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  • The decomposition of a compound A follows a first order rate law. If it takes 15 min for 20% of the initial compound to decompose, then calculate the value of rate constant

The decomposition of a compound A follows a first order rate law. If it takes 15 min for 20% of the initial compound to decompose, then calculate the value of rate constant:

 

Option: 1

3.34 \mathrm{~min}^{-1} \\


Option: 2

2.12 \mathrm{~min}^{-1} \\


Option: 3

0.22 \mathrm{~min}^{-1} \\


Option: 4

0.014 \mathrm{~min}^{-1}


Answers (1)

best_answer

For a first order reaction:
\mathrm{A \rightarrow}Products
\mathrm{ [A]=\left[A_0\right] e^{-k t} .}
Here,
\mathrm{ [A]=.} Concentration of \mathrm{ \mathrm{A}} at time t
\mathrm{ \left[A_0\right]=}  Concentration of A initially \mathrm{ k=}  Rate constant
Given:
\mathrm{ \text { At } t=15 \min \Rightarrow[A]=0.8\left[A_0\right] }
Putting the value in (i)

\mathrm{ 0.8\left[A_0\right]=\left[A_0\right] e^{-k \times 15} \\ }

\mathrm{ \ln (0.8)=-k \times 15 \\ }

\mathrm{ k=\frac{0.22}{15}=0.014 \mathrm{~min}^{-1} }.
 

Posted by

himanshu.meshram

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