Question

The rate constant value for a reaction is $1.75\times {10}^2{L}^2{mol}^{-2}{sec}^{-1}$.The half-life period

$t_{1/2}\propto$ ____.

• A. ${\left[R_0\right]}^{-1}$
• B. ${\left[R_0\right]}^{-2}$
• C. ${\left[R_0\right]}^2$
• D. ${\left[R_0\right]}^{}$

Answer 1

The correct option is B ${\left[R_0\right]}^{-2}$

$L^{2}mo{l}^{-1}se{c}^{-1}$ is SI units for third order reaction whose rate law is

$\frac{1}{a^2}=\frac{1}{a_0^2}+2kt$

for$a=\frac{a_0}{2}:$

$t_{\frac{1}{2}}=\frac{3}{2k{a}_0^2}\Rightarrow t_{\frac{1}{2}}\propto a_0^{-2}(\equiv [R_0{]}^{-2})$
Option B is correct.