Cell reaction is spontaneous, when:

• a. G is negative
• b. E is negative
• c. G is positive
• d. E is positive

To determine when a cell reaction is spontaneous, we need to look at the Gibbs free energy change (G) and the cell potential (E). The correct answer to your question is that a cell reaction is spontaneous when G is negative. Let's break this down further to understand why that is the case.

Understanding Gibbs Free Energy (G)

The Gibbs free energy is a thermodynamic potential that helps predict whether a reaction will occur spontaneously at constant temperature and pressure. A negative change in Gibbs free energy (ΔG < 0) indicates that the process can occur without the input of external energy, meaning it is spontaneous.

Relationship Between Gibbs Free Energy and Cell Potential

In electrochemistry, the relationship between Gibbs free energy and cell potential is given by the equation:

ΔG = -nFE

• ΔG is the change in Gibbs free energy.
• n is the number of moles of electrons transferred in the reaction.
• F is Faraday's constant (approximately 96485 C/mol).
• E is the cell potential (voltage) of the electrochemical cell.

From this equation, we can see that if the cell potential (E) is positive, then ΔG will be negative, indicating that the reaction is spontaneous. Conversely, if E is negative, ΔG will be positive, and the reaction will not be spontaneous.

Examples to Illustrate

Consider a simple electrochemical cell, such as a zinc-copper cell. In this cell:

• The zinc electrode undergoes oxidation, losing electrons.
• The copper electrode undergoes reduction, gaining electrons.

The overall cell reaction has a positive cell potential (E), which means that the Gibbs free energy change (ΔG) is negative, confirming that the reaction is spontaneous.

Why Other Options Are Incorrect

• Option b (E is negative): This indicates a non-spontaneous reaction, as ΔG would be positive.
• Option c (G is positive): This also indicates a non-spontaneous reaction.
• Option d (E is positive): This is actually the condition for spontaneity, but it does not directly answer the question about G.

In summary, a cell reaction is spontaneous when the Gibbs free energy change (G) is negative. This is directly linked to the cell potential (E) being positive, which indicates that the reaction can proceed without external energy input. Understanding this relationship is crucial for predicting the behavior of electrochemical cells in various applications.