To determine the expression for the equilibrium constant ([tex]\( K_{eq} \)[/tex]) for the given reaction, we follow these steps:
1. Write the balanced chemical equation:
[tex]\[
\mathrm{C_2H_4O_2(g) + 2H_2(g) \rightleftharpoons C_2H_6O(g) + H_2O(g)}
\][/tex]
2. Understand the equilibrium constant expression:
The equilibrium constant ([tex]\( K_{eq} \)[/tex]) for a reaction is given in terms of the concentrations (or partial pressures for gases) of the reactants and products at equilibrium. For a general reaction:
[tex]\[
aA + bB \rightleftharpoons cC + dD
\][/tex]
The equilibrium constant expression is:
[tex]\[
K_{eq} = \frac{[C]^c[D]^d}{[A]^a[B]^b}
\][/tex]
where [tex]\([X]\)[/tex] denotes the concentration or partial pressure of the species [tex]\(X\)[/tex].
3. Apply the general form to the given reaction:
For the reaction:
[tex]\[
\mathrm{C_2H_4O_2(g) + 2H_2(g) \rightleftharpoons C_2H_6O(g) + H_2O(g)}
\][/tex]
The equilibrium constant expression would be:
[tex]\[
K_{eq} = \frac{[\mathrm{C_2H_6O}][\mathrm{H_2O}]}{[\mathrm{C_2H_4O_2}][\mathrm{H_2}]^2}
\][/tex]
### Conclusion:
The equilibrium constant expression for the given equation is:
[tex]\[
K_{eq} = \frac{[\mathrm{C_2H_6O}][\mathrm{H_2O}]}{[\mathrm{C_2H_4O_2}][\mathrm{H_2}]^2}
\][/tex]
