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  4. If 50 % of the reactant is converted into a product in a first order reaction in 25 minutes, how much of it would react in 100 minutes ?

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Q. If $50\%$ of the reactant is converted into a product in a first order reaction in $25$ minutes, how much of it would react in $100$ minutes ?

KCETKCET 2013Chemical Kinetics

Solution:

Number of half-lives $=\frac{100}{25}=4$ i.e., $n=4$

Amount of the substance left after 4 half-lives

$=\frac{A^{0}}{2^{n}} \,\,\,\,\, (\because n=4) $

$=\frac{A^{0}}{2^{4}}=\frac{A^{0}}{16}=\frac{100}{16}=6.25 \%$

$\therefore $ Amount of the substance converted into the product in $100\, \min =100-6.25=93.75 \%$