Question

For a second order reaction, $2A⟶$ Products, a plot of $\log t_{1/2}$ vs $\log a$ (where, $a$ is initial concentration) will give an intercept equal to which one of the following?

• A. $\frac{1}{k}$
• B. $\log \left(\frac{1}{2k}\right)$
• C. $\log \left(\frac{1}{k}\right)$
• D. $\log k$

Answer 1

The correct option is C $\log \left(\frac{1}{k}\right)$

For a second order reaction, $\frac{1}{a_t}=\frac{1}{a}+kt$

For $t_{1/2}$, $a_t=\frac{a}{2}$

$\frac{1}{a}=k{t}_{1/2}$

Taking logarithm, $-loga=logk+log{t}_{1/2}$

or $log{t}_{1/2}=-loga-logk=-loga+log\frac{1}{k}$

Intercept=$log1/k$