A reversible reaction is endothermic in forward direction. Then which of the following is (are) correct?

Options

A. In K vs `1//T` will be a straight line with negative slope
B. `d/(dT) ln K gt 0`
C. A plot of d ln K against `1//T^(2)` will have positive slope
D. An increase in temperature will shift the reaction in the forward direction.

Explanation

To solve the question about a reversible endothermic reaction, we will analyze each option based on the principles of chemical equilibrium and the Van't Hoff equation.

### Step-by-Step Solution:

1. **Understanding Endothermic Reactions**:
- In an endothermic reaction, heat is absorbed during the reaction. This means that if we increase the temperature, the equilibrium will shift towards the products to absorb the added heat.

2. **Using the Van't Hoff Equation**:
- The Van't Hoff equation relates the change in the equilibrium constant (K) with temperature (T) and enthalpy change (ΔH). The equation is:
\[ \frac{d \ln K}{dT} = \frac{\Delta H^\circ}{R T^2} \]
- Here, ΔH is positive for endothermic reactions, R is the universal gas constant, and T is the temperature.

3. **Analyzing Option 1**:
- The question states that \( \ln K \) versus \( \frac{1}{T} \) will be a straight line with a negative slope.
- From the rearranged Van't Hoff equation:
\[ \ln K = \frac{\Delta H^\circ}{R} \left(-\frac{1}{T}\right) + C \]
- This is in the form of \( y = mx + c \) where the slope (m) is negative. Thus, **Option 1 is correct**.

4. **Analyzing Option 2**:
- The equation \( \frac{d \ln K}{dT} > 0 \) indicates that as temperature increases, \( \ln K \) also increases.
- Since ΔH is positive for endothermic reactions, this means that **Option 2 is also correct**.

5. **Analyzing Option 3**:
- The plot of \( \frac{d \ln K}{dT} \) against \( \frac{1}{T^2} \) can be derived from the first equation:
\[ \frac{d \ln K}{dT} = \frac{\Delta H^\circ}{R} \cdot \frac{1}{T^2} \]
- This is a linear relationship where the slope is positive, indicating that **Option 3 is correct**.

6. **Analyzing Option 4**:
- According to Le Chatelier's principle, increasing the temperature of an endothermic reaction shifts the equilibrium towards the products.
- This means that the reaction will favor the forward direction upon heating, confirming that **Option 4 is correct**.

### Conclusion:
All options provided in the question are correct.