Reaction Rate Laws Worked Examples Cheat Sheet

A printable reference covering rate laws, reaction order, initial rates, integrated laws, half-life, and worked examples for grades 11-12.

Download PNG

Related Tools

Related Labs

Related Worksheets

Related Infographics

Reaction rate laws describe how the speed of a chemical reaction depends on reactant concentrations. This cheat sheet helps students solve worked examples using initial rate data, rate law equations, integrated rate laws, and half-life relationships. These skills are essential for interpreting kinetics experiments and predicting how concentration changes affect reaction speed. The main idea is to connect measured rates to a mathematical model such as $\text{rate} = k[A]^m[B]^n$ . Students need to determine reaction orders, calculate the rate constant $k$ , and choose the correct integrated rate law for concentration versus time. Graph shapes, units of $k$ , and half-life patterns help identify whether a reaction is zero order, first order, or second order.

Key Facts

A general rate law has the form $\text{rate} = k[A]^m[B]^n$ , where $m$ and $n$ are experimentally determined reaction orders.
The overall reaction order is the sum of the exponents in the rate law, so for $\text{rate} = k[A]^m[B]^n$ , the overall order is $m+n$ .
If doubling $[A]$ doubles the rate while other concentrations stay constant, the reaction is first order in $A$ because $2^1=2$ .
If doubling $[A]$ quadruples the rate while other concentrations stay constant, the reaction is second order in $A$ because $2^2=4$ .
For a zero-order reaction, the integrated rate law is $[A]_t = -kt + [A]_0$ and a graph of $[A]$ versus $t$ is linear.
For a first-order reaction, the integrated rate law is $\ln[A]_t = -kt + \ln[A]_0$ and the half-life is $t_{1/2}=\frac{0.693}{k}$ .
For a second-order reaction in one reactant, the integrated rate law is $\frac{1}{[A]_t}=kt+\frac{1}{[A]_0}$ and the half-life is $t_{1/2}=\frac{1}{k[A]_0}$ .
The units of $k$ depend on overall order, such as $\mathrm{M\,s^{-1}}$ for zero order, $\mathrm{s^{-1}}$ for first order, and $\mathrm{M^{-1}\,s^{-1}}$ for second order.

Vocabulary

Reaction rate: Reaction rate is the change in concentration of a reactant or product per unit time, often measured in $\mathrm{M\,s^{-1}}$ .
Rate law: A rate law is an equation that relates reaction rate to reactant concentrations using experimentally determined exponents.
Rate constant: The rate constant $k$ is the proportionality value in a rate law and changes with temperature and catalysts.
Reaction order: Reaction order is the exponent on a concentration term in a rate law, such as $m$ in $[A]^m$ .
Integrated rate law: An integrated rate law relates reactant concentration to time, allowing students to calculate $[A]_t$ , $t$ , or $k$ .
Half-life: Half-life $t_{1/2}$ is the time required for a reactant concentration to decrease to one-half of its initial value.

Common Mistakes to Avoid

Using balanced equation coefficients as rate law exponents is wrong because rate law exponents must be determined experimentally unless the reaction is known to be an elementary step.
Changing two reactant concentrations at once when finding order is wrong because the effect of one reactant cannot be isolated unless the other concentration is held constant.
Forgetting that $k$ has different units is wrong because the units must make the rate come out in $\mathrm{M\,s^{-1}}$ for the specific overall order.
Using the first-order half-life formula for every reaction is wrong because $t_{1/2}=\frac{0.693}{k}$ applies only to first-order reactions.
Choosing the wrong graph to identify reaction order is wrong because zero order gives a straight line for $[A]$ versus $t$ , first order for $\ln[A]$ versus $t$ , and second order for $\frac{1}{[A]}$ versus $t$ .

Practice Questions

1 Initial rate data show that doubling $[A]$ while holding $[B]$ constant changes the rate from $2.0\times10^{-3}\,\mathrm{M\,s^{-1}}$ to $8.0\times10^{-3}\,\mathrm{M\,s^{-1}}$ . What is the order in $A$ ?
2 For the rate law $\text{rate}=k[A]^2[B]$ , calculate $k$ if $[A]=0.20\,\mathrm{M}$ , $[B]=0.50\,\mathrm{M}$ , and $\text{rate}=1.6\times10^{-2}\,\mathrm{M\,s^{-1}}$ .
3 A first-order reaction has $k=0.035\,\mathrm{s^{-1}}$ . Calculate the half-life using $t_{1/2}=\frac{0.693}{k}$ .
4 A student claims that the reaction order can always be read directly from the coefficients in the balanced chemical equation. Explain why this claim is not valid for most rate law problems.

Sign in to save