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

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

• A. Positive
• B. Negative
• C. Zero
• D. Indeterminate

Answer: (B)

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.

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.