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  4. A first order reaction is 60 % complete in 20 minutes. How long will the reaction take to be 84 % complete ?

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Q. A first order reaction is $60\%$ complete in $20$ minutes. How long will the reaction take to be $84\%$ complete ?

KCETKCET 2012Chemical Kinetics

Solution:

For a first order reaction

$k=\frac{2.303}{t} \log \frac{a}{a-x}$

I Case $k=\frac{2.303}{t} \log \frac{100}{100-60}$

$=\frac{2.303}{20} \log \frac{100}{40}$

$=\frac{2.303}{20}(\log 10-\log 4)$

$=\frac{2.303}{20}(1-0.6020)$

$=0.046$

II Case $k=\frac{2.303}{t} \log \frac{100}{100-84}$

$t=\frac{2.303}{0.046} \log \frac{100}{16}$

$=\frac{2.303}{0.046}(\log 100-\log 16 )$

$=\frac{2.303}{0.046}(2-1.2041)$

$=39.84 \,min =40 \,min$