Ratio of Oxygen and Nitrogen by weight

The given gaseous mixture contains oxygen and nitrogen in the ratio of 1:4 by weight. This means that for every 1 gram of oxygen, there are 4 grams of nitrogen in the mixture.

Ratio of Number of Molecules

To find the ratio of the number of molecules of oxygen and nitrogen, we need to use the Avogadro's number (6.022 × 10²³). The Avogadro's number represents the number of atoms or molecules in a mole.

The atomic mass of oxygen is 16 g/mol and that of nitrogen is 14 g/mol. Using these values and the ratio of their weights in the mixture, we can find the number of moles of oxygen and nitrogen in the mixture.

Let's assume we have 100 grams of the mixture, then:

- Oxygen = (1/5) × 100 = 20 grams
- Nitrogen = (4/5) × 100 = 80 grams

Number of moles of oxygen = 20 g / 16 g/mol = 1.25 mol
Number of moles of nitrogen = 80 g / 14 g/mol = 5.71 mol

Now, we can find the ratio of the number of molecules of oxygen and nitrogen by multiplying their respective mole values with the Avogadro's number.

Ratio of number of molecules of oxygen and nitrogen = (1.25 mol × 6.022 × 10²³) : (5.71 mol × 6.022 × 10²³)
= 7.52 × 10²³ : 3.44 × 10²⁴

Simplifying this ratio by dividing both sides by 7.52 × 10²³, we get:

Ratio of number of molecules of oxygen and nitrogen = 1 : 4.57

Rounding off to the nearest whole number, we get:

Ratio of number of molecules of oxygen and nitrogen = 1 : 5

The given options do not match with our calculated ratio, but we can see that option C (7:32) is the closest match to our answer. Therefore, the correct answer is option C - 7 : 32.