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5.3Kinetics

Concentration Changes Over Time — AP CHEMISTRY Revision Notes & Topical Questions

5 min read 8 parts Lesson 6 of 14 1 quiz

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Lesson summary

5.3 Concentration Changes Over Time — AP CHEMISTRY notes: Use integrated rate laws, linear plots and half-life to analyse how reactant concentration changes with time.Zero order — [A] against t is a straight line going downThe slope is −k and the rate is constant.First order — [A…

  • Second order
  • Calculating concentration
  • Linear plot method
  • Half-life t1/2
  • Radioactive decay
  • Course focus

Part 1 of 6Concentration-time graphs

1Zero order
  • [A] against t is a straight line going down
  • The slope is −k and the rate is constant.
2First order
  • [A] against t is a curve that falls and levels out
  • The rate falls in proportion to [A].
3Second order
  • [A] against t is a steeper curve that falls and then flattens
  • It starts falling faster and levels more gradually than a first-order curve.

Part 2 of 6Integrated rate laws

OrderIntegrated rate lawLinear plotSlopey-intercept
Zero[A]t = −kt + [A]0[A] against t−k[A]0
Firstln[A]t = −kt + ln[A]0ln[A] against t−kln[A]0
Second1/[A]t = kt + 1/[A]01/[A] against t+k1/[A]0

Part 3 of 6Using the integrated laws

1Calculating concentration
  • Calculating concentration substitute k, the initial concentration and the time to find [A] at any time
2Linear plot method
  • Linear plot method only the correct order gives a straight line
  • The plot that is linear identifies the order with respect to A.
  • The slope of that line gives the rate constant k.

Part 4 of 6Half-life of a first-order reaction

1Half-life t1/2
  • Half-life t1/2 the time taken for the reactant concentration to fall to half its value
2First order
  • First order t1/2 = 0.693/k
  • It depends only on k, so it is constant throughout the reaction.
  • The k must be in units of s-1, min-1 or h-1 for first-order use.
3Radioactive decay
  • Radioactive decay a standard example of first-order kinetics

Part 5 of 6Half-life of zero- and second-order reactions

Zero order
  • Zero order t1/2 = [A]0/2k, so it decreases as the reaction proceeds
Second order
  • Second order t1/2 = 1/(k[A]0), so it increases as [A] falls and depends on the initial concentration
Course focus
  • AP Chemistry assesses half-life only for first-order reactions

Part 6 of 6More from the specification

More from the specification
Integrated rate equations over time
  • Integrated rate equations over time plotting logarithmic reactant concentration against time provides a graphical means to identify first-order reaction kinetics.
Mechanism
  • The sequence of steps by which reactants form products.
Decomposition
  • A reaction where one compound breaks down into simpler substances.
Hydrogen
  • A gas that gives a squeaky pop with a lighted splint.
Activation energy
  • The minimum energy colliding particles need to react.
Overall order
  • The sum of the orders with respect to each reactant.
Successful collision
  • A collision with the correct orientation and enough energy to react.
Reaction mechanism
  • The sequence of elementary steps in a reaction.
Catalyst
  • A substance that speeds up a reaction and is not used up.
Gradient
  • The change in y divided by the change in x on a graph.
Product
  • A substance formed in a reaction.

Key terms

TermMeaning
Integrated rate lawEquation giving concentration as a function of time for a given order.
Half-lifeTime for the concentration of a reactant to fall to half.
First-order half-lifet1/2 = 0.693/k, independent of concentration.
Linear plotGraph of a function of [A] against t that gives a straight line for one order only.

Avoid these mistakes

1
Plotting [A] against t for a first-order reaction and expecting a line — a first-order line needs ln[A] against t.
2
Using the sign of the slope as k directly — for zero and first order the slope is −k, for second order it is +k.
3
Saying first-order half-life depends on initial concentration — it depends only on k.
4
Taking the rate constant units from the wrong order — the units of k are set by the overall order.

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