The half life of a first order reaction is 2000 years. If the concentration after 8000 years is $0.02…

The half life of a first order reaction is 2000 years. If the concentration after 8000 years is $0.02 \mathrm{M}$, then the initial concentration was :
  1. $0.16 \mathrm{M}$
  2. $0.32 \mathrm{M}$
  3. $0.08 \mathrm{M}$
  4. $0.04 \mathrm{M}$

Solution

Half life period $\left(t_{1 / 2}\right)=2000$ years
$\begin{aligned}
k & =\frac{0.693}{2000} \\
k & =\frac{2.303}{t} \log \frac{[\mathrm{A}]_o}{[\mathrm{~A}]_t} \\
\frac{0.693}{2000} & =\frac{2.303}{8000} \log \frac{[\mathrm{A}]_o}{0.02} \\
\therefore \quad[\mathrm{A}]_o & =0.32 \mathrm{M}
\end{aligned}$

Asked in: NEET 2022 (Phase 2)

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