An equilibrium constant is the ratio between the concentration of products and reactants, considering their stoichiometric numbers. In a general equation, for example:
![aA\text{ + bB }\rightleftarrows\text{ cC + dD}](https://img.qammunity.org/2023/formulas/chemistry/college/ywnwhviq29mzx9anosz8ed3b7h9d24am0f.png)
the equilibrium constant would be:
![K_c=(\lbrack C\rbrack^c*\lbrack D\rbrack^d)/(\lbrack A\rbrack^a*\lbrack B\rbrack^b)](https://img.qammunity.org/2023/formulas/chemistry/college/g8ynufaxssmviqfi2iz0an2j81xvq8wubs.png)
(where [C] = product C concentration, [D] = product D concentration etc.)
Considering that definition and the reaction given in the question, we could write the equilibrium constant as:
![K_c=\frac{\lbrack CH_3OH\rbrack^{}}{\lbrack CO_{}\rbrack^{}*\lbrack H_2\rbrack^2}](https://img.qammunity.org/2023/formulas/chemistry/college/k1gvu11rrsm1xjfhiao1bw6drvsgk92gr1.png)
Note that the coefficient for both CH3OH and CO2 is 1, so we don't need to show it on the Kc formula.
Therefore, the numerator would be [CH3OH] and the denominator would have the terms [CO] and [H2]^2.