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 of gases A and B, we will follow these steps:

### Step 1: Determine the mass of A
Given:
- Moles of A = 2 moles
- Atomic weight of A = 60 g/mol

To calculate the mass of A:
\[ \text{Mass of A} = \text{Moles} \times \text{Molecular Weight} = 2 \, \text{moles} \times 60 \, \text{g/mol} = 120 \, \text{grams} \]

### Step 2: Determine the mass of B
From the reaction:
\[ A(g) \rightleftharpoons 2B(g) \]
For every 1 mole of A that reacts, 2 moles of B are produced. Since we start with 2 moles of A, we will produce:
\[ \text{Moles of B} = 2 \times 2 = 4 \, \text{moles} \]

### Step 3: Calculate the mass of B
Assuming B has the same atomic weight as A (as it is not given, we will consider it for calculation):
- Atomic weight of B = 60 g/mol (for simplicity, we assume it is the same as A)

To calculate the mass of B:
\[ \text{Mass of B} = \text{Moles of B} \times \text{Molecular Weight} = 4 \, \text{moles} \times 60 \, \text{g/mol} = 240 \, \text{grams} \]

### Step 4: Calculate the total mass of the mixture
The total mass of the equilibrium mixture is the sum of the masses of A and B:
\[ \text{Total Mass} = \text{Mass of A} + \text{Mass of B} = 120 \, \text{grams} + 240 \, \text{grams} = 360 \, \text{grams} \]

### Step 5: Determine the volume of the mixture
The volume of the vessel is given as:
\[ \text{Volume} = 2 \, \text{liters} \]

### Step 6: Calculate the density of the mixture
Density is defined as mass per unit volume:
\[ \text{Density} = \frac{\text{Total Mass}}{\text{Volume}} = \frac{360 \, \text{grams}}{2 \, \text{liters}} = 180 \, \text{grams/liter} \]

### Final Answer
The density of the equilibrium mixture is:
\[ \text{Density} = 180 \, \text{grams/liter} \]

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