The values of `K_(p_(1))` and `K_(p_(2))` for the reactions
`X hArr Y+Z` ….(i)
and `A hArr 2B` …(ii)
are in ratio of 9 : 1. If degree of dissociation of X and A be equal, then total presure at equilibrium (i) and (ii) are in the ratio.

Options

A. `1:1`
B. `3:1`
C. `1:9`
D. `36 :1`

Answer

To solve the problem, we need to analyze the two reactions and their equilibrium constants, as well as the degree of dissociation. Let's break it down step by step.

### Step 1: Define the Reactions and Their Equilibrium Constants
We have two reactions:
1. \( X \rightleftharpoons Y + Z \) (Reaction (i))
2. \( A \rightleftharpoons 2B \) (Reaction (ii))

Given that the equilibrium constants are in the ratio:
\[ K_{p1} : K_{p2} = 9 : 1 \]

### Step 2: Express the Equilibrium Constants
For reaction (i):
\[ K_{p1} = \frac{P_Y \cdot P_Z}{P_X} \]
For reaction (ii):
\[ K_{p2} = \frac{(P_B)^2}{P_A} \]

### Step 3: Degree of Dissociation
Let the degree of dissociation for both reactions be denoted as \( \alpha \).

For reaction (i):
- Initial moles of \( X \) = 1
- At equilibrium, moles of \( X \) = \( 1 - \alpha \)
- Moles of \( Y \) = \( \alpha \)
- Moles of \( Z \) = \( \alpha \)

Thus, the total pressure at equilibrium for reaction (i) can be expressed as:
\[ P_{total1} = P_X + P_Y + P_Z = (1 - \alpha) + \alpha + \alpha = 1 + \alpha \]

For reaction (ii):
- Initial moles of \( A \) = 1
- At equilibrium, moles of \( A \) = \( 1 - \alpha \)
- Moles of \( B \) = \( 2\alpha \)

Thus, the total pressure at equilibrium for reaction (ii) can be expressed as:
\[ P_{total2} = P_A + P_B = (1 - \alpha) + 2\alpha = 1 + \alpha \]

### Step 4: Ratio of Total Pressures
Since we have established that both total pressures are equal:
\[ P_{total1} = 1 + \alpha \]
\[ P_{total2} = 1 + \alpha \]

Thus, the ratio of total pressures at equilibrium for both reactions is:
\[ \frac{P_{total1}}{P_{total2}} = \frac{1 + \alpha}{1 + \alpha} = 1 \]

### Conclusion
The total pressures at equilibrium for reactions (i) and (ii) are in the ratio of:
\[ \text{Ratio} = 1 : 1 \]