Answer: 0.309 atm for CO2 and 1.191 atm for CO
Step-by-step explanation:
The given reaction is:
FeO(s) + CO(g) ↔ Fe(s) + CO2(g)
This is a reversible reaction, and the equilibrium constant expression (Kp) is given by the ratio of the partial pressures of the products to the reactants at equilibrium.
To solve for the equilibrium partial pressures, we can set up an ICE table:
FeO(s) CO(g) Fe(s) CO2(g)
Initial 1.000 1.000 0.000 0.500
Change -x x x -x
Equilibrium 1.000-x 1.000+x x 0.500-x
The equilibrium constant expression can be written as:
Kp = PCO2 / PCO
Note: Because FeO and Fe are solids, their concentrations do not appear in the equilibrium expression, as their activities are considered to be 1.
Substituting the given Kp value (0.259) and the equilibrium pressures from the ICE table:
0.259 = (0.5 + x) / (1.0 - x)
Solving for x:
0.259 * (1.0 - x) = 0.5 + x
0.259 - 0.259x = 0.5 + x
0.259 - 0.259x - x = 0.5
0.259 - 1.259x = 0.5
-1.259x = 0.5 - 0.259
-1.259x = 0.241
x = 0.241 / -1.259
x = -0.191
Substituting x back into the equilibrium expressions gives the equilibrium partial pressures:
PCO2 = 0.5 + x = 0.5 - 0.191 = 0.309 atm
PCO = 1.0 - x = 1.0 + 0.191 = 1.191 atm