Question

Cell reaction is spontaneous when:

• A. \( E^\circ_{\text{red}} \) is negative
• B. \( \Delta G^\circ \) is negative
• C. \( E^\circ_{\text{oxidation}} \) is positive
• D. \( \Delta G^\circ \) is positive

Hint:

Remember the relation: \[ \Delta G^\circ = -nFE^\circ_{\text{cell}} \] \[ E^\circ_{\text{cell}} > 0 \Rightarrow \Delta G^\circ < 0 \] Positive cell potential always indicates a spontaneous electrochemical reaction.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Spontaneity refers to the tendency of a physical or chemical process to occur on its own without requiring a continuous input of energy.
The absolute thermodynamic criterion for spontaneity in any process occurring at constant temperature and pressure is a decrease in Gibbs free energy (\(\Delta G\)).
If \(\Delta G\) is negative, the reaction can proceed forward. If \(\Delta G\) is positive, the reaction is non-spontaneous and requires external work to occur.
Step 2: Key Formula or Approach:
In electrochemistry, the Gibbs free energy change of a cell reaction is directly related to the electromotive force (EMF) or cell potential (\(E_{cell}\)) by the following equation:
\[ \Delta G = -n \cdot F \cdot E_{cell} \]
Where:
\(n\) is the number of moles of electrons transferred.
\(F\) is Faraday's constant ($96,500 C/mol$).
\(E_{cell}\) is the cell potential.
For standard conditions, the equation is:
\[ \Delta G^{\circ} = -n \cdot F \cdot E_{cell}^{\circ} \]
Step 3: Detailed Explanation:
Let's analyze the signs in the formula:
Since \(n\) and \(F\) are always positive constants, the sign of \(\Delta G^{\circ}\) is always the opposite of the sign of \(E_{cell}^{\circ}\).
1. For Spontaneous Reactions: \(\Delta G^{\circ}\) must be negative ($< 0$). To achieve this, \(E_{cell}^{\circ}\) must be positive ($> 0$).
2. For Non-Spontaneous Reactions: \(\Delta G^{\circ}\) is positive ($> 0$), which occurs when \(E_{cell}^{\circ}\) is negative ($< 0$).
3. For Equilibrium: \(\Delta G^{\circ} = 0\) and \(E_{cell}^{\circ} = 0\).
Reviewing the options:
(A) \(E_{red}^{\circ}\) negative: This describes a single electrode, not the whole cell.
(B) \(\Delta G^{\circ}\) negative: This is the definitive condition for spontaneity in all thermodynamics.
(C) \(E_{oxidation}^{\circ}\) positive: Again, this only describes one half-cell and doesn't confirm the spontaneity of the combined cell reaction.
(D) \(\Delta G^{\circ}\) positive: This indicates a non-spontaneous reaction.
Step 4: Final Answer:
A cell reaction is spontaneous when the standard Gibbs free energy change (\(\Delta G^{\circ}\)) is negative.