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 $1000s$.
B. The reaction has a half-life of $500s$.
C. The time required for $10\%$ completion is $25$ times the time required for $90\%$ completion.
D. The degree of dissociation is equal to $\left(1-e^{-kt}\right)$
E. The rate and the rate constant have the same unit.

Answer 1

Answer: 2

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