MRD:01503126
Exercise one: H + H2 system
On a potential energy surface diagram, how is the transition state mathematically defined? 'How can the transition state be identified, and how can it be distinguished from a local minimum of the potential energy surface? The transition state would be local maxima on the local maxima of the minimum energy path. When the transition state is reached, since force is the derivative of potential energy, The force would be zero.
Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory.
The best estimate of the transition state position exists when both the distances of AB and BC are 90.8 pm, the hydrogens have no momentum.
According to the Internuclear Distance vs Time plot, the distance remains unchanged, which corresponds to the zero forces acting on AB and BC hydrogens, so stationary nuclei at the transition state.
Comment on how the mep and the trajectory you just calculated differ.
The difference between the two calculation types is whether the atomic motion is included or not. In mep the trajectory is a straight line since it does not take atomic motion into account. In dynamic the trajectory is more like a wavy curve, since it includes the atomic motion.
Complete the table above by adding the total energy, whether the trajectory is reactive or unreactive, and provide a plot of the trajectory and a small description for what happens along the trajectory. What can you conclude from the table?
According to the results in the table, the hypothesis that all trajectories starting with the same positions but with higher values of momenta (higher kinetic energy) would be reactive, as they have enough kinetic energy to overcome the activation barrier is incorrect. For the 4th cases, p1 is -5.1 g.mol-1.pm.fs-1 and p2 is -10.1 g.mol-1.pm.fs-1, which both have greater kinetic energy to overcome the activation barrier, but the reactants are still unreactive
Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values? The reaction rate predicted by Transition State Theory is overestimated comparing with the experimental values. Even if a hydrogen atom collides with an H2 molecule, it might bounce off and regenerate the reactants as an unreactive trajectory. The transition state theory does not take an unreactive trajectory into account so that the reaction rate is overestimated than the experimental values.
Exercise two
By inspecting the potential energy surfaces, classify the F + H2 and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved?
For F + H2, it's an exothermic reaction, which formed HF and H. So according to the FHH contour plot, the distance AB would decrease and distance BC would increase during the reaction, it's an exothermic reaction since the H-F bond formed is a stronger bond.
The reaction between H + HF is endothermic since the bond broken is weaker than the bond formed.
Locate the approximate position of the transition state.
For F + H2: p1= 180.6 pm, p2= 74.5 pm
For H + HF: p1= 74.5 pm, p2= 180.6 pm
Report the activation energy for both reactions.
The activation energy is calculated from the difference between the energy of saddle point (maximum energy of a reaction) and the energy of reactants. For F + H2 system, the maximum energy at the saddle point is -433.981 kJ/mol. In order to find the energy of reactants, the distance between F and H2 is adjusted to a large value (10000 pm) to ensure no reactions could occur, then the energy of reactants could be found as -435.075 kJ/mol, so the activation energy for FHH system can be calculated to be 1.088 kJ/mol (dynamic).
For H + HF system. the maximum energy at the saddle point is -433.981 kJ/mol. To find the energy of reactants, the distance between H atom and HF molecule and the intermolecular distance in H2 are both decreases, then the lowest energy of reactants can be found from the Energy vs time graph as -560.256 kJ/mol. So the activation energy for HHF system can be calculated to be 126.275 kJ/mol.
