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

  2. The general concept is the same as in radioactivity

  3. 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.

  4. 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…..

  5. 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.

  6. 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!

  7. 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.

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

  9. 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.

  10. 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.

  11. Concentration/time graph for a zero order reaction.

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