Question

If half life period of first order reaction is x and 3/4 th life period of same reaction is y.how are x and y related to each other?

Answer 1

T1/2=ln2/K=x(given)----------(1)

and t=ln(1/(1−3/4))/k=y (given)

or , t=ln(4)/k=y----------(2)

So (1) /(2)

xy=12

or , 2x=y

Hope it helps

Answer 2

half life of first order reaction, $T_{1/2}=x$

but we know from formula of half life in case of first order reaction, $T_{1/2}=\frac{ln2}{k}$, where k is rate constant.

now, x = ln2/k ......(1)

again, 3/4th life period of same reaction is y.

equation of first order reaction, t = $\frac{1}{k}ln\left[\frac{a}{a-x}\right]$

where a is initial amount of substance and (a - x) is amount of substance after time t.

here, x = (3/4)a and t = y

so, y = (1/k)ln[a/(1-3/4)a] = (1/k)ln4

y = 2ln2/k = 2(ln2/k)

from equation (1),

y = 2x

hence, relation between x and y is $\boxed{y=2x}$