A gaseous mixture of `H_(2)` and `CO_(2)` gas contains `88%` by mass
of `CO_(2)`. The vapour density of the mixture is :

Options

A. `19.48`
B. `11.5`
C. `6.25`
D. Cannot be determined

Explanation

To find the vapor density of a gaseous mixture of H₂ and CO₂ that contains 88% by mass of CO₂, we can follow these steps:

### Step 1: Determine the mass of each component in the mixture.
Assume the total mass of the gaseous mixture is 100 grams. Since CO₂ constitutes 88% by mass, we have:
- Mass of CO₂ = 88 grams
- Mass of H₂ = 100 grams - 88 grams = 12 grams

### Step 2: Calculate the number of moles of each gas.
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
- For CO₂ (molar mass = 44 g/mol):
\[ \text{Moles of CO₂} = \frac{88 \text{ g}}{44 \text{ g/mol}} = 2 \text{ moles} \]
- For H₂ (molar mass = 2 g/mol):
\[ \text{Moles of H₂} = \frac{12 \text{ g}}{2 \text{ g/mol}} = 6 \text{ moles} \]

### Step 3: Calculate the total number of moles in the mixture.
\[ \text{Total moles} = \text{Moles of CO₂} + \text{Moles of H₂} = 2 + 6 = 8 \text{ moles} \]

### Step 4: Calculate the average molar mass of the mixture.
The average molar mass (M_avg) can be calculated using the total mass and total moles:
\[ M_{\text{avg}} = \frac{\text{Total mass}}{\text{Total moles}} = \frac{100 \text{ g}}{8 \text{ moles}} = 12.5 \text{ g/mol} \]

### Step 5: Calculate the vapor density of the mixture.
The vapor density (VD) is given by:
\[ \text{Vapor Density} = \frac{M_{\text{avg}}}{2} \]
Substituting the average molar mass:
\[ \text{Vapor Density} = \frac{12.5 \text{ g/mol}}{2} = 6.25 \]

### Final Answer:
The vapor density of the mixture is **6.25**.

---