Answer
$-42.0\,J/K$
The sign of $\Delta S^{\circ}_{rxn}$ is negative. But, we cannot predict the sign because the number of moles of gas is constant.
Work Step by Step
$\Delta S^{\circ}_{rxn}=\Sigma n_{p}S^{\circ}(products)-\Sigma n_{r}S^{\circ}(reactants)$
$=[1\,mol\times S^{\circ}(H_{2},g)+1\,mol\times S^{\circ}(CO_{2},g)]-[1\,mol\times S^{\circ}(CO,g)+1\,mol\times S^{\circ}(H_{2}O,g)]$
$=[1\,mol(130.7\,Jmol^{-1}K^{-1})+1\,mol(213.8\,Jmol^{-1}K^{-1})]-[1\,mol(197.7\,Jmol^{-1}K^{-1})+1\,mol(188.8\,Jmol^{-1}K^{-1})]$
$=-42.0\,J/K$
The sign of $\Delta S^{\circ}_{rxn}$ is negative. But, we cannot predict the sign because the number of moles of gas is constant.
