The ratio of the half-life time $\left(t_{1/2}\right),$ to the three quarter life-time, $\left(t_{3/4}\right),$ for a reaction that is sècond order

For the reaction,

$A+B\to P=-\frac{d\left[A\right]}{dt}=-\frac{d\left[B\right]}{dt}=k\left[A\right]\left[B\right]$ and

$kt=\frac{1}{[A{]}_0-[B{]}_0}\ln \frac{\left[A\right][B{]}_0}{\left[B\right][A{]}_0}$ when, $[A{]}_0\ne [B{]}_0$
If, $[A{]}_0=[B{]}_0$ then the integrated rate law will he