The vapour density of a mixture containing `NO_(2)` and `N_(2)O_(4)` is `38.3` at `27^(@)C`. Calculate the mole of `NO_(2)` in `100` mole mixture.

Explanation

To solve the problem, we need to determine the number of moles of \( NO_2 \) in a mixture of \( NO_2 \) and \( N_2O_4 \) given the vapor density of the mixture. Here’s a step-by-step solution:

### Step 1: Understand the Concept of Vapor Density
Vapor density (VD) is defined as the mass of a certain volume of gas compared to the mass of an equal volume of hydrogen at the same temperature and pressure. The vapor density is also equal to the molar mass of the gas divided by 2.

### Step 2: Calculate the Molar Masses
- Molar mass of \( NO_2 \) = 14 (N) + 2 × 16 (O) = 14 + 32 = 46 g/mol
- Molar mass of \( N_2O_4 \) = 2 × 14 (N) + 4 × 16 (O) = 28 + 64 = 92 g/mol
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