Question

A gaseous mixture containing H\(_2\), He, and O\(_2\) exerts a pressure of 1 bar. The weight percentage of H\(_2\) and He is 20 and 16 respectively. What is the ratio of partial pressures of O\(_2\), He and H\(_2\)?

• A. 1 : 2 : 5
• B. 5 : 2 : 1
• C. 2 : 1 : 5
• D. 2.5 : 1 : 1

Hint:

Partial pressure \(\propto\) mole fraction \(\propto \frac{\text{mass}}{\text{molar mass}}\)

Answer 1

The Correct Option is A

Given: - Weight % of H\(_2\) = 20% - Weight % of He = 16% - So, O\(_2\) = 100 - 20 - 16 = 64% Let’s convert to moles: \[ \text{Moles of H}_2 = \frac{20}{2} = 10
\text{Moles of He} = \frac{16}{4} = 4
\text{Moles of O}_2 = \frac{64}{32} = 2 \] Total moles = \(10 + 4 + 2 = 16\)
Partial pressure \(\propto\) mole fraction:
\[ P_{H_2} : P_{He} : P_{O_2} = \frac{10}{16} : \frac{4}{16} : \frac{2}{16} = 5 : 2 : 1 \Rightarrow \boxed{1 : 2 : 5} \text{ (in reverse)} \] As the question asks for \(O_2 : He : H_2\), the correct order is: \[ \boxed{1 : 2 : 5} \]

Answer 2

A gaseous mixture containing H₂, He, and O₂ exerts a pressure of 1 bar. The weight percentage of H₂ and He is 20 and 16 respectively. What is the ratio of partial pressures of O₂, He and H₂?

Step 1: Let the total mass of the gas mixture be 100 g (for simplicity):
- Mass of H₂ = 20 g
- Mass of He = 16 g
- Mass of O₂ = 100 – (20 + 16) = 64 g

Step 2: Calculate number of moles of each gas:
- Molar mass of H₂ = 2 g/mol → Moles of H₂ = 20 / 2 = 10 mol
- Molar mass of He = 4 g/mol → Moles of He = 16 / 4 = 4 mol
- Molar mass of O₂ = 32 g/mol → Moles of O₂ = 64 / 32 = 2 mol

Step 3: Total moles of the mixture:
\[ n_{\text{total}} = 10 + 4 + 2 = 16\ \text{mol} \]

Step 4: Calculate mole fractions (and hence partial pressures):
Total pressure = 1 bar
Partial pressure is proportional to mole fraction:

- \( P_{\text{H}_2} = \frac{10}{16} \times 1 = 0.625\ \text{bar} \)
- \( P_{\text{He}} = \frac{4}{16} \times 1 = 0.25\ \text{bar} \)
- \( P_{\text{O}_2} = \frac{2}{16} \times 1 = 0.125\ \text{bar} \)

Step 5: Ratio of partial pressures:
O₂ : He : H₂ = 0.125 : 0.25 : 0.625
Now divide all terms by 0.125:
\[ 1 : 2 : 5 \]

Final Answer:
\[ \boxed{1 : 2 : 5} \]