The correct mathematical representation of the rate of a reaction is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rate law equation
The rate of a reaction at a given temperature depends on the concentrations of the reactants. The expression that gives the rate in terms of the molar concentrations of the reactants, each raised to some power, is the rate law (also called the rate equation or rate expression). For \( a\mathrm{A} + b\mathrm{B} \rightarrow \text{products} \):
\( \displaystyle \text{Rate} = -\frac{d[\mathrm{R}]}{dt} = k[\mathrm{A}]^{x}[\mathrm{B}]^{y} \)
The powers x and y need not equal the coefficients a and b; they are found by experiment. So the mathematical representation of the rate of a reaction is the rate law equation.
Why the other options are incorrect
Option (1) Arrhenius equation — Incorrect. \( k = A\,e^{-E_a/RT} \) gives the dependence of the rate constant on temperature, not the rate in terms of concentration.
Option (2) Collision frequency — Incorrect. It is the number of collisions per second per unit volume of the reaction mixture (ZAB), a quantity used in collision theory, not an expression for the rate.
Option (3) Molecularity of a reaction — Incorrect. It is the number of reacting species taking part in an elementary step; it is a number (1, 2 or 3), not a rate expression.
NCERT (2026-27 edition):
Dependence of Rate on Concentration
