For a spontaneous process,

Options

A. `DeltaG_("system")=+ve` only
B. `DeltaG_("system")` = zero
C. `DeltaS_("total")=-ve`
D. `DeltaS_("total")=+ve`

Answer

To determine the conditions for a spontaneous process in thermodynamics, we can analyze the Gibbs free energy change (ΔG) using 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-by-Step Solution:

1. **Understanding Spontaneity**:
- A process is considered spontaneous when it occurs without the need for external energy. This is typically indicated by a negative change in Gibbs free energy (ΔG < 0).

2. **Analyzing the Gibbs Free Energy Equation**:
- From the equation ΔG = ΔH - TΔS, we can infer that for ΔG to be negative (indicating spontaneity), the term ΔH - TΔS must also be negative.

3. **Conditions for ΔG < 0**:
- **Case 1**: If ΔH is negative (exothermic reaction) and ΔS is positive (increase in entropy), then ΔG will definitely be negative, indicating a spontaneous process.
- **Case 2**: If ΔH is positive (endothermic reaction) but ΔS is significantly positive, then at high temperatures, TΔS can outweigh ΔH, making ΔG negative.
- **Case 3**: If ΔH is negative and ΔS is negative, ΔG could be negative at low temperatures.

4. **Evaluating the Given Options**:
- **Option A**: ΔG positive → This indicates a non-spontaneous process.
- **Option B**: ΔG = 0 → This indicates a system at equilibrium, not spontaneous.
- **Option C**: ΔS total negative → If ΔS is negative, it can lead to a positive ΔG if ΔH is not sufficiently negative, indicating non-spontaneity.
- **Option D**: ΔS total positive → If ΔS is positive, it can lead to a negative ΔG, indicating a spontaneous process.

5. **Conclusion**:
- The correct condition for a spontaneous process is when the total change in entropy (ΔS) is positive. Therefore, the answer is **Option D**: ΔS total positive.