Twenty individual collision events between reactant molecules A and B are observed in a molecular-dynamics simulation. The translational energies (in kJ mol⁻¹) associated with the relative motion of the reactants in each collision are listed below:
78 62 81 95 74 69 102 58 83 77 64 80 88 73 90 70 76 85 68 96
For the reaction A + B → products, the activation energy is 75 kJ mol⁻¹. Only collisions that meet or exceed this energy and have a favorable orientation lead to reaction; statistical studies indicate that, among those energetic collisions, the probability of a proper orientation is 0.50.
(a) Determine how many of the twenty collisions have enough energy to satisfy the activation energy requirement.
(b) Using the orientation probability given, calculate the expected number of successful collisions in this sample and the corresponding percentage expressed to the nearest whole number.
(c) Briefly comment on how increasing the orientation probability to 0.80 would affect the percentage of successful collisions, assuming the energy distribution remains unchanged.