A mixture of `NH_(3(g))` and `N_(2)H_(4_((g)))` is placed in a sealed container at `300 K`. The total pressure is `0.5 atm`. The container is heated to `1200 K`, at which time both substances decompose completely according to the equations:
`2NH_(3(g))rarrN_(2(g))+3H_(2(g))`
`N_(2)H_(4_((g)))rarrN_(2(g))+2H_(2(g))`
After decomposition is complete, the total pressure at `1200 K` is found to be `4.5 atm`. Find the amount (mole) per cent of `N_(2)H_(4(g))` in the original mixture.

Answer

25

Explanation

Let initial mixture contains `n_(1)` and `n_(2)` moles of `NH_(3)` and `N_(2)H_(4)` respectively.
Total moles of gases originally present = `n_(1) + n_(2)`
Total moles of gases after decomposition of gases
`=2n_(1) + 3n_(2)`
`0.5 xx V = (n_(1) + n_(2))R xx 1200`
`(2n_(1) + 3n_(2))/(n_(1) + n_(2)) = 9/4`
`n_(2)/(n_(1)+n_(2)) xx 100 = 25%`