Question

Assertion (A): A fractional order reaction must be a complex reaction.
Reason (R): Fractional order of RDS equals to the overall order of a complex reaction.
A. Both (A) and (R) are true, and (R) is the correct explanation for (A).
B. Both (A) and (R) are true, but (R) is not the correct explanation for (A).
C. (A) is true, but (R) is false
D. (A) is false, but (R) is true
E. Both (A) and (R) are false

Answer 1

Think about what exactly it means to have a fractional order for a reaction and what it means for the consumption of reactions in the rate determining step. Consider the rate law and rules about single step reactions.

Complete step by step solution:
When the speed of a reaction depends on the concentration of a certain reaction, those reactants are said to contribute to the rate of the reaction. The concentration of these reactants is considered while determining the order of the reaction.
Let us consider the assertion ‘Assertion (A): A fractional order reaction must be a complex reaction.’
We know that for normal, single-step reactions; the order of the reactions can only be in integers. It is impossible for the order of a single-step reaction to be fractional since the reactants will be consumed according to the limiting reagents and the rate will depend on the whole of the reactants present.
If the reaction is complex, it will have one rate determining step. In this step, if only part of the total concentration of the reactants is required, then the order of the reaction will be fractional
For example, if we consider the reaction
$3A\to C$
Where the two steps are:
$2A\xrightarrow{RDS}B$
$B+A\to C$
Here, we can see that only 2 out of the three moles of a reactant are required in the rate determining step, and the order will be fractional.
Thus, if the order of a reaction is fractional, it has to be a multi-step complex reaction.
Let us consider the reason ‘Reason (R): Fractional order of RDS equals the overall order of a complex reaction.’
The rate-determining step is representative of the whole reaction in terms of order. The order of the rate determining step will always be equal to the overall order of the reaction. This will apply even if the order is fractional and not an integer.
Hence, (R) is true.
Here, we see that even if both the statements are true individually, they do not necessarily explain each other. They are individual statements relating to the same topic but the reason does not sufficiently explain the assertion.

Hence, the correct answer is ‘B. Both (A) and (R) are true, but (R) is not the correct explanation for (A).’

Note: Even if in a single-step reaction, a reagent is present in excess and only part of the reagent is used, this does not lead to the order of the reaction being fractional as the excess reagent is not essential for the completion of the reaction and can be ignored.
Even if the reason is not the correct explanation of the assertion, do not be misled into thinking that they are not related at all. The statements are related since an RDS can only be seen in complex reactions and not single-step reactions; we also know that only complex reactions have a fractional order which is due to the RDS.