The mathematical expression that relates the rate of a reaction to the concentrations of the reactants is known as the rate expression, rate equation or rate law.
For the reaction \(A + B \rightarrow \text{Products}\), the rate equation is
\[\text{Rate} \propto [A][B]\]
\[\text{Rate} = k[A][B]\]
k is known as the rate constant or specific reaction rate. The units of the rate constant are \((\text{mol})^{1-n}\,(\text{L})^{n-1}\,\text{s}^{-1}\), where n is the order of the reaction.
The rate law for any reaction cannot be predicted by merely looking at the balanced chemical equation, i.e., theoretically, but must be determined experimentally.
Several chemical reactions take place in a sequence of steps, and the overall rate of the reaction is governed by the slowest step, called the rate determining step.
How does the half-life period of a reaction change with an increase in temperature?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → It decreases
The half-life (t1/2) is the time in which the concentration of a reactant falls to half its initial value. It is inversely proportional to the rate constant k:
\( \displaystyle \text{First order: } t_{1/2}=\frac{0.693}{k} \qquad \text{Zero order: } t_{1/2}=\frac{[\mathrm{R}]_0}{2k} \)
When the temperature rises, k increases (it nearly doubles for a 10° rise), so the reaction goes faster and t1/2 becomes shorter.
Why the other options are incorrect
Option (1) It increases — Incorrect. A longer half-life would need a smaller k, but k grows with temperature.
Option (3) It remains unchanged — Incorrect. The half-life of a first order reaction is independent of the initial concentration, not of temperature; it changes whenever k changes.
Option (4) It first increases and then decreases — Incorrect. k rises steadily with temperature, so t1/2 keeps falling; there is no stage where it rises.
NCERT (2026-27 edition):
3.4 Temperature Dependence of the Rate of a Reaction – “Most of the chemical reactions are accelerated by increase in temperature. For example, in decomposition of N2O5, the time taken for half of the original amount of material to decompose is 12 min at 50°C, 5 h at 25°C and 10 days at 0°C.”
“It has been found that for a chemical reaction with rise in temperature by 10°, the rate constant is nearly doubled.”