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.
A
0.2
B
0.25
C
0.5
D
0.75
Text Solution
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The correct Answer is:
b
(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%`
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