The weight of gaseous mixture containing `6.02xx10^(23)` molecules of nitrogen and `3.01xx10^(23)` molecules of sulphur dioxide are

Options

A. 28
B. 30
C. 31.36
D. 35

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: Determine the number of moles of nitrogen (N₂)
The number of moles can be calculated using Avogadro's number, which states that 1 mole of any substance contains \(6.02 \times 10^{23}\) molecules.

\[ \text{Moles of } N_2 = \frac{6.02 \times 10^{23} \text{ molecules of } N_2}{6.02 \times 10^{23} \text{ molecules/mole}} = 1 \text{ mole} \]

### Step 2: Calculate the mass of nitrogen (N₂)
The molar mass of nitrogen (N₂) is calculated as follows:
- Atomic mass of nitrogen (N) = 14 g/mol
- Therefore, molar mass of N₂ = \(2 \times 14 = 28 \text{ g/mol}\)

Now, using the number of moles:
\[ \text{Mass of } N_2 = \text{moles} \times \text{molar mass} = 1 \text{ mole} \times 28 \text{ g/mol} = 28 \text{ g} \]

### Step 3: Determine the number of moles of sulfur dioxide (SO₂)
Using the same method:
\[ \text{Moles of } SO_2 = \frac{3.01 \times 10^{23} \text{ molecules of } SO_2}{6.02 \times 10^{23} \text{ molecules/mole}} = 0.5 \text{ moles} \]

### Step 4: Calculate the mass of sulfur dioxide (SO₂)
The molar mass of sulfur dioxide (SO₂) is calculated as follows:
- Atomic mass of sulfur (S) = 32 g/mol
- Atomic mass of oxygen (O) = 16 g/mol
- Therefore, molar mass of SO₂ = \(32 + (2 \times 16) = 32 + 32 = 64 \text{ g/mol}\)

Now, using the number of moles:
\[ \text{Mass of } SO_2 = \text{moles} \times \text{molar mass} = 0.5 \text{ moles} \times 64 \text{ g/mol} = 32 \text{ g} \]

### Step 5: Calculate the total mass of the gaseous mixture
Now, we can find the total mass of the gaseous mixture by adding the masses of nitrogen and sulfur dioxide:
\[ \text{Total mass} = \text{Mass of } N_2 + \text{Mass of } SO_2 = 28 \text{ g} + 32 \text{ g} = 60 \text{ g} \]

### Final Answer:
The weight of the gaseous mixture is **60 grams**.

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