206 Carbon-14 (14C) a radioactive isotope of carbon, is used to determine the ag

Question

206 Carbon-14 (14C) a radioactive isotope of carbon, is used to determine the age of artifacts and natural samples via carbon dating. The half-life of ac, which undergoes first order decay, is 6270 years. You will want to use some form of the integrated rate law for afirst-order reaction. One form of this equation is given below for a generic reactant A [A] kt [Ale What is k, the rate constant, for this reaction? You may use whatever units you choose, but you must use units, and they must be correct.

Explanation / Answer

Integrated rate law for a first order reaction

ln([A]/[Ao])=-kt ..........................equation (1)

where [A]=Concentration of reactant at time t

[Ao]=Initial Concentration of reactant

k=Rate constant

t=Time taken

Half life means time taken to reduce the concentration of the reactant to half of its initial value

i.e. [A]=1/2([Ao])

or [A]/[Ao]=1/2 ............equation (2)

Given tha half life of 14C which undergoes first order decay is 6270 years (=t1/2=time taken to reduce the concentration to half of its initil concentration)

So substituting in integrated rate law

ln([A]/[Ao])=-kt

ln(1/2)=-k(6270 years)

-0.693=-k(6270 years)

k=0.693/6270 years

k=1.11x10-4 /year or 1.11x10-4 year-1

So rate constant for this reaction is 1.11x10-4 year-1

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