If the cell reaction is spontaneous then:

Options

A. `DeltaG^(o) `is + ve
B. `E^(o) "" _(red)` is - ve
C. `E^(o) "" _(red)` is +ve
D. `DeltaG^(o) `is - ve

Answer

To determine the conditions under which a cell reaction is spontaneous, we can follow these steps:

### Step 1: Understand the definition of spontaneity
A spontaneous reaction is one that occurs without the need for external energy or force. This means the reaction can proceed on its own.

**Hint:** Think of natural processes that occur without any intervention, like a waterfall flowing down.

### Step 2: Relate spontaneity to Gibbs Free Energy
For a reaction to be spontaneous, the change in Gibbs Free Energy (ΔG) must be negative. This is a fundamental criterion in thermodynamics.

**Hint:** Remember that a negative ΔG indicates that the process can occur naturally.

### Step 3: Connect Gibbs Free Energy to standard electrode potential
The relationship between Gibbs Free Energy and standard electrode potential (E°) is given by the equation:
\[ \Delta G° = -nFE° \]
where:
- \( n \) = number of moles of electrons transferred
- \( F \) = Faraday's constant (approximately 96500 C/mol)
- \( E° \) = standard electrode potential

**Hint:** The negative sign in the equation indicates that if E° is positive, ΔG° will be negative.

### Step 4: Determine the implications of E°
If ΔG° must be negative for spontaneity, then E° must be positive. If E° were negative, ΔG° would become positive, indicating a non-spontaneous process.

**Hint:** Think about how the sign of E° affects the sign of ΔG°.

### Step 5: Conclusion
Therefore, for a cell reaction to be spontaneous, the following conditions must hold:
- ΔG° must be negative
- E° must be positive

In summary, if the cell reaction is spontaneous, then ΔG° is negative, which implies that E° is positive.

**Final Answer:** If the cell reaction is spontaneous, then ΔG° must be negative.