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 . Students need to determine reaction orders, calculate the rate constant , and choose the correct integrated rate law for concentration versus time. Graph shapes, units of , 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 , where and are experimentally determined reaction orders.
- The overall reaction order is the sum of the exponents in the rate law, so for , the overall order is .
- If doubling doubles the rate while other concentrations stay constant, the reaction is first order in because .
- If doubling quadruples the rate while other concentrations stay constant, the reaction is second order in because .
- For a zero-order reaction, the integrated rate law is and a graph of versus is linear.
- For a first-order reaction, the integrated rate law is and the half-life is .
- For a second-order reaction in one reactant, the integrated rate law is and the half-life is .
- The units of depend on overall order, such as for zero order, for first order, and for second order.
Vocabulary
- Reaction rate
- Reaction rate is the change in concentration of a reactant or product per unit time, often measured in .
- Rate law
- A rate law is an equation that relates reaction rate to reactant concentrations using experimentally determined exponents.
- Rate constant
- The rate constant 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 in .
- Integrated rate law
- An integrated rate law relates reactant concentration to time, allowing students to calculate , , or .
- Half-life
- Half-life 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 has different units is wrong because the units must make the rate come out in for the specific overall order.
- Using the first-order half-life formula for every reaction is wrong because applies only to first-order reactions.
- Choosing the wrong graph to identify reaction order is wrong because zero order gives a straight line for versus , first order for versus , and second order for versus .
Practice Questions
- 1 Initial rate data show that doubling while holding constant changes the rate from to . What is the order in ?
- 2 For the rate law , calculate if , , and .
- 3 A first-order reaction has . Calculate the half-life using .
- 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.
Understanding Reaction Rate Laws Worked Examples
A worked rate-law problem usually starts with a table of trials. The useful comparisons are pairs where only one reactant concentration changes. This isolates that reactant's effect.
For example, if a concentration is tripled and the measured rate becomes nine times larger, the exponent for that reactant is two. Dividing the rate change by the concentration change is not enough because the relationship may be curved. Use powers instead.
After finding each exponent, substitute data from one complete trial to find the rate constant. Then test the result with another trial. If it does not predict the second rate, revisit the comparison choices and arithmetic.
Reaction orders come from measurements, not from the balanced chemical equation. This is important because an equation describes the total chemical change, while a rate law reflects the slow sequence of particle events. A reaction may need several collisions before products form.
One slow step can control the observed speed. For an elementary step, coefficients often match the rate-law exponents, but this shortcut is unsafe for a multistep reaction. Catalysts matter here.
A catalyst provides a different pathway with a lower activation energy, so it changes the rate constant. It does not get used up or alter the final equilibrium position.
Integrated rate-law questions use concentration data collected over time rather than separate initial trials. The best graph is the one that makes a straight line. Students should check all three possible graph forms rather than choosing based on guesswork.
The slope contains the rate constant, though its sign depends on the graph form. A graph that is nearly straight may still have scatter from timing errors, temperature drift, or imprecise concentration measurements. Half-life data give another clue.
In a first-order process, equal fractions disappear in equal time intervals. In a second-order process, later half-lives become longer as the reactant becomes dilute. This pattern is often easier to notice in a table before making a graph.
These ideas appear outside the laboratory in medicine, environmental science, and industry. Drug removal from the body is often modeled as first order over a useful concentration range. Pollutant breakdown in water can change rate when sunlight, temperature, or another chemical becomes limiting.
Food spoilage and battery aging slow or speed up under different conditions for similar reasons. In school problems, pay close attention to units. Convert minutes to seconds when needed, and keep concentration units consistent.
Report the rate constant with units because the number alone has no complete meaning. Finally, distinguish rate from concentration. A high concentration does not guarantee a high rate when the reaction has zero order in that substance or when another step is limiting.