In a reversible reaction `K_(c) gt K_(p) and Delta ` H = + 40 K. Cal. The product will be obtained in less amount on

Options

A. Increasing both pressure & temperature
B. Decreasing both pressure & temperature
C. Decreasing pressure & increasing temperature
D. Increasing pressure & decreasing temperature

Answer

To solve the problem, we need to analyze the given information about the reversible reaction.

### Step 1: Understand the relationship between Kc and Kp
We know that:
- \( K_c \) is the equilibrium constant in terms of concentration.
- \( K_p \) is the equilibrium constant in terms of partial pressure.

The relationship between \( K_c \) and \( K_p \) is given by the equation:
\[ K_p = K_c \left( RT \right)^{\Delta n} \]
where \( \Delta n \) is the change in the number of moles of gas, calculated as:
\[ \Delta n = \text{moles of products} - \text{moles of reactants} \]

### Step 2: Analyze the given condition \( K_c > K_p \)
Since \( K_c > K_p \), this implies that:
\[ \Delta n < 0 \]
This means that the number of moles of products is less than the number of moles of reactants. Therefore, the forward reaction produces fewer moles of gas.

### Step 3: Consider the effect of temperature and enthalpy change
We are given that:
\[ \Delta H = +40 \, \text{kcal} \]
This indicates that the reaction is endothermic (absorbs heat). According to Le Chatelier's principle:
- If we increase the temperature, the endothermic reaction (forward reaction) will be favored.
- If we decrease the temperature, the exothermic reaction (backward reaction) will be favored.

### Step 4: Analyze the effect of pressure
In terms of pressure:
- If the number of moles decreases in the forward reaction (as we found earlier), increasing the pressure will favor the forward reaction.
- Conversely, decreasing the pressure will favor the backward reaction.

### Step 5: Conclusion
From the analysis:
- The backward reaction is favored by decreasing temperature and decreasing pressure.
- Since \( K_c > K_p \) and \( \Delta H \) is positive, the products will be obtained in less amount under conditions of lower temperature and lower pressure.

Thus, the product will be obtained in less amount when the temperature and pressure are decreased.

### Final Answer
The product will be obtained in less amount on decreasing temperature and pressure.

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