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Chemistry Question on Chemical Kinetics

In a first order reaction, the time taken for 90% decay is 12 days. The time taken for 99% decay is

A

36 days

B

18 days

C

24 days

D

48 days

Answer

24 days

Explanation

Solution

For first order reaction,
k=2.303tlog⁡aa−xk = \frac{2.303}{t}\log \frac{a}{a-x}
k=2.30312log⁡(100100−90) days−1k = \frac{2.303}{12}\log \bigg( \frac{100}{100 -90} \bigg) \,{ days^{-1}}
k=2.30312log⁡ 10=2.30312 days−1k = \frac{2.303}{12}\log \, 10 = \frac{2.303}{12} \,{ days^{-1}}
Now, for 99% decay,
k=2.303tlog⁡(100100−90)2.30312=2.303tlog⁡ 100 112=2tlog⁡ 10 ⇒t=24 daysk = \frac{2.303}{t}\log \bigg( \frac{100}{100 -90} \bigg) \frac{2.303}{12} = \frac{2.303}{t} \log \, 100 \, \frac{1}{12} = \frac{2}{t} \log \, 10 \, \Rightarrow t = 24 \, {days}