Question

The ratio mass of oxygen and nitrogen of a particular gaseous mixture is $1 : 4$ The ratio of number of their molecule is

• A. $1 : 4$
• B. $7 : 32$
• C. $1 : 8$
• D. $3 : 16$

Answer 1

The Correct Option is B

To determine the ratio of the number of molecules of oxygen and nitrogen in a mixture where the ratio of their masses is given as 1 : 4, we need to consider their respective molar masses and use the concept of number of moles.

1. The molar mass of oxygen (O₂) is approximately 32 \, \text{g/mol} and for nitrogen (N₂), it is approximately 28 \, \text{g/mol}.
2. The number of moles of a substance is given by the formula: \text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}}
3. Let's assume the mass of oxygen is M and the mass of nitrogen is 4M since the mass ratio is 1 : 4.
4. The number of moles of O₂ is: \frac{M}{32}
5. The number of moles of N₂ is: \frac{4M}{28}
6. The ratio of the number of molecules, which is proportional to the number of moles, will be: \frac{\left(\frac{M}{32}\right)}{\left(\frac{4M}{28}\right)}
7. Simplifying the molecules ratio: \frac{M}{32} \times \frac{28}{4M} = \frac{28}{128} = \frac{7}{32}

Thus, the ratio of the number of molecules of oxygen to nitrogen is 7 : 32.

Therefore, the correct answer is 7 : 32. This is due to the inversely proportional relationship between the number of moles and molar mass when the masses are constant.