Passage
Chemical Kinetics
Some reactions such as ionic reactions occur very fast, for example, precipitation of silver chloride occurs instantaneously by mixing of aqueous solutions of silver nitrate and sodium chloride. On the other hand, some reactions are very slow, for example, rusting of iron in the presence of air and moisture. The sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction. Another property of a reaction called molecularity helps in understanding its mechanism. The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction is called molecularity of a reaction. The half-life (t1/2) of a reaction is the time in which the concentration of a reactant is reduced to one-half of its initial concentration.
For reaction 3P → 2Q, the expression for rate of formation of Q i.e. \( \displaystyle \frac{d[\mathrm{Q}]}{dt} \) is equal to:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \displaystyle -\frac{2d[\mathrm{P}]}{3dt} \)
The rate of a reaction must have one value, whichever species is used to measure it. So the rate of change of each concentration is divided by its stoichiometric coefficient; a minus sign is used for reactants (their concentration falls) and a plus sign for products:
\( \displaystyle a\,\ce{A}\rightarrow b\,\ce{B}:\quad \text{Rate}=-\frac{1}{a}\frac{d[\mathrm{A}]}{dt}=+\frac{1}{b}\frac{d[\mathrm{B}]}{dt} \)
For 3P → 2Q:
\( \displaystyle -\frac{1}{3}\frac{d[\mathrm{P}]}{dt}=\frac{1}{2}\frac{d[\mathrm{Q}]}{dt} \)
\( \displaystyle \frac{d[\mathrm{Q}]}{dt}=-\frac{2}{3}\frac{d[\mathrm{P}]}{dt}=-\frac{2d[\mathrm{P}]}{3dt} \)
This makes sense: for every 3 mol of P used up, only 2 mol of Q are formed, so Q forms at two-thirds of the rate at which P disappears.
Why the other options are incorrect
Option (1) \( \displaystyle -\frac{3d[\mathrm{P}]}{2dt} \) — Incorrect. The ratio of the coefficients is inverted; Q would then form faster than P is used up.
Option (2) \( \displaystyle -\frac{d[\mathrm{P}]}{3dt} \) — Incorrect. This is the rate of the reaction, not the rate of formation of Q (which is twice this).
Option (3) \( \displaystyle \frac{2d[\mathrm{P}]}{dt} \) — Incorrect. The minus sign is missing (d[P]/dt is negative), and the factor 3 is lost.
NCERT (2026-27 edition):
Rate of a Chemical Reaction – …
