Question

The half life of a reaction is $46$ minutes when the initial concentration of the reactant is $0.4$ mole/lit and $92$ minutes when the initial concentration is $0.2$ mole/ lit. The order of the reaction is:

• A. 0
• B. $0.5$
• C. $2$
• D. $1$

Answer 1

The correct option is C $2$

$\begin{array}{cc}{t}_{1/2}\alpha {\left[Ao\right]}^{1-n}& \begin{array}{c}{t}_{1/2\left(1\right)}=46minA{o}_1=0.4mole/L\\ t_{1/2\left(2\right)}=96minA{o}_2=0.2mole/L\end{array}\\ \frac{t_{1/2\left(1\right)}}{t_{1/2\left(2\right)}}=\frac{{\left(A{o}_1\right)}^{1-n}}{{\left(A{o}_2\right)}^{1-n}}\Rightarrow {\left(\frac{0.4}{0.2}\right)}^{1-n}=\frac{46}{92}& \begin{array}{c}1-n=-1\\ n=2\end{array}\\ {\left(2\right)}^{1-n}=\frac{1}{2}& \\ {\left(2\right)}^{1-n}=2^{-1}& \end{array}$

C option is correct.