate the new equilibrium concentrations:
[CO2] = 0.25 - 0.0153 = 0.235 M
[H2] = 0.045 - 0.0153 = 0.0297 M
[CO] = 0.050 + 0.0153 = 0.0653 M
[H2O] = 0.040 + 0.0153 = 0.0553 M.
If these new concentrations are replaced into the equilibrium expression, the original Kc is obtained, so the answers check.