The given balanced chemical equation is:

[C_2H_4(g) + H_2(g) \rightarrow C_2H_6(g)]

We need to write the expression for the equilibrium constant ((K_{\text{eq}})) for this reaction

The equilibrium constant, K_eq, for the reaction is given by the expression:

K_eq = [C₂H₆] / ([C₂H₄] * [H₂])

Where:
[C₂H₆], [C₂H₄], and [H₂] are the concentrations of ethane, ethylene, and hydrogen gases respectively at equilibrium.