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 A first order reaction completes 50% in 69.3 minute. How much time it will take for 90% completion?

 

Option: 1

230.3 minutes


Option: 2

115.15 minutes


Option: 3

460.6 minutes


Option: 4

None of these


Answers (1)

best_answer

For a first order reaction,

rate constant,    \mathrm{k=\frac{0.693}{t_{1 / 2}}=\frac{0.693}{69.3}=0.01 \mathrm{~min}^{-1} }
             \mathrm{k=\frac{2.303}{t} \log _{10} \frac{a}{a-x}}

where, \mathrm{a=}  initial amount of reactant

\mathrm{(a-x)=} amount of reactant remaining after time t

\mathrm{\mathrm{} ' t^{\prime}=0.1 }a for 90 % completion

\mathrm{ 0.01=\frac{2.303}{t} \log _{10} \frac{a}{0.1 a} \\ }

\mathrm{ t=\frac{2.303}{0.01}=230.3 \mathrm{~min} }
 

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