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

Concept: A chemical or electrochemical reaction is said to be spontaneous if it can proceed on its own under given conditions. In electrochemistry, spontaneity is related to Gibbs free energy change and cell potential by the relation: \[ \Delta G^\circ = -nFE^\circ_{\text{cell}} \] where:
• \( \Delta G^\circ \) = standard Gibbs free energy change
• \( n \) = number of electrons transferred
• \( F \) = Faraday constant
• \( E^\circ_{\text{cell}} \) = standard cell potential For a spontaneous reaction: \[ \Delta G^\circ 0 \]

Step 1: Understanding the condition for spontaneity.}
If a reaction occurs spontaneously, the Gibbs free energy of the system decreases. Therefore: \[ \Delta G^\circ < 0 \] This is the fundamental thermodynamic condition for spontaneity.

Step 2: Relating Gibbs free energy with cell potential.}
From the equation: \[ \Delta G^\circ = -nFE^\circ_{\text{cell}} \] we observe that:
• If \( E^\circ_{\text{cell}} > 0 \), then \( \Delta G^\circ < 0 \)
• If \( E^\circ_{\text{cell}} < 0 \), then \( \Delta G^\circ > 0 \) Thus, spontaneous reactions always have negative Gibbs free energy.

Step 3: Checking the given options.}

• \( E^\circ_{\text{red}} \) is negative: Not necessarily true for spontaneity.
• \( \Delta G^\circ \) is negative: Correct condition for spontaneous reaction.
• \( E^\circ_{\text{oxidation}} \) is positive: Alone this does not determine spontaneity.
• \( \Delta G^\circ \) is positive: Indicates non-spontaneous reaction. Therefore, the correct answer is: \[ \boxed{\Delta G^\circ < 0} \]