One mole of a mixture of `N_(2),NO_(2)` and `N_(2)O_(4)`, has a mean molar mass of `55.4`. On heating to a temperature at which `N_(2)O_(4)` may be dissociated `:N_(2)O_(4)rarr2NO_(2)`, the mean molar mass tends to the lower value of `39.6`. What is the mole ratio of `N_(2) : NO_(2) : N_(2)O_(4)` in the original mixture?

Explanation

To solve the problem, we need to find the mole ratio of \(N_2\), \(NO_2\), and \(N_2O_4\) in the original mixture given the mean molar masses before and after dissociation. Here’s a step-by-step breakdown of the solution:

### Step 1: Define Variables
Let:
- \(x\) = moles of \(NO_2\)
- \(y\) = moles of \(N_2O_4\)
- Moles of \(N_2\) = \(1 - x - y\) (since the total moles in the mixture is 1)

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