How do you find the equilibrium constant for the reverse reaction of this problem?

Question

Given :
Temperature : 1500 degrees Celcius
Equilibrium Constant : 0.1764
Balanced equation: $C O + 3 H_{2} = C H_{4} + H_{2} O$ $CO + 3 H_2 = CH_4 + H_2O$

Need:
Equilibrium Constant for $C H_{4} + H_{2} O = C O + 3 H_{2}$ $CH_4 + H_2O = CO + 3H_2$

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Answer 1 · 2016-08-19T19:35:02

$K'=5.670$

The equilibrium constant for the reaction:

$CO+3H_2rightleftharpoons CH_4+H_2O$

is written as:

$K=([CH_4][H_2O])/([CO][H_2]^3)=0.1764$

The equilibrium constant for the opposite reaction:

$CH_4+H_2OrightleftharpoonsCO+3H_2$

is written as:

$K'=( [CO][H_2]^3)/([CH_4][H_2O])=1/K=1/(0.1764)=5.670$

Here is a video that explains this topic in details:
Chemical Equilibrium | The Equilibrium Conditions.