A : For an isolated system `Delta G = - TDeltaS_("total")`
R: For an isolated system q = 0.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion , then mark (1)
B. If both Assertion & Reason are true and the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion Reason is false, then mark

Answer

To solve the question, we need to analyze the assertion (A) and reason (R) provided regarding an isolated system.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states: "For an isolated system, ΔG = -TΔS_total."
- In thermodynamics, Gibbs free energy (G) is defined as:
\[ \Delta G = \Delta H - T \Delta S \]
- For an isolated system, there is no heat exchange (Q = 0) and no work done (W = 0). Therefore, the change in internal energy (ΔU) is also 0.

2. **Analyzing Internal Energy Change**:
- According to the first law of thermodynamics:
\[ \Delta U = Q + W \]
- Since both Q and W are 0 for an isolated system:
\[ \Delta U = 0 \]

3. **Understanding Enthalpy Change (ΔH)**:
- The enthalpy change is given by:
\[ \Delta H = \Delta U + P\Delta V \]
- Since ΔU = 0 and for an isolated system, there is no volume change (ΔV = 0), we have:
\[ \Delta H = 0 \]

4. **Substituting into the Gibbs Free Energy Equation**:
- Now substituting ΔH = 0 into the Gibbs free energy equation:
\[ \Delta G = 0 - T \Delta S \]
- This simplifies to:
\[ \Delta G = -T \Delta S_{total} \]
- Therefore, the assertion is true.

5. **Understanding the Reason (R)**:
- The reason states: "For an isolated system, Q = 0."
- This is a fundamental property of isolated systems, as they do not exchange heat or matter with their surroundings. Thus, this statement is also true.

6. **Evaluating the Relationship Between Assertion and Reason**:
- While both the assertion and reason are true, the reason does not explain the assertion. The reason simply states a property of isolated systems without linking it to the Gibbs free energy equation.

### Conclusion:
- Both the assertion (A) and reason (R) are true, but the reason does not correctly explain the assertion. Therefore, the correct option is option 2.