2 mole of A (atomic weight =60 ) is taken in a 2 litre vessel which immediately comes into equilibrium with B as follows,
`A(g) hArr 2B(g)`
The density of the equilibrium mixture is

Options

A. 0.6 gm/L
B. 0.06 gm/mL
C. 3.6 gm/L
D. data insufficient

Answer

To find the density of the equilibrium mixture in the given reaction \( A(g) \rightleftharpoons 2B(g) \), we can follow these steps:

### Step 1: Determine the initial conditions
We are given:
- 2 moles of A
- Atomic weight of A = 60 g/mol
- Volume of the vessel = 2 liters

### Step 2: Calculate the mass of A
The mass of A can be calculated using the formula:
\[ \text{Mass} = \text{Moles} \times \text{Molecular Weight} \]
Substituting the values:
\[ \text{Mass of A} = 2 \, \text{moles} \times 60 \, \text{g/mol} = 120 \, \text{grams} \]

### Step 3: Understand the reaction at equilibrium
The reaction is:
\[ A \rightleftharpoons 2B \]
At equilibrium, if \( x \) moles of A dissociate, then:
- Moles of A at equilibrium = \( 2 - x \)
- Moles of B at equilibrium = \( 2x \)

### Step 4: Apply conservation of mass
Since the total mass before and after the reaction remains the same, we can say:
\[ \text{Total mass at equilibrium} = \text{Mass of A} + \text{Mass of B} \]
However, we know that the mass of the system remains 120 grams (as calculated from A).

### Step 5: Calculate the total moles at equilibrium
At equilibrium, the total moles can be expressed as:
\[ \text{Total moles} = (2 - x) + 2x = 2 + x \]
Assuming complete dissociation of A (i.e., \( x = 2 \)):
\[ \text{Total moles} = 2 + 2 = 4 \, \text{moles} \]

### Step 6: Calculate the density
Density is defined as:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
Substituting the values we have:
\[ \text{Density} = \frac{120 \, \text{grams}}{2 \, \text{liters}} = \frac{120 \, \text{grams}}{2000 \, \text{milliliters}} = 0.06 \, \text{grams/milliliter} \]

### Conclusion
The density of the equilibrium mixture is \( 0.06 \, \text{grams/milliliter} \).

### Final Answer
The correct option is 2: \( 0.06 \, \text{grams/milliliter} \).

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