For a reaction `nA hArr A_n`, degree of dissociation when A trimerises is

Options

A. `2((d-D)/d)`
B. `3/2((d-D)/d)`
C. `4/3((d-D)/d)`
D. `2((D-d)/d)`

Answer

To solve the problem regarding the degree of dissociation when A trimerizes (i.e., \( nA \rightleftharpoons A_n \)), we will follow these steps:

### Step 1: Understand the Reaction
The reaction given is \( 3A \rightleftharpoons A_3 \). This means that three moles of A combine to form one mole of the trimer \( A_3 \).

### Step 2: Define Initial Conditions
Initially, we have:
- Moles of A = 1 (let's assume we start with 1 mole of A)
- Moles of \( A_3 \) = 0

### Step 3: Define Degree of Dissociation
Let \( \alpha \) be the degree of dissociation of A. This means that a fraction \( \alpha \) of A has reacted to form \( A_3 \).

### Step 4: Calculate Final Moles
After dissociation:
- Moles of A remaining = \( 1 - \alpha \)
- Moles of \( A_3 \) formed = \( \frac{\alpha}{3} \) (since 3 moles of A form 1 mole of \( A_3 \))

### Step 5: Total Moles After Reaction
The total number of moles after the reaction can be calculated as:
\[ \text{Total moles} = (1 - \alpha) + \frac{\alpha}{3} \]
This simplifies to:
\[ \text{Total moles} = 1 - \alpha + \frac{\alpha}{3} = 1 - \frac{3\alpha}{3} + \frac{\alpha}{3} = 1 - \frac{2\alpha}{3} \]

### Step 6: Relate Density to Moles
Let \( D \) be the density before dissociation and \( d \) be the density after dissociation. The density is directly proportional to the number of moles, so we can write:
\[ D \propto 1 \quad \text{(before reaction)} \]
\[ d \propto 1 - \frac{2\alpha}{3} \quad \text{(after reaction)} \]

### Step 7: Set Up the Equation
From the proportionality, we can set up the equation:
\[ \frac{d}{D} = 1 - \frac{2\alpha}{3} \]
Rearranging gives:
\[ \frac{d}{D} = 1 - \frac{2\alpha}{3} \implies 2\alpha = 3(1 - \frac{d}{D}) \implies \alpha = \frac{3}{2}(1 - \frac{d}{D}) \]

### Step 8: Final Expression for Degree of Dissociation
Thus, we can express the degree of dissociation \( \alpha \) as:
\[ \alpha = \frac{3}{2} \left( \frac{D - d}{D} \right) \]

### Conclusion
The degree of dissociation when A trimerizes is given by:
\[ \alpha = \frac{3}{2} \frac{D - d}{D} \]