Physical chemistryLesson 2 of 2 in the course Kinetics

Integrated Rate Laws, Diagnostic Plots, and Half-Lives by Reaction Order

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

Differential rate laws describe how reaction rate depends on reactant concentration. Integrated rate laws connect concentration to elapsed time, allowing us to predict how much reactant remains or how long a reaction will take to reach a particular extent.

A differential rate law describes the instantaneous rate of a reaction. For a first-order reaction involving reactant A, the rate is proportional to its concentration: rate=k[A]\text{rate} = k[A]. Integrating this relationship over time gives an equation that predicts the concentration at any elapsed time.

All flashcards

Integrated rate law
An equation that relates reactant concentration to elapsed reaction time.
First-order integrated rate law
[A]t=[A]0e−kt[A]_t = [A]_0e^{-kt}
First-order reaction time
t=1kln⁡([A]0[A]t)t = \frac{1}{k}\ln\left(\frac{[A]_0}{[A]_t}\right)
Zero-order integrated rate law
[A]t=[A]0−kt[A]_t = [A]_0 - kt
First-order half-life
t1/2=0.693kt_{1/2} = \frac{0.693}{k}; it does not depend on the initial concentration.

Quiz questions

  1. What relationship does a differential rate law describe?Answer: How the instantaneous reaction rate depends on reactant concentration.
  2. Which plot is expected to be linear for a first-order reaction?Answer: ln⁡[A]\ln[A] versus time, with slope −k-k.
  3. Which integrated rate law applies to a simple second-order reaction in one reactant?Answer: 1[A]t=kt+1[A]0\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}
  4. What are the units of a zero-order rate constant when concentration is measured in molarity and time in seconds?Answer: M s−1M\,s^{-1}
  5. How does the half-life of a first-order reaction depend on its initial concentration?Answer: It is independent of the initial concentration.

Based on Chemistry 2e by Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson, PhD (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

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