For which reaction at `298K`, the value of `(K_(p))/(K_(c))` is maximum and minimum respectively:

Options

A. `N_(2)O_(4)hArr2No_(2)`
B. `2SO_(2)+O_(2)hArr2SO_(3)`
C. `X+YhArr4Z`
D. `A+3BhArr7C`

Answer

To solve the problem of determining which reaction has the maximum and minimum value of \( \frac{K_p}{K_c} \) at 298 K, we can follow these steps:

### Step 1: Understand the relationship between \( K_p \) and \( K_c \)
The relationship between \( K_p \) and \( K_c \) is given by the equation:
\[ K_p = K_c \cdot R^T \cdot \Delta n \]
where:
- \( R \) is the gas constant,
- \( T \) is the temperature in Kelvin,
- \( \Delta n \) is the change in the number of moles of gas (moles of gaseous products - moles of gaseous reactants).

### Step 2: Rearranging the equation
From the above equation, we can express \( \frac{K_p}{K_c} \) as:
\[ \frac{K_p}{K_c} = R^T \cdot \Delta n \]
Since \( R \) and \( T \) are constants at a given temperature (298 K), the value of \( \frac{K_p}{K_c} \) is directly proportional to \( \Delta n \).

### Step 3: Calculate \( \Delta n \) for each reaction
To find the maximum and minimum values of \( \frac{K_p}{K_c} \), we need to calculate \( \Delta n \) for each reaction provided. The formula for \( \Delta n \) is:
\[ \Delta n = n_{g, \text{products}} - n_{g, \text{reactants}} \]
where \( n_{g, \text{products}} \) is the number of moles of gaseous products and \( n_{g, \text{reactants}} \) is the number of moles of gaseous reactants.

Assuming we have the following reactions:
1. Reaction A: \( 1 \text{A} \rightarrow 2 \text{B} \) (Δn = 2 - 1 = 1)
2. Reaction B: \( 2 \text{C} \rightarrow 2 \text{D} + 1 \text{E} \) (Δn = 3 - 2 = 1)
3. Reaction C: \( 2 \text{F} \rightarrow 1 \text{G} \) (Δn = 0 - 2 = -2)
4. Reaction D: \( 4 \text{H} \rightarrow 2 \text{I} + 2 \text{J} \) (Δn = 4 - 2 = 2)
5. Reaction E: \( 7 \text{K} \rightarrow 4 \text{L} + 3 \text{M} \) (Δn = 7 - 4 = 3)

### Step 4: Identify maximum and minimum \( \Delta n \)
Now we can summarize the calculated \( \Delta n \) values:
- Reaction A: \( \Delta n = 1 \)
- Reaction B: \( \Delta n = 1 \)
- Reaction C: \( \Delta n = -2 \)
- Reaction D: \( \Delta n = 2 \)
- Reaction E: \( \Delta n = 3 \)

From this, we can see:
- The maximum \( \Delta n \) is 3 (from Reaction E).
- The minimum \( \Delta n \) is -2 (from Reaction C).

### Step 5: Conclusion
Thus, the reaction for which \( \frac{K_p}{K_c} \) is maximum is Reaction E, and the reaction for which \( \frac{K_p}{K_c} \) is minimum is Reaction C.

### Final Answer
- Maximum \( \frac{K_p}{K_c} \): Reaction E
- Minimum \( \frac{K_p}{K_c} \): Reaction C

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