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  • The rate constant of a first order reaction is <img alt="\mathrm{13.8 \times 10^{-2} \mathrm{~s}^{-1}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B13.8%20%5Ctimes%2010%5E%7B-2

The rate constant of a first order reaction is \mathrm{13.8 \times 10^{-2} \mathrm{~s}^{-1}}. How much time will it take to reduce the concentration to its \mathrm{\frac{1}{9}} th value?

Option: 1

16 s


Option: 2

24 s


Option: 3

32 s


Option: 4

40 s


Answers (1)

best_answer

\mathrm{\begin{gathered} k=\frac{1}{t} \ln \frac{\left[R_0\right]}{[R]} \Leftrightarrow \frac{0.693}{t_{1 / 2}}=\frac{1}{t} \ln \frac{\left[R_0\right]}{[R]} \\\\ 13.8 \times 10^{-2}=\frac{1}{t} \ln \frac{1}{1 / 9} \Rightarrow t=\frac{\ln 9}{13.8 \times 10^{-2}} \\\\ t=16s \end{gathered}}

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Ritika Harsh

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