The half-life of a first order reaction is in how much τtime, the concentration of the reactant halves. After one half-life, the concentration of the reactant becomes half its initial value. After another half-life, itsconcentration becomes (M: initial concentration): [tex] (\frac{1}{2} *M)* \frac{1}{2} = \frac{1}{4} * M
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In general, after n half-lifes, the concentration of the reactant becomes: [tex]( \frac{1}{2} ^ n)*M[/tex]
Since 1/16=[tex] (\frac{1}{2}) ^ 4[/tex] , we have that 4 half-lifes need to pass so that the concentration of the reactant becomes 1/16 of the initial one (=1/16*M). Hence, 4*22.9 sec=91.6 seconds is the required time.
