Question

A first order reaction has the rate constant, $k =4.6 \times 10^{-3} s ^{-1}$. The number of correct statement/s from the following is/are _______
Given: $\log 3=0.48$
A. Reaction completes in $1000 \,s$.
B. The reaction has a half-life of $500 \, s$.
C. The time required for $10 \%$ completion is $25$ times the time required for $90 \%$ completion.
D. The degree of dissociation is equal to $\left(1-e^{-k t }\right)$
E. The rate and the rate constant have the same unit.

Answer 1

$ t _{10 \%}=\frac{1}{ K } \ln \left(\frac{ a }{ a - x }\right)=\frac{1}{ K } \ln \left(\frac{100}{90}\right) $
$ t _{10 \%}=\frac{2.303}{ K }(\log 10-\log 9) $
$ t _{10 \%}=\frac{2.093}{ K } \times(0.04)$
Similarly
$ t _{90 \%}=\frac{1}{ K } \ln \left(\frac{100}{10}\right)$
$ t _{90 \%}=\frac{2.303}{ K } $
$ \frac{ t _{90 \%}}{ t _{10 \%}}=\frac{1}{0.04}=25 $
$e ^{ kt }=\frac{ a }{ a - x } $
$ \frac{ a - x }{ a }= e ^{- kt } $
$ 1-\frac{ x }{ a }= e ^{- kt } $
$ x = a \left(1- e ^{- kt }\right) $
$\alpha=\frac{ x }{ a }=\left(1- e ^{- kt }\right)$