A gaseous mixture of `H_(2)` and `CO_(2)` gas contains 66 mass `%` of `CO_(2)` . The vapour density of the mixture is `:`

Options

A. `6.1`
B. `5.4`
C. `2.7`
D. `10.8`

Explanation

To find the vapor density of a gaseous mixture of \( H_2 \) and \( CO_2 \) that contains 66 mass % of \( CO_2 \), we can follow these steps:

### Step 1: Calculate the mass of each component in a 100 g sample
Since we are considering a 100 g sample of the mixture:
- Mass of \( CO_2 \) = 66 g (since it is 66 mass %)
- Mass of \( H_2 \) = 100 g - 66 g = 34 g

### Step 2: Calculate the number of moles of each component
- Molar mass of \( CO_2 \) = 44 g/mol
- Molar mass of \( H_2 \) = 2 g/mol

Now, we can calculate the number of moles:
- Moles of \( CO_2 \):
\[ \text{Moles of } CO_2 = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{66 \text{ g}}{44 \text{ g/mol}} = 1.5 \text{ moles} \]

- Moles of \( H_2 \):
\[ \text{Moles of } H_2 = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{34 \text{ g}}{2 \text{ g/mol}} = 17 \text{ moles} \]

### Step 3: Calculate the total number of moles in the mixture
Total moles in the mixture:
\[ \text{Total moles} = \text{Moles of } CO_2 + \text{Moles of } H_2 = 1.5 + 17 = 18.5 \text{ moles} \]

### Step 4: Calculate the average molar mass of the mixture
To find the average molar mass, we can use the formula:
\[ \text{Average Molar Mass} = \frac{\text{Total mass of the mixture}}{\text{Total moles}} = \frac{100 \text{ g}}{18.5 \text{ moles}} \approx 5.41 \text{ g/mol} \]

### Step 5: Calculate the vapor density of the mixture
The vapor density (VD) is given by the formula:
\[ \text{Vapor Density} = \frac{\text{Average Molar Mass}}{2} \]
Thus,
\[ \text{Vapor Density} = \frac{5.41 \text{ g/mol}}{2} \approx 2.70 \text{ g/mol} \]

### Final Answer
The vapor density of the mixture is approximately \( 2.7 \text{ g/mol} \).

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