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Enthalpy

Heat of atomi...

Question

Heat of atomisation of $N H_{3}$ and $N_{2} H_{4}$ are $x k c a l m o l^{- 1}$ and $y k c a l m o l^{- 1}$ respectively. Average bond energy of $N - - N$ bond is:

A

\frac{3 y - 4 x}{3} k c a l m o l^{- 1}

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B

\frac{3 y - x}{5} k c a l m o l^{- 1}

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C

\frac{2 y - 4 x}{4} k c a l m o l^{- 1}

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D

None of these

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Solution

The correct option is A $\frac{3 y - 4 x}{3} k c a l m o l^{- 1}$
$N H_{3} ⟶ N (g) + 3 H (g); Δ H_{1} = x k c a l m o l^{- 1}$
$N_{2} H_{4} ⟶ 2 N (g) + 4 H (g); Δ H_{2} = y k c a l m o l^{- 1}$
$Δ H_{1} = 3 \times e_{N - - H} = x$ ...(i)
$Δ H_{2} = 4 \times e_{N - - H} + e_{N - - N} = y$ ...(ii)
From eqs. (i) and (ii)
$∴ y = 4. \frac{x}{3} + e_{N - - N}$
$∴ e_{N - - N} = y - \frac{4 x}{3}$
$= \frac{3 y - 4 x}{3} k c a l m o l^{- 1}$

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