Question

Give relation between half-reaction time $\left(t_{1/2}\right)$ and initial concentration of reactant for $(n-1)$ order reaction.

• A. $t_{1/2}\propto {\left[R\right]}_0$
• B. $t_{1/2}\propto {\left[R\right]}_0^{2-n}$
• C. $t_{1/2}\propto {\left[R\right]}_0^{n+1}$
• D. $t_{1/2}\propto {\left[R\right]}_0^{n-2}$

Answer 1

Answer: (B)

$t_{1/2}\propto {\left[R\right]}_0^{2-n}$

For nth order reacition half life is-
$t_{\frac{1}{2}}=\frac{2^{n-1}-1}{(n-1)[A_o{]}^{n-1}{k}_A}$
For (n-1)th order reaction,

$t_{\frac{1}{2}}=\frac{2^{n-2}-1}{(n-2)[A_o{]}^{n-2}{k}_A}$
$t_{\frac{1}{2}}\propto [A_o{]}^{2-n}$
or $t_{\frac{1}{2}}\propto [R_o{]}^{2-n}$
Option B is correct.