Question

# First order reaction completes $$20\%$$ in $$5$$ min. How much time it will take for $$60\%$$ completion?

A
26.5 min
B
20.5 min
C
19.5 min
D
18 min

Solution

## The correct option is B $$20.5$$ minIn 5 minutes, the reaction is 20% complete.$$\displaystyle [A]_0=100$$ and $$\displaystyle [A]=100-20=80$$$$\displaystyle k= \dfrac {2.303}{t} log_{10} \dfrac {[A]_0}{[A]}$$$$\displaystyle k= \dfrac {2.303}{5 \ min} log_{10} \dfrac { 100}{80}$$$$\displaystyle k=0.0446 \ min^{-1}$$Now, the reaction is 60% complete.$$\displaystyle [A]_0=100$$ and $$\displaystyle [A]=100-60=40$$$$\displaystyle t= \dfrac {2.303}{k} log_{10} \dfrac {[A]_0}{[A]}$$$$\displaystyle t= \dfrac {2.303}{0.0446 \ min^{-1}} log_{10} \dfrac { 100}{40}$$$$\displaystyle t=20.5 \ min$$Chemistry

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