Chemical Kinetics & Reaction Rates Cheat Sheet

Key Facts

• For $aA + bB \rightarrow pP$, the average reaction rate is $\text{rate} = -\frac{1}{a}\frac{\Delta[A]}{\Delta t} = \frac{1}{p}\frac{\Delta[P]}{\Delta t}$.
• A general rate law has the form $\text{rate} = k[A]^m[B]^n$, where $m$ and $n$ must be found from experimental data.
• The overall reaction order is $m+n$ for the rate law $\text{rate} = k[A]^m[B]^n$.
• A zero-order reaction follows $[A]_t = -kt + [A]_0$ and has half-life $t_{1/2} = \frac{[A]_0}{2k}$.
• A first-order reaction follows $\ln[A]_t = -kt + \ln[A]_0$ and has half-life $t_{1/2} = \frac{0.693}{k}$.
• A second-order reaction in one reactant follows $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$ and has half-life $t_{1/2} = \frac{1}{k[A]_0}$.
• The Arrhenius equation is $k = Ae^{-E_a/(RT)}$, where increasing $T$ usually increases $k$ by giving more particles enough energy to react.
• A catalyst lowers activation energy $E_a$ and increases rate, but it does not change $\Delta H$, $\Delta G$, or the equilibrium constant $K$.

Vocabulary

Reaction rate

Reaction rate is the change in concentration of a reactant or product per unit time, often written as $\frac{\Delta[\text{substance}]}{\Delta t}$.

Rate law

A rate law is an experimentally determined equation, such as $\text{rate} = k[A]^m[B]^n$, that relates reaction rate to reactant concentrations.

Rate constant

The rate constant $k$ is the proportionality factor in a rate law, and its value depends on temperature and the reaction pathway.

Reaction order

Reaction order is the exponent on a concentration term in a rate law, and the overall order is the sum of all exponents.

Activation energy

Activation energy $E_a$ is the minimum energy needed for reacting particles to form the activated complex and proceed to products.

Catalyst

A catalyst is a substance that speeds up a reaction by providing a lower-energy pathway without being consumed overall.