What is K of Fe(S) + H2O(g)=FeO(s) + H2(g)

Question

Given the following:
2H20(g) + 2CO(g) 2H2(g) + 2CO2(g) K = 2.56
3FeO(s) + 3CO(g) 3Fe(s) + 3CO2(g) K = .301

Answer 1

I assume the K values shown are for the equations AS WRITTEN.
2H20(g) + 2CO(g) ==> 2H2(g) + 2CO2(g) K = 2.56
3FeO(s) + 3CO(g) ==> 3Fe(s) + 3CO2(g) K = .301
You want this. Fe(s) + H2O(g) ==> FeO(s) + H2(g)

Leave eqn 1 as is with K = 2.56
Reverse eqn 2 so K for eqn 2 is 1/0.301 = 3.22
2H20(g) + 2CO(g) ==> 2H2(g) + 2CO2(g) K = 2.56
3Fe(s) + 3CO2(g) ==> 3FeO(s) + 3CO(g) K = 3.22

Next leave eqn 1 as is.
Divide the coefficients of eqn 2 by 3 and multiply by 2, The K = (3.22)^2/3
2H20(g) + 2CO(g) ==> 2H2(g) + 2CO2(g) K = 2.56
2Fe(s) + 2CO2(g) ==> 2FeO(s) + 2CO(g) K = (3.22)^2/3

Now add the last two equations.
2Fe(s) + 2H2O(g) ==> 2FeO(s) + 2H2(g) K = 2.56 x (3.22)^2/3 but this is for double what you want so take the square root of the result.
Post your work if you get stuck.

Answer 2

So the answer is 2.36?