1.38 mmol of K-40 are created by the decay of Ar-40. There are 1.14 mmol of Ar-40 left in the world. The initial moles of Ar-40 will be equal to the sum of the moles of K-40 and the remaining moles of Ar-40.
A reaction's half-life is the amount of time needed for a reactant to reach half of its starting concentration or pressure. The half-life is concentration-independent and constant over time for a first-order reaction.
t(1/2) = 1.25 x 10 ^(9) year
conc K(40) = 1.38 mmol
conc( Ar40) = 1.14
n(Ar40) = 1.38 + 1.50 = 2.88 mmol
half time of the reaction = 1.25 x 10 ^ ( 9) year
k = 0.693/ 1.25 x 10^(9) = 5.54 x 10 ^( -10) year ^(-1)
t = ( 2.303/k ) log ( 2.88/1.14) = (2.303/5.54 x 10 ^(-10)) log (2.88/1.14)
t = 3.38 x 10^(9) years
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