Problem: Find ΔS°rxn for the combustion of ethane (C2H6) to carbon dioxide and gaseous water. Is the sign of ΔS°rxn as expected?

Step 1:

C₂H₆ (g) + 7/2 O₂ (g) → 2 CO₂ (g) + 3 H₂O (g)

          Reactant          Product

C            2                       1 2

H            6                       2 6

O            2 7                    3 7

Balanced chemical equation

2 C₂H₆ (g) + 7 O₂ (g) → 4 CO₂ (g) + 6 H₂O (g)

9 mol gas reactant → 10 mol gas reactant

increase in entropy

sign of ΔS should be positive

Step 2:

$$\begin{gathered} \boxed{\mathbf{∆}\mathbf{S}{\mathbf{°}}_{\mathbf{rxn}}\mathbf{ }\mathbf{=}\mathbf{S}{\mathbf{°}}_{\mathbf{product}}\mathbf{ }\mathbf{-}\mathbf{ }\mathbf{S}{\mathbf{°}}_{\mathbf{reactant}}} \\ \mathbf{∆}\mathbf{S}{\mathbf{°}}_{\mathbf{rxn}}\mathbf{ }\mathbf{=}[S{°}_{{\mathrm{CO}}_2 \left(g\right)} +S{°}_{H_{2}O \left(g\right)} ]\mathbf{ }\mathbf{-}\mathbf{ }[S{°}_{C_2{H}_6 \left(g\right)} + S{°}_{O_2 \left(g\right)}] \end{gathered}$$