Question

Calculate the resonance energy of $N_{2}O$ from the following data; $\text{Δ}_{\text{f}} \text{H}$ of $N_{2}O$ is 82 KJ $mol^{- 1}N\equiv N,$ 946 KJ $mol^{- 1}$ , $N=N$ , 418 KJ $mol^{- 1}$ , 0 = 0, 498 KJ $mol^{- 1}$ , $N=0,607$ KJ $mol^{- 1}$ .

• A. $+ 8.85 \, \text{kJ} \, \text{mol}^{- 1}$
• B. $- 88 \, \text{kJ} \, \text{mol}^{- 1}$
• C. $- 8.8 \, \text{kJ} \, \text{mol}^{- 1}$
• D. $+ 88 \, \text{kJ} \, \text{mol}^{- 1}$

Answer 1

Answer: (B)

Reaction $\text{N}_{\text{2}} \, \text{+} \, \frac{\text{1}}{\text{2}} \text{O}_{\text{2}} \rightarrow \text{N}_{\text{2}} \text{O;} \, \text{ΔH} \, \text{=} \, \text{82} \, \text{kJ} \, \text{mol}^{- \text{1}}$
The structure of $N_{2}O$ is $N=N=O$
$\text{Δ}_{\text{f}} \text{H}$ (calculated) = Bond energy of reactant - Bond energy of product
$=\left[\left(\right. N \equiv N \left.\right) + \frac{1}{2} \left(\right. O = O \left.\right)\right]-\left[\right.\left(\right.N=N\left.\right)+\left(\right.N=O\left.\right)\left]\right.$
$\text{=} \, \left[\text{946} \, \text{+} \, \frac{\text{1}}{\text{2}} \text{498}\right] - \left[\text{418} \, \text{+} \, \text{607}\right] \, \text{=} \, \text{170} \, \text{kJ}$
Resonance energy = experimental $\left(\text{Δ}\right)_{\text{f}} \text{H} \left(\left(\text{N}\right)_{\text{2}} \text{O}\right) -$ calculated $\left(\text{Δ}\right)_{\text{f}} \text{H} \left(\left(\text{N}\right)_{\text{2}} \text{O}\right)$
$\text{=} \, \text{82} - \text{170} \, \text{=} \, - \text{88} \, \text{kJ} \, \text{mol}^{- \text{1}}$ .