Question

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

• A. 54 mins
• B. 68 mins
• C. 40 mins
• D. 76 mins

Answer 1

Answer: (C)

40 mins

Answer 2

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 $k=\frac{2.303}{t} \log \frac{100}{100-84}$
$t=\frac{2.303}{0.046} \log \frac{100}{16}$
$=\frac{2.303}{0.046}(\log 100-\log 16 )$
$=\frac{2.303}{0.046}(2-1.2041)$
$=39.84 \,min =40 \,min$