The relative density of a mixture of ${\mathrm{CO}}_2\left(\mathrm{g}\right)$ and ${\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$ w.r.t. gaseous hydrogen atoms is 30. The mol% of the ${\mathrm{CO}}_2$ is :

Given Data:

• The mixture consists of CO₂(g) and H₂O(g).
• Relative density of the mixture w.r.t. hydrogen atoms = 30.
• Molar mass of hydrogen atoms (H) = 1 g/mol.

Relative Density Formula:

Relative density = (Average molar mass of the mixture) / (Molar mass of reference)

Here, the reference is hydrogen atoms (1 g/mol). Thus:

Average molar mass of the mixture = Relative density × Molar mass of hydrogen atoms

Substitute the values:

Average molar mass of the mixture = 30 × 1 = 30 g/mol.

Mole Fractions:

• Mole fraction of CO₂: x
• Mole fraction of H₂O: 1 - x

Average Molar Mass of the Mixture:

Average molar mass = x × (Molar mass of CO₂) + (1 - x) × (Molar mass of H₂O)

• Molar mass of CO₂: 44 g/mol
• Molar mass of H₂O: 18 g/mol

Thus:

30 = x × 44 + (1 - x) × 18

Expand the equation:

30 = 44x + 18 - 18x

30 = 26x + 18

26x = 12

x = 12/26 = 6/13

Mole percent of CO₂:

Mole percent = x × 100 = (6/13) × 100 = 600/13

Final Answer:

The mol% of CO₂ is: 600/13