Answer
$\Delta S^{\circ}_{rxn}=-120.8\,J/K$
$\Delta S^{\circ}_{rxn}$ is negative because there is a decrease in the number of moles of gas.
Work Step by Step
$\Delta S^{\circ}_{rxn}=\Sigma n_{p}S^{\circ}(products)-\Sigma n_{r}S^{\circ}(reactants)$
$=[1\,mol\times S^{\circ}(C_{2}H_{6},g)]-[1\,mol\times S^{\circ}(C_{2}H_{4},g)+1\,mol\times S^{\circ}(H_{2},g)]$
$=[1\,mol(229.2\,Jmol^{-1}K^{-1})]-[1\,mol(219.3\,Jmol^{-1}K^{-1})+1\,mol(130.7\,Jmol^{-1}K^{-1})]$
$=-120.8\,J/K$
$\Delta S^{\circ}_{rxn}$ is negative because there is a decrease in the number of moles of gas.
