For a chemical reaction, which can never be a fractional number?

Molecularity

The correct answer is option 3. Molecularity.

Let us delve deeper into each term and its characteristics to understand why molecularity can never be a fractional number.

 1. Order

The order of a reaction is the sum of the powers of the concentration terms in the rate law expression. For a reaction of the form:

\(\text{Rate} = k[A]^m[B]^n \)

The order of the reaction is \( m + n \), where \( m \) and \( n \) are the orders with respect to the individual reactants \( A \) and \( B \), respectively.

Fractional Order: The order can indeed be a fractional number. For example, in a reaction where the rate law is:

\(\text{Rate} = k[A]^{0.5}[B]^2\)

The overall order of the reaction is \( 0.5 + 2 = 2.5 \). Fractional orders can occur due to complex reaction mechanisms or intermediates.

2. Half-life

The half-life (\( t_{1/2} \)) of a reaction is the time required for the concentration of a reactant to reduce to half of its initial value. It is often expressed as:

\(t_{1/2} = \frac{0.693}{k}\)

for first-order reactions, or in more complex forms for other reaction orders.

Fractional Half-life: While the numerical value of the half-life can be fractional, it is not inherently restricted by the nature of the reaction. The time required for half-life can be any positive value, including fractional values.

3. Molecularity

Molecularity refers to the number of reactant molecules or ions involved in an elementary reaction step. It describes the reaction mechanism and is defined as:

Unimolecular (1 molecule)

Bimolecular (2 molecules)

Trimolecular (3 molecules)

Whole Number Requirement: Molecularity must be a whole number because it represents the actual count of reacting species in an elementary reaction step. For instance:

A unimolecular reaction involves one reactant molecule.

A bimolecular reaction involves two reactant molecules interacting.

It is impossible to have a fraction of a molecule participating in a reaction; hence, molecularity is always a whole number (1, 2, 3, etc.).

4. Rate Constant

The rate constant (\( k \)) is a proportionality constant in the rate law expression. Its value is dependent on the reaction conditions and can be calculated from experimental data.

Fractional Rate Constant: The rate constant can be any positive value, including fractional numbers, depending on the reaction order and conditions.

Conclusion:

Molecularity can never be a fractional number because it directly counts the number of reacting species involved in an elementary reaction step, which inherently requires whole numbers. In contrast, other parameters like reaction order, half-life, and rate constant can have fractional values due to their nature and calculations.

So, the characteristic that distinguishes molecularity from the others is its necessity to be a whole number, hence: Molecularity.