Calculate the value of Kp for the equation Cs CO2g 2COg Kp

Calculate the value of Kp for the equation.

C(s) + CO2(g) <=> 2CO(g) Kp=?

given that at a certain temperature

C(s) + 2H2O(g) <=> CO2(g) + 2H2(g) Kp1= 3.09

H2(g) + CO2(g) <=> H2O(g) + CO(g) Kp2=0.619

Kp=?????

Solution

Add the two given reactions together in a way that, when added, give the desired reaction.

Leave the first reaction as it is written; multiply the second reaction by 2, then add it to the first.

C(s) + 2H2O(g) <--> CO2(g) + 2H2(g)..... Kp1 = 3.09 = P(CI2) P^2(H2) / P^2(H2O)
2H2(g) + 2CO2(g) <--> 2H2O(g) + 2CO(g)...... Kp2 = (0.619)^2 = P^2(H2O) P^2(CO) / P^2(H2) P^2(CO2)

Note that doubling the second reaction causes its Kp value to be squared.
Adding the two reactions together gives the overall reaction.

K = {P(CO2) P^2(H2) / P^2(H2O)} x {P^2(H2O) P^2(CO) / P^2(H2) P^2(CO2)} = P^2(CO) / P(CO2)
K = Kp1 x Kp2^2 = 3.09 x 0.619^2 = 1.18