If Ecell is positive, what is the sign of ∆rG?

In electrochemistry, the relationship between the cell potential (Ecell) and the Gibbs free energy change (∆rG) is defined by the equation:

[ \Delta_r G = -nFE_{cell} ]

In this equation, (n) represents the number of moles of electrons transferred in the electrochemical reaction, and (F) is Faraday's constant, which is a positive value.

When Ecell is positive, it indicates that the electrochemical reaction can occur spontaneously. The cell potential being positive results in a negative value for ∆rG since it is multiplied by -nF. This means that the change in Gibbs free energy is negative for spontaneous reactions. A negative ∆rG indicates that the reaction can proceed forward in the direction of the products without external energy input.

Thus, when Ecell is positive, the sign of ∆rG must be negative, confirming that the reaction is energetically favorable. This principle is foundational in thermodynamics and electrochemistry, linking the spontaneity of reactions to changes in Gibbs free energy.