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Thermodynamics

# Calculate the resonance energy of $N_2O$ from the following data: $\Delta H_f^{\circ}$ of $N_2O = 82 \: kJ/mol$, Bond energies of $N≡N,\: N=N,\: O=O \: and\: N=O$ bonds are $946,\: 418,\: 498\: and\: 607\: kJ/mol$ respectively

$\begin {array} {1 1} (A)\;88 \: kJ/mol & \quad (B)\;96 \: kJ/mol \\ (C)\;-88 \: kJ/mol & \quad (D)\;-96 \: kJ/mol \end {array}$

$N≡N (g) + \large\frac{1}{2} $$O=\overline {O(g)} \rightarrow N = N^+ = O(g) \Delta H^{\circ} = [Energy required] – [Energy released] = ( \Delta H_{N≡N} + \large\frac{1}{2}$$ \Delta H_{O=O}) – ( \Delta H_{N=N} + \Delta H_{N=O})$
$= (946 + \large\frac{1}{2}$$\times 498) – (418+607) = 170\: kJ/mol$
So, Resonance energy = Expected value of ∆Hfo – Observed value of $\Delta H_f^{\circ} = 170 – 82 = 88\: kJ/mol$
Ans : (A)