The weight of gaseous mixture containing `6.02 xx 10^(23)` molecules of nitrogen and `3.01 xx 10^(23)` molecules of sulphur dioxide are

Options

A. 46
B. 92
C. 60
D. 30

Explanation

To find the weight of the gaseous mixture containing \(6.02 \times 10^{23}\) molecules of nitrogen (N₂) and \(3.01 \times 10^{23}\) molecules of sulfur dioxide (SO₂), we will follow these steps:

### Step 1: Calculate the molecular mass of nitrogen (N₂)
- The atomic mass of nitrogen (N) is 14 g/mol.
- Since nitrogen is diatomic (N₂), the molecular mass of nitrogen is:
\[ \text{Molecular mass of N₂} = 2 \times 14 \, \text{g/mol} = 28 \, \text{g/mol} \]

### Step 2: Calculate the molecular mass of sulfur dioxide (SO₂)
- The atomic mass of sulfur (S) is 32 g/mol and the atomic mass of oxygen (O) is 16 g/mol.
- The molecular mass of sulfur dioxide is:
\[ \text{Molecular mass of SO₂} = 32 \, \text{g/mol} + 2 \times 16 \, \text{g/mol} = 32 \, \text{g/mol} + 32 \, \text{g/mol} = 64 \, \text{g/mol} \]

### Step 3: Calculate the weight of nitrogen (N₂) in the mixture
- We know that \(6.02 \times 10^{23}\) molecules correspond to 1 mole, which weighs 28 g.
- Therefore, the weight of \(6.02 \times 10^{23}\) molecules of nitrogen is:
\[ \text{Weight of N₂} = 28 \, \text{g} \]

### Step 4: Calculate the weight of sulfur dioxide (SO₂) in the mixture
- For sulfur dioxide, we have \(3.01 \times 10^{23}\) molecules.
- We know that \(6.02 \times 10^{23}\) molecules correspond to 64 g (1 mole).
- To find the weight of \(3.01 \times 10^{23}\) molecules, we can use the unitary method:
\[ \text{Weight of SO₂} = \left(\frac{64 \, \text{g}}{6.02 \times 10^{23} \, \text{molecules}}\right) \times 3.01 \times 10^{23} \, \text{molecules} \]
\[ \text{Weight of SO₂} = \frac{64 \, \text{g}}{2} = 32 \, \text{g} \]

### Step 5: Calculate the total weight of the gaseous mixture
- Now, we can find the total weight of the gaseous mixture by adding the weights of nitrogen and sulfur dioxide:
\[ \text{Total weight of gaseous mixture} = \text{Weight of N₂} + \text{Weight of SO₂} \]
\[ \text{Total weight of gaseous mixture} = 28 \, \text{g} + 32 \, \text{g} = 60 \, \text{g} \]

### Final Answer
The weight of the gaseous mixture is \(60 \, \text{g}\).

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