Question

Consider the following reactions:
Reaction 1:
$W\to P_1$
Reaction 2:
$X\to P_2$
Reaction 3:
$Y\to P_3$
Reaction 4:
$Z\to P_4$
The order of the above reactions are $0,1,2\&3$ respectively. The graph between $\log \left[rate\right]$ (y-axis) vs. $\log \left[\text{concentration of reactant}\right]$ (x-axis) is plotted.
Which of the following reaction will have the highest slope?

• A. Reaction 1
• B. Reaction 2
• C. Reaction 3
• D. Reaction 4

Answer 1

The correct option is D Reaction 4

For a $n^{th}$ order reaction
$A\to P$
$\text{Rate}=k[A{]}^n$
$k$ is rate constant
Taking log both sides
$\log \left[\text{Rate}\right]=\log \left(k\right[A{]}^n)$
$\log \left[\text{Rate}\right]=n\log \left[A\right]+\log \left(k\right)$
Compare with
$y=mx+c$
where
$y=\log \left[\text{Rate}\right]$
$m=\text{Slope}=n\text{i.e. the order of reaction}$
$x=\log \left[A\right]$
$c=\log \left(k\right)$
Since the slope of the graph between $\log \left[rate\right]$ (y-axis) vs. $\log \left[\text{concentration of reactant}\right]$ (x-axis) gives the order of the reaction.
The reaction which has a higher order will have a higher value of slope.
So reaction 4 has the highest slope