An exothermic reaction is represented by the graph :

Options

A.
B.
C.
D.

Answer

To solve the question regarding the graph representing an exothermic reaction, we can follow these steps:

### Step 1: Understand the Relationship Between ΔG, ΔH, and ΔS
The Gibbs free energy change (ΔG) is related to the enthalpy change (ΔH) and entropy change (ΔS) by the equation:
\[ \Delta G^0 = \Delta H^0 - T \Delta S^0 \]

### Step 2: Relate ΔG to the Equilibrium Constant (Kp)
The standard Gibbs free energy change is also related to the equilibrium constant (Kp) by the equation:
\[ \Delta G^0 = -RT \ln K_p \]

### Step 3: Combine the Two Equations
We can substitute the second equation into the first:
\[ -RT \ln K_p = \Delta H^0 - T \Delta S^0 \]

### Step 4: Rearrange the Equation
Now, divide both sides by \(-RT\):
\[ \ln K_p = -\frac{\Delta H^0}{R} \cdot \frac{1}{T} + \frac{\Delta S^0}{R} \]

### Step 5: Identify the Linear Relationship
This equation can be compared to the linear equation \(y = mx + c\), where:
- \(y = \ln K_p\)
- \(x = \frac{1}{T}\)
- The slope \(m = -\frac{\Delta H^0}{R}\)
- The intercept \(c = \frac{\Delta S^0}{R}\)

### Step 6: Determine the Sign of the Slope for an Exothermic Reaction
For an exothermic reaction, ΔH^0 is negative. Therefore, the slope \(m\) becomes:
\[ m = -\frac{\Delta H^0}{R} \quad \text{(where ΔH^0 < 0)} \]
This means that the slope will be positive since a negative divided by a negative is positive.

### Step 7: Identify the Correct Graph
Since the slope is positive and there is an intercept, the graph that represents this relationship will be a straight line with a positive slope. Therefore, the correct graph will show a positive slope with an intercept.

### Conclusion
The graph representing an exothermic reaction, based on the analysis above, will be the one with a positive slope and an intercept.

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