Chemistry - Chemical Kinetics Question with Solution | TestHub

Given:

$t_{1/2}(A)=5min$, $t_{1/2}(B)=15min$

Initially:

$[A{]}_0=4[B{]}_0$

For a first-order reaction:

$[A]=[A{]}_0{\left(\frac{1}{2}\right)}^{t/5}$

$[B]=[B{]}_0{\left(\frac{1}{2}\right)}^{t/15}$

When concentrations become equal:

$$4[B{]}_0{\left(\frac{1}{2}\right)}^{t/5}=[B{]}_0{\left(\frac{1}{2}\right)}^{t/15}$$

$$4={\left(\frac{1}{2}\right)}^{t/15-t/5}$$

$$4={\left(\frac{1}{2}\right)}^{-2t/15}=2^{2t/15}$$

$$2^2=2^{2t/15}$$

$$\frac{2t}{15}=2$$

$$t=15min$$