The standard reaction Gibbs energy for a temperature T is given by
`Delta_(r)G^(@)= A-Bt`
Where A and B are non-zero constants.
Which of the following is TRUE about this reaction ?

Options

A. Exothermic if `B lt 0`
B. Exothermic if `A gt 0` and `B lt 0`
C. Endothermic if `A lt 0` and `B gt 0`
D. Endothermic if `A gt 0`

Explanation

To solve the problem, we need to analyze the given equation for the standard reaction Gibbs energy:

\[ \Delta_r G^\circ = A - BT \]

where \( A \) and \( B \) are non-zero constants, and \( T \) is the temperature.

### Step-by-step Solution:

1. **Understanding the Gibbs Free Energy Equation**:
The Gibbs free energy change for a reaction at standard conditions is given by:
\[ \Delta G^\circ = \Delta H^\circ - T \Delta S^\circ \]
where \( \Delta H^\circ \) is the change in enthalpy and \( \Delta S^\circ \) is the change in entropy.

2. **Setting the Given Equation**:
We compare the provided equation \( \Delta_r G^\circ = A - BT \) with the standard Gibbs free energy equation. This gives us:
\[ A = \Delta H^\circ \quad \text{and} \quad -B = -\Delta S^\circ \]
Therefore, we can deduce:
\[ \Delta S^\circ = B \]

3. **Determining Spontaneity**:
A process is spontaneous when \( \Delta G^\circ < 0 \). Thus, we set up the inequality:
\[ A - BT < 0 \]
Rearranging this gives:
\[ A < BT \]

4. **Analyzing the Conditions**:
- If \( A < BT \), then as temperature \( T \) increases, the term \( BT \) increases, which means that for a given \( B \), there will be a temperature above which the reaction becomes spontaneous.
- If \( A \) is a constant and \( B \) is positive, then there exists a temperature \( T \) such that the reaction can switch from non-spontaneous to spontaneous.

5. **Considering the Sign of \( A \)**:
- If \( A > 0 \), then \( \Delta H^\circ \) is positive, indicating an endothermic reaction.
- If \( A < 0 \), then \( \Delta H^\circ \) is negative, indicating an exothermic reaction.

6. **Conclusion**:
Since \( A \) is a constant and we are looking for conditions under which the reaction can be spontaneous, we conclude that if \( A > 0 \), the reaction is endothermic. Thus, the correct statement about the reaction is that it is endothermic if \( A > 0 \).

### Final Answer:
The correct statement about this reaction is that it is **endothermic if \( A > 0 \)**.