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Question

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


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

The correct option is B $$20.5$$ min
In 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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