I was given a problem that my book did not explain how to do, so I attempted to figure it out myself. Let me know if my conclusion is fallacious.
Given the reactions
H2O(g) + CO(g) <--> H2(g) + CO2(g), K= 1.6
FeO(s) + CO(g) <--> Fe(s) + CO2(g), K= .67
Find K for the reaction
Fe(s) + H2O(g) <--> FeO(s) + H2(g)
I looked through the numbers and thought this:
In the second reaction, the K value is essentially based on CO(g) and CO2(g), because the pure solids have little/no effect on K. Looking at the reaction I am trying to find, I see that I am essentially finding K for H2O(g) <--> H2(g), because the pure solids do not affect the K value. With this knowledge, I subtracted the K value for [essentially] CO(g)<-->CO2(g) from the K value for H2O(g) + CO(g)<-->H2(g) + CO2(g), leaving me with the K value of H2O(g)<-->H2(g) [or .93]. Does this make sense?
No, it doens't.
H2O(g) + CO(g) <-> H2(g)+CO2(g) K= 1.6
FeO(s) + CO(g) <-> Fe(s)+ CO2(g) K=0.67
Call the first equation #1 and the second #2.
Reverse equation 2. K for that reversed is 1/K = 1/0.67.
Now add equation #1 to the reversed equation #2 to obtain the reaction you want. When adding equations, multiply Ks. So (1/0.67)x 1.6 = K for the final reaction.
Your conclusion is fallacious. Let's break down the correct method for finding the equilibrium constant (K) for the reaction Fe(s) + H2O(g) <--> FeO(s) + H2(g):
First, you should write the balanced equations for the given reactions:
Equation 1: H2O(g) + CO(g) <--> H2(g) + CO2(g) with K = 1.6
Equation 2: FeO(s) + CO(g) <--> Fe(s) + CO2(g) with K = 0.67
To find K for the desired reaction, you need to combine the given reactions so that the desired reaction is obtained. Let's manipulate the equations to achieve that:
Reverse equation 2:
Equation 2 (reversed): Fe(s) + CO2(g) <--> FeO(s) + CO(g) with K = 1/0.67 (= 1.49)
Now, add equation 1 to the reversed equation 2 to obtain the desired reaction:
Desired reaction: H2O(g) + Fe(s) <--> H2(g) + CO2(g)
When combining equations, you also multiply the equilibrium constants:
K for the desired reaction = K(1) x K(2)
K for the desired reaction = 1.6 x 1/0.67
K for the desired reaction = 2.39
Therefore, the correct value of K for the reaction Fe(s) + H2O(g) <--> FeO(s) + H2(g) is 2.39, not 0.93 as you concluded.