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)

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

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

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

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

$=39.84min=40min$