Cell reaction is spontlaneous when

Options

A. `DeltaG^(@)` is negative
B. `DeltaG^(@)` is positive
C. `DeltaE_("Red")^(@)` is positive
D. `DeltaE_("Red")^(@)` is negative

Answer

To determine when a cell reaction is spontaneous, we can use the Gibbs free energy change (ΔG) as a criterion. Here’s a step-by-step solution:

### Step 1: Understand Gibbs Free Energy (ΔG)
Gibbs free energy is a thermodynamic potential that can be used to predict whether a reaction will occur spontaneously at constant temperature and pressure. The change in Gibbs free energy (ΔG) is given by the equation:

\[ \Delta G = \Delta H - T \Delta S \]

Where:
- ΔG = change in Gibbs free energy
- ΔH = change in enthalpy
- T = temperature (in Kelvin)
- ΔS = change in entropy

### Step 2: Analyze the Sign of ΔG
For a reaction to be spontaneous, the change in Gibbs free energy (ΔG) must be negative:

\[ \Delta G < 0 \]

This indicates that the reaction can occur without the input of external energy.

### Step 3: Consider the Components of ΔG
- **ΔH (Enthalpy Change)**: If ΔH is negative (exothermic reaction), it favors spontaneity.
- **TΔS (Temperature and Entropy Change)**: If ΔS is positive, it also favors spontaneity, especially at higher temperatures.

### Step 4: Conclusion
A cell reaction is spontaneous when:

1. ΔG is negative.
2. This can occur under conditions where ΔH is negative, ΔS is positive, or both.

### Final Answer
A cell reaction is spontaneous when ΔG < 0.

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