How can standard reaction entropy be determined from standard emf temperature dependence?

The determination of standard reaction entropy from the temperature dependence of standard emf is grounded in thermodynamic principles that connect electrochemical properties with thermodynamic quantities. The expression for standard reaction entropy, Δ_rS®, is derived from the relationship between the cell potential (emf) and temperature.

The correct formulation states that the change in standard reaction entropy can be determined using the relationship:

Δ_rS® = νF(dE/dT)

Here, ν represents the number of moles of electrons transferred in the reaction, F is Faraday's constant, and dE/dT is the change in the standard electromotive force with respect to temperature. This relationship arises from the fundamental equation of thermodynamics that links Gibbs free energy (G) to emf (E), showing that the change in Gibbs energy of a system is related to its entropy.

Using this equation provides a clear connection between the electrochemical behavior of a reaction and its thermodynamic properties, illustrating how shifts in temperature influence system entropy. This approach is particularly useful because measuring emf is often easier than directly calculating the entropy changes through other methods.

Thus, the first option embodies this connection accurately, reflecting both the dependency of emf on temperature and the amount of charge represented by νF for ionic or electron