Effect of temperature of equilibrium constant is given by `logK_(2)-logK_(1)=(-DeltaH)/(2.303R)[(1)/(T_(2))-(1)/(T_(1))](" where "T_(2)gtT_(1))`. Then for a endothermic reaction the false statement is

Options

A. `[(1)/(T_(2))-(1)/(T_(1))]=" positive"`
B. `logK_(2)gt logK_(1)`
C. `DeltaH=" positive"`
D. `K_(2)gtK_(1)`

Answer

To solve the question regarding the effect of temperature on the equilibrium constant for an endothermic reaction, we will analyze the given equation and the implications of the statements provided.

### Step-by-Step Solution:

1. **Understanding the Van 't Hoff Equation**:
The equation given is:
\[ \log K_2 - \log K_1 = \frac{-\Delta H}{2.303R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \]
where \( K_1 \) and \( K_2 \) are the equilibrium constants at temperatures \( T_1 \) and \( T_2 \) respectively, \( \Delta H \) is the change in enthalpy, and \( R \) is the ideal gas constant.

2. **Identifying the Reaction Type**:
For an endothermic reaction, \( \Delta H \) is positive. This means that as temperature increases, the equilibrium constant \( K \) should also increase, indicating that the forward reaction is favored.

3. **Analyzing the Temperature Condition**:
The condition states that \( T_2 > T_1 \). Therefore, the term \( \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \) will be negative because \( \frac{1}{T_2} < \frac{1}{T_1} \).

4. **Substituting into the Equation**:
Since \( \Delta H \) is positive for an endothermic reaction, the left side of the equation must also be positive for the equation to hold true. Thus:
\[ \log K_2 - \log K_1 = \text{positive} \]
implies that \( K_2 > K_1 \).

5. **Evaluating the Statements**:
- **Statement 1**: If the reaction is endothermic, the statement that the difference in temperatures leads to a negative value is incorrect. This implies that the statement is false.
- **Statement 2**: \( K_2 > K_1 \) is true for an endothermic reaction as explained.
- **Statement 3**: \( \Delta H \) should be positive for an endothermic reaction, which is also true.
- **Statement 4**: The relationship between \( K \) and temperature for endothermic reactions holds true.

6. **Conclusion**:
The false statement regarding the endothermic reaction is the first one, as it incorrectly interprets the relationship between temperature and the equilibrium constant.

### Final Answer:
The false statement regarding the endothermic reaction is **Statement 1**.

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