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.

Options

A. 20%
B. 25%
C. 50%
D. 75%

Answer

b

Explanation

(b) 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)`
`0.5xxV=(n_(1)+n_(2))Rxx300`
`4.5xxV=(2n_(1)+3n_(2))Rxx1200`
`(2n_(1)+3n_(2))/(n_(1)+n_(2))=(9)/(4)`
`(n_(1))/(n_(2))=(1)/(3)`
`(n_(2))/(n_(1)+n_(2))xx100=25%`