Q.For a reaction $A + B \rightarrow$ Products, the rate law is — Rate $= k[A][B]^{3/2}$
Can the reaction be an elementary reaction? Explain.

The key idea is that for an elementary reaction, the rate law must match the stoichiometric coefficients exactly — the molecularity determines the exponents.

Reasoning:

1. The given reaction is $A + B \rightarrow \text{Products}$, so if it were elementary, the rate law would be:

   $\text{Rate} = k[A]^1[B]^1$.

2. However, the actual rate law is $\text{Rate} = k[A][B]^{3/2}$. The exponent of $[B]$ is $3/2$, which is not an integer. …

The question asks whether a reaction with the given rate law can be an elementary reaction. This is a classic test of the definition of an elementary reaction.

An elementary reaction is one that occurs in a single step, exactly as written in the chemical equation. For such a reaction, the rate law is directly determined by the molecularity — the number of molecules that must collide simultaneously. The exponents in the rate law must be the stoichiometric coefficients of the reactants in that step.

Now look at the given reaction: $A + B \rightarrow$ Products. The stoichiometric coefficients are 1 for A and 1 for B. If this were an elementary reaction, the rate law would have to be:

But the actual rate law given is:

The exponent on $[B]$ is $3/2$, which is a fraction. This is the critical point.

1. Fractional orders are impossible in elementary reactions. Why? Because an elementary step represents a physical collision event. You cannot have half a molecule colliding. The number of molecules involved must be an integer — 1, 2, or 3. So the exponent must be a whole number.

2. The exponent 3/2 is not a whole number. This alone is sufficient to rule out an elementary reaction. Even if the exponent were a whole number but didn't match the stoichiometric coefficient (e.g., Rate $= k[A]^2[B]$), it would still not be elementary. Here, the mismatch is even more fundamental. …

Method: Elementary Reaction Check Using Molecularity and Rate Law Consistency

Concept First — Why This Method Works

An elementary reaction is one that occurs in a single step, with no intermediates. For such a reaction, the rate law can be written directly from the stoichiometric coefficients (the numbers in front of reactants in the balanced equation). This is because the probability of collision depends on how many molecules of each type must meet.

If the given rate law does not match the stoichiometric coefficients, the reaction cannot be elementary.

Steps

1. Write the stoichiometric coefficients from the balanced equation For:

Coefficient of $A = 1$, coefficient of $B = 1$.

2. Write the expected rate law if the reaction were elementary For an elementary reaction, the exponents equal the coefficients:

3. Compare with the given rate law Given:

• Expected exponent of $[B]$ = 1
• Given exponent of $[B]$ = $3/2$ (which is not an integer)

4. Apply the rule …

Here are the common mistakes students make with this question, along with how to avoid each.

Mistake 1: Confusing "Molecularity" with "Order"

The Mistake: Students see the rate law $\text{Rate} = k[A][B]^{3/2}$ and immediately say "The order is $1 + 1.5 = 2.5$, so it cannot be elementary because the molecularity must be a whole number."

While the conclusion is correct, the reasoning is often incomplete or muddled. They forget that molecularity (the number of molecules colliding) must be a positive integer (1, 2, or rarely 3), while order is an experimental value that can be fractional.

How to Avoid:

• Define both terms clearly before answering.
  • Molecularity: The number of reactant particles taking part in an elementary step. It is always a whole number (1, 2, or 3).
  • Order: The sum of the exponents in the experimentally determined rate law. It can be fractional, zero, or negative.
• Connect them correctly: For an elementary reaction, the order equals the molecularity for each reactant. Therefore, the exponents in the rate law must be integers (1, 2, or 3) that sum to a small integer.

Mistake 2: Ignoring the Fractional Exponent

The Mistake: Students see the $[B]^{3/2}$ term and think "It's just a power, maybe it's possible." They fail to recognize that a fractional exponent ($3/2$) is a red flag for an elementary reaction.

How to Avoid:

• Memorize the rule: For an elementary reaction, the exponents in the rate law are the stoichiometric coefficients of the balanced equation. Since coefficients are whole numbers, the exponents must be whole numbers.
• Spot the contradiction: The exponent $3/2$ means the reaction would require 1.5 molecules of B to collide simultaneously. This is physically impossible. A molecule is a discrete entity; you cannot have half a molecule in a collision.

Mistake 3: Forgetting to State the "Why"

The Mistake: Students simply answer "No" without explaining why the fractional order makes it impossible. In an exam, the explanation is worth more marks than the yes/no answer.

How to Avoid:

• Structure your answer in two parts:
  1. Conclusion: No, it cannot be an elementary reaction. …