Question

For a given reaction $A$ $\to$ Products, rate is $1\times {10}^{-4}M{s}^{-1}$ when $\left[A\right]=0.01$ M and rate is $1.41\times {10}^{-4}M{s}^{-1}$ when $\left[A\right]=0.02$ M. Hence, rate law is:

• A. $-\frac{d\left[A\right]}{dt}=k[A{]}^2$
• B. $-\frac{d\left[A\right]}{dt}=k\left[A\right]$
• C. $-\frac{d\left[A\right]}{dt}=\frac{k}{4}\left[A\right]$
• D. $-\frac{d\left[A\right]}{dt}=k[A{]}^{1/2}$

Answer 1

The correct option is D $-\frac{d\left[A\right]}{dt}=k[A{]}^{1/2}$

For reaction,

$A$ $\to$ Products

We know,

Rate $=k$ $[A{]}^n$

$1\times {10}^{-4}=k[0.01{]}^n$ ...(1)

$1.41\times {10}^{-4}=k[.02{]}^n$ ...(2)

Dividing both equations,

$\frac{1}{1.41}={\left(\frac{1}{2}\right)}^n$

$n=\frac{1}{2}$

Hence, $\frac{-d\left[A\right]}{dt}=k[A{]}^{1/2}$