Half lives
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Half lives. The half life is the time it takes for the concentration of a substance to decline to half its initial value. The general concept is the same as in radioactivity. After two half lives ; ½ + ½ ( ½ ) = ¾ will have reacted. Leaving only ¼ of the initial concentration.

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Half lives

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Half lives

Half lives

The half life is the time it takes for the concentration of a substance to decline to half its initial value.


The general concept is the same as in radioactivity

The general concept is the same as in radioactivity


Half lives

  • After two half lives;

  • ½ + ½ (½ ) = ¾ will have reacted.

  • Leaving only ¼ of the initial concentration.

  • After three half lives;

  • ½ + ½ (½ ) + ½[½ (½ )] = 7/8 will have reacted.

  • Leaving only 1/8 of the initial value.

  • After four half lives;

  • ½ + ½ (½ ) + ½[½ (½ )] +½{½[½ (½ )]} =15/16 will have reacted.

  • Leaving only 1/16 of the initial value.


Eg the isotope carbon 14 is radioactive

Eg; The isotope Carbon-14 is radioactive.

  • It has a half life of 5,730 years

  • This means that after 5,730 years have passed only half of the original amount of C14 will remain.

  • After 2 x 5730 = 11,460 years there will be ½ x ½ = ¼.

  • After 3 x 5730 = 17190 years there will be ½ x ½ x ½ = 1/8…..


Half lives

  • C14 is made by the action of cosmic rays.

  • Life is based on carbon.

  • Whilst organisms are alive C14 will be absorbed at the same rate as C12.

  • As C14 decays it is continually replaced.

  • But after death no more C14 is absorbed.

  • It is as if a stop clock is started.

  • Archaeologists have only to measure the C14 in bones, wood, hair…. to date them.


Half lives

  • The technique can be used for objects up to 48,000 years old.

  • But when the ages of historic artefacts several millennia old were compared to the radiocarbon dates they were found to be too young.

  • It seems that C14 is not always produced at the same rate.

  • So the dates have been calibrated using the wood of the Bristlecone Pine, which lives for over 7,000 years!


Half lives of first order reactions

Half lives of first order reactions

  • For a first order reaction the half life is constant.

  • The time taken for the concentration to fall from the initial value to ½, from ½ to ¼, from ¼ to 1/8 …is exactly the same.

  • t½= 0.693 / k

  • Where k = rate constant.

  • Half lives can be determined by plotting concentration of a reactant against time then measuring the time take for the initial concentration to halve.


Eg the decarboxylation of 2 4 6 trinitrobenzoic acid

Eg; The decarboxylation of 2,4,6 trinitrobenzoic acid.


Half lives of second order reactions

Half lives of second order reactions.

  • Second order half lives are not constant.

  • A basic plot of concentration against time starts off as a much steeper curve, then levels off.

  • This means that the half lives become progressively longer.


Zero order

Zero order

  • NB For a zero order reaction the rate is independent of the concentration.

  • Thus a plot of concentration against time is a straight line, rather than a curve.


Concentration time graph for a zero order reaction

Concentration/time graph for a zero order reaction.


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