The thermal decomposition reaction of nitrosyl halides is important in tropospheric chemistry. For example, consider the decomposition of NOCl:
$2 NOCl\left( g \right)\to 2 NO\left( g \right)+Cl_{2}\left( g \right)$
The Arrhenius parameters for this reaction are $A=1.00×10^{13} M^{-1} s^{-1}$ and $E_{a}=104.0 kJ mol^{-1}$ . Calculate $\Delta H^{\ddagger }$ and $\Delta S^{\ddagger }$ for this reaction with $T=300. K$ .

Question

The thermal decomposition reaction of nitrosyl halides is important in tropospheric chemistry. For example, consider the decomposition of NOCl:

[latex]2 NOCl\left( g ight) o 2 NO\left( g ight)+Cl_{2}\left( g ight)[/latex]

The Arrhenius parameters for this reaction are [latex]A=1.00×10^{13} M^{-1} s^{-1}[/latex] and [latex]E_{a}=104.0 kJ mol^{-1}[/latex]. Calculate [latex]\Delta H^{\ddagger }[/latex] and [latex]\Delta S^{\ddagger }[/latex] for this reaction with [latex]T=300. K[/latex].

Accepted Answer

This is a bimolecular reaction such that

[latex]\Delta H^{\ddagger }=E_{a}-2RT=104 kJ mol^{-1}-2\left( 8.314 J mol^{-1} K^{-1}\right)\left( 300. K \right)[/latex]

[latex]=104.0 kJ mol^{-1}-\left( 4.99×10^{3} J mol^{-1}\right)\left( \frac{1 kJ}{1000 J} \right)=99.0 kJ mol^{-1}[/latex]

[latex]\Delta S^{\ddagger}=R\ln\left( \frac{Ahc°}{e^{2}kT} \right)[/latex]

[latex]=\left( 8.314 J mol^{-1} K^{-1}\right)\ln\left( \frac{\left( 1.00 ×10^{13} M^{-1} s^{-1} \right)\left( 6.626×10^{-34} J s \right)\left( 1 M \right)}{e^{2}\left( 1.38×10^{-23} J K^{-1}\right)\left( 300. K \right)} \right)[/latex]

[latex]=-12.7 J mol^{-1}K^{-1}[/latex]

One of the utilities of this calculation is that the sign and magnitude of [latex]\Delta S^{\ddagger}[/latex] provide information on the structure of the activated complex at the transition state relative to the reactants. The negative value in this example illustrates that the activated complex has a lower entropy (or is more ordered) than the reactants. This observation is consistent with a mechanism in which the two NOCl reactants form a complex that eventually decays to produce NO and Cl.

Question 18.10: The thermal decomposition reaction of nitrosyl halides is im...

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