Summarizing Collision Theory

Key Equations

• \(k=A{e}^{\text{−}{E}_{\text{a}}\text{/}RT}\)
• \(\text{ln}\phantom{\rule{0.2em}{0ex}}k=\left(\cfrac{\text{−}{E}_{\text{a}}}{R}\right)\phantom{\rule{0.2em}{0ex}}\left(\cfrac{1}{T}\right)+\text{ln}\phantom{\rule{0.2em}{0ex}}A\)
• \(\text{ln}\phantom{\rule{0.2em}{0ex}}\cfrac{{k}_{1}}{{k}_{2}}\phantom{\rule{0.1em}{0ex}}=\phantom{\rule{0.1em}{0ex}}\cfrac{{E}_{\text{a}}}{R}\phantom{\rule{0.2em}{0ex}}\left(\cfrac{1}{{T}_{2}}\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\cfrac{1}{{T}_{1}}\right)\)

Key Equations

• \(k=A{e}^{\text{−}{E}_{\text{a}}\text{/}RT}\)
• \(\text{ln}\phantom{\rule{0.2em}{0ex}}k=\left(\cfrac{\text{−}{E}_{\text{a}}}{R}\right)\phantom{\rule{0.2em}{0ex}}\left(\cfrac{1}{T}\right)+\text{ln}\phantom{\rule{0.2em}{0ex}}A\)
• \(\text{ln}\phantom{\rule{0.2em}{0ex}}\cfrac{{k}_{1}}{{k}_{2}}\phantom{\rule{0.1em}{0ex}}=\phantom{\rule{0.1em}{0ex}}\cfrac{{E}_{\text{a}}}{R}\phantom{\rule{0.2em}{0ex}}\left(\cfrac{1}{{T}_{2}}\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\cfrac{1}{{T}_{1}}\right)\)

Glossary

activated complex

(also, transition state) unstable combination of reactant species representing the highest energy state of a reaction system

activation energy (E_a)

energy necessary in order for a reaction to take place

Arrhenius equation

mathematical relationship between the rate constant and the activation energy of a reaction

collision theory

model that emphasizes the energy and orientation of molecular collisions to explain and predict reaction kinetics

frequency factor (A)

proportionality constant in the Arrhenius equation, related to the relative number of collisions having an orientation capable of leading to product formation