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# Half lives - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Half lives' - gayle

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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.

• 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.

• 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…..

• 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.

• 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!

• 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.

• 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.

• 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.