Calculation of Percentage Dissociation of N2O4

1. Introduction
The vapour density of a compound is the ratio of the mass of a given volume of the substance to the mass of an equal volume of hydrogen gas at the same temperature and pressure. In this case, we are given the vapour density of N2O4 before and after dissociation.

2. Given Data
- Vapour density of N2O4 before dissociation = 46
- Vapour density of N2O4 after dissociation = 24.5

3. Understanding the Dissociation Reaction
The dissociation reaction of N2O4 can be represented as follows:

N2O4 ⇌ 2NO2

This reaction shows that one molecule of N2O4 dissociates into two molecules of NO2. If we assume that x% of N2O4 dissociates, then the remaining (100 - x)% would still be in the form of N2O4.

4. Calculation Process
To calculate the percentage dissociation of N2O4, we need to determine the moles of N2O4 before and after dissociation.

4.1 Moles of N2O4 before dissociation:
The molar mass of N2O4 is 92 g/mol. Since the vapour density is given as 46, it means that the compound is half as heavy as hydrogen. Therefore, the moles of N2O4 before dissociation can be calculated as follows:

Moles of N2O4 before dissociation = Vapour density of N2O4 / 2 = 46 / 2 = 23

4.2 Moles of N2O4 after dissociation:
The molar mass of NO2 is 46 g/mol. Since the vapour density is given as 24.5, it means that the compound is 24.5 times as heavy as hydrogen. Therefore, the moles of N2O4 after dissociation can be calculated as follows:

Moles of NO2 after dissociation = Vapour density of N2O4 / 24.5 = 24.5 / 24.5 = 1

Since 2 moles of NO2 are formed from 1 mole of N2O4, the moles of N2O4 after dissociation would be half of the moles of NO2:

Moles of N2O4 after dissociation = 1 / 2 = 0.5

5. Calculation of Percentage Dissociation
The percentage dissociation of N2O4 can be calculated using the formula:

Percentage dissociation = (Moles of N2O4 before dissociation - Moles of N2O4 after dissociation) / Moles of N2O4 before dissociation * 100

Plugging in the values, we get:

Percentage dissociation = (23 - 0.5) / 23 * 100 = 22.5 / 23 * 100 = 97.83%

Therefore, the percentage dissociation of N2O4 is approximately 97.83%.

6. Conclusion
The percentage dissociation of N2O4 is