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Question 45

Higher order (>3) reactions are rare due to:

First, recall the statement of the rate law for an elementary reaction. For any elementary step involving $$m+n+\dots$$ reacting molecules, collision theory tells us that its rate is directly proportional to the product of the concentrations of all those molecules, i.e.

$$\text{Rate}=k[A]^m[B]^n\dots$$

Here $$k$$ is the rate constant. The presence of each extra reactant concentration term reflects the fact that all of those molecules must collide simultaneously in the correct orientation for a successful reaction event.

Now consider what happens when the molecularity, and therefore the order, becomes large, say greater than $$3$$. For four different species the elementary event must involve a simultaneous collision of four particles. According to the kinetic theory of gases, the probability of such a four-body collision occurring in a tiny volume element in a very short time interval is proportional to the product of four separate number densities.

Mathematically, using simple probability arguments, if the probability of finding one specified molecule in that small region is $$p$$, then the probability of locating two independent specified molecules there together is $$p^2$$, for three it is $$p^3$$, and for four it falls to $$p^4$$. Because $$p<1$$, every additional multiplying factor makes the overall probability shrink drastically:

$$p > p^2 > p^3 > p^4 \quad (\text{for }0<p<1).$$

Thus, when more than three reactant molecules have to strike one another at exactly the same instant, the likelihood becomes so vanishingly small that, in practice, such elementary steps are almost never observed. Instead, reactions that appear overall to involve many molecules actually proceed through a sequence of simpler bimolecular or termolecular elementary steps.

Let us now weigh each option against this reasoning:

Option A talks about a loss of active species on collision. While some collisions may indeed be ineffective, that fact does not specifically explain why orders >3 are rare.

Option B states that the probability of the simultaneous collision of all reacting species is very low. This argument matches exactly with the statistical reasoning we have just developed, so it directly addresses the rarity of high-order reactions.

Option C claims that entropy and activation energy necessarily rise when more molecules are involved. Although activation energies can change, that is not the central, universally valid reason for the scarcity of elementary steps of order >3.

Option D refers to an equilibrium shift owing to elastic collisions, which is unrelated to the fundamental kinetics question being asked.

Therefore, only Option B pinpoints the core kinetic explanation: the extremely low probability of so many molecules meeting simultaneously with the correct orientation and energy.

Hence, the correct answer is Option B.

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