Question 18.10: The thermal decomposition reaction of nitrosyl halides is im...
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.
This is a bimolecular reaction such that
\Delta H^{\ddagger }=E_{a}-2RT=104 kJ mol^{-1}-2\left( 8.314 J mol^{-1} K^{-1}\right)\left( 300. K \right)=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}
\Delta S^{\ddagger}=R\ln\left( \frac{Ahc°}{e^{2}kT} \right)
=\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)
=-12.7 J mol^{-1}K^{-1}
One of the utilities of this calculation is that the sign and magnitude of \Delta S^{\ddagger} 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.