Question

$A\to Bzeroorderreaction$
$C\to Dfirstorderreaction$
If the first order reaction gets 75% completed in
40 minutes and zero order reaction gets 75%
completed in 30 minutes then calculate the value
of Z, where Z is ratio of half life of first order and zero order reaction

Answer 1

The integral rate equation for first order reaction is $t=\frac{1}{k}\ln \frac{a}{a-x}$
Now $40=\frac{1}{k}\ln \frac{a}{a-0.75a}$
$k=\frac{2}{40}\left(\ln 2\right)mi{n}^{-1}$
$t_{1/2}=\frac{ln2}{k}=20min$
for zero order reaction rate of reaction does not depend on concentration and it is constant through out the reaction progress so if 75 % is consumed in 30 min then by unitary method $t_{1/2}=20min$
so $Z=\frac{20}{20}=1$