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. 1.Exothermic if `B lt 0`
B. 2.Exothermic if `A gt 0 and B lt 0`
C. 3.Endothermic if `A lt 0 and B gt 0`
D. 4.Endothermic if `A gt 0`

Explanation

To solve the problem, we need to analyze the relationship between the standard reaction Gibbs energy (ΔG°) and the temperature (T) as given by the equation:

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

where A and B are non-zero constants.

### Step 1: Understand the Gibbs Free Energy Equation
The Gibbs free energy change is related to enthalpy (ΔH) and entropy (ΔS) by the equation:

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

For standard conditions, we can write:

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

### Step 2: Compare the Two Equations
From the given equation, we have:

\[ \Delta G^\circ = A - Bt \]

We can equate this to the standard Gibbs free energy equation:

\[ A - Bt = \Delta H^\circ - T\Delta S^\circ \]

### Step 3: Rearranging the Equation
Rearranging gives us:

\[ \Delta H^\circ = A + T\Delta S^\circ - Bt \]

### Step 4: Analyze Conditions for Spontaneity
For a spontaneous process, we need ΔG° to be less than zero:

\[ A - Bt < 0 \]

This implies:

\[ A < Bt \]

### Step 5: Consider the Signs of A and B
1. **If A > 0**: This suggests that ΔH° could be positive (endothermic).
2. **If A < 0**: This suggests that ΔH° could be negative (exothermic).

Since we are looking for conditions under which the reaction is spontaneous, we need to ensure that the inequality \(A < Bt\) holds true.

### Step 6: Conclusion
From the analysis, we conclude that:

- If A is positive (endothermic reaction), the reaction can still be spontaneous at high temperatures if \(B\) is positive and \(t\) is sufficiently large.
- If A is negative (exothermic reaction), the reaction is likely to be spontaneous at lower temperatures.

Thus, the true statement about the reaction is that it is endothermic if \(A > 0\).

### Final Answer
The correct option is that the reaction is endothermic if \(A > 0\).

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