Standard reaction entropy

Just as the standard reaction enthalpy is

the standard reaction entropy of a system is

where v_P and v_R are the stoichiometric coefficients of the products and reactants respectively.

The difference between ΔH_f^o and S_m^o is that the former is the relative energy between a substance and the constituents of the substance in their reference states, while the latter is the absolute energy of the substance. This is why ΔH_f^o[C(graphite)] = 0 but S_m^o[C(graphite)] ≠ 0. Despite the difference, the quantities of ΔH_r^o and ΔS_r^o are comparable, as the zero-enthalpies of reference states in and cancel out when we compute ΔH_r^o (see articles on standard enthalpy change of formation and Hess Law for details).

 

 

The positive change in standard reaction entropy of the incomplete combustion of carbon illustrates the dependency of the change in entropy of a system on the change in the number of moles of gas in a reaction. In the above example, the double in number of moles of gas outweighs the removal of a mole of carbon solid in the system, as the increase in the number of moles of gas leads to the dispersal of energy over a greater number of translational energy states of the system. This implies that ΔS_r^o can be negative when we have a reaction that results in a decrease the number of moles of gas.

 

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