Final answer:
The fraction of collisions with the activation energy to react is calculated using the Arrhenius equation, focusing on the exponential term e-Ea/RT. The rate constants and activation energies are inversely related at a given temperature. Activation energies can also be determined from potential energy diagrams or from the slope of Arrhenius plots.
Step-by-step explanation:
To calculate the fraction of collisions with the activation energy to react, you can use the Arrhenius equation. The formula is k = Ae-Ea/RT, where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the ideal gas constant (8.314 J/mol/K), T is the temperature in Kelvin, and e is the base of natural logarithms (approximately 2.7183). This equation essentially gives us insight into the fraction of molecule collisions that have enough energy to overcome the activation energy barrier and thus react.
To find the fraction of collisions, we focus on the exponential part of the Arrhenius equation, e-Ea/RT. As Ea increases, or as temperature decreases, the exponential term decreases, indicating that a smaller fraction of molecules have the required activation energy to react.
The activation energies between different reactions can be compared by looking at their respective rate constants. Higher activation energies generally result in lower rate constants at a given temperature, indicating that fewer collisions result in a successful reaction. It is also possible to calculate activation energies by analyzing potential energy diagrams or experimentally by measuring the rate constants at different temperatures and using Arrhenius plots (a plot of ln(k) versus 1/T), where the slope yields -Ea/R.