For a reaction `nA hArr A_b`, 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 find the degree of dissociation when A trimerizes in the reaction \( nA \rightleftharpoons A_b \), we can follow these steps:

### Step 1: Define the initial conditions
Assume we start with 1 mole of A. Therefore, the initial concentration of A is 1 mole.

### Step 2: Define the degree of dissociation
Let \( \alpha \) be the degree of dissociation. This means that at equilibrium, a fraction \( \alpha \) of A has dissociated.

### Step 3: Determine the changes in concentration
When A trimerizes, it forms \( A_b \). For every 3 moles of A that react, 1 mole of \( A_b \) is produced. Therefore, if \( \alpha \) moles of A dissociate, the change in concentration can be expressed as:
- Moles of A remaining: \( 1 - \alpha \)
- Moles of \( A_b \) produced: \( \frac{\alpha}{3} \)

### Step 4: Calculate total moles at equilibrium
The total moles at equilibrium can be calculated as:
\[ \text{Total moles} = (1 - \alpha) + \frac{\alpha}{3} \]
This simplifies to:
\[ \text{Total moles} = 1 - \alpha + \frac{\alpha}{3} = 1 - \frac{2\alpha}{3} \]

### Step 5: Relate density to volume
Density (\( D \)) is defined as mass per unit volume. The density before dissociation is inversely proportional to the volume. Thus, we can express the density before and after dissociation:
- Before dissociation: \( D \propto \frac{1}{V} \)
- After dissociation: \( d \propto \frac{1}{V(1 - \frac{2\alpha}{3})} \)

### Step 6: Set up the density ratio
We can set up the ratio of densities before and after dissociation:
\[ \frac{D}{d} = \frac{1}{1 - \frac{2\alpha}{3}} \]

### Step 7: Solve for \( \alpha \)
Rearranging the equation gives:
\[ d = D \cdot (1 - \frac{2\alpha}{3}) \]
From this, we can express \( \alpha \) in terms of the densities:
\[ \frac{D}{d} = 1 - \frac{2\alpha}{3} \]
Solving for \( \alpha \):
\[ \frac{D}{d} - 1 = -\frac{2\alpha}{3} \]
\[ \alpha = \frac{3}{2} \left(1 - \frac{D}{d}\right) \]

### Conclusion
The degree of dissociation \( \alpha \) when A trimerizes can be expressed in terms of the densities before and after the reaction.