Chemical Kinetics – JEE Main ChemistryPractice Questions & PYQs

Radioactive beta decay occurs when a nucleus attempts to stabilize its composition by transforming a constituent neutron into a proton. During this specific nuclear transmutation, the change in charge necessitates the creation and release of an electron, known as the $\beta$-particle, to satisfy fundamental conservation laws. This physical process is represented by the equation
${}_{0}^{1}n \rightarrow {}_{+1}^{1}p + {}_{-1}e$
which demonstrates that the emission arises specifically from the internal conversion of a neutron within the nucleus.

The half-life represents the time required for a substance to reduce to half its initial quantity, so we find the number of cycles by dividing the total time by the half-life period, calculated as $n = \frac{15}{5} = 3$. Applying the decay formula $N = N_0 \times (1/2)^n$ to an initial amount of 64 grams, we find the remaining substance by calculating $N = 64 \times (1/2)^3$. This calculation yields a final remaining mass of 8 grams.

The rate of a chemical reaction represents the change in concentration per unit time, expressed by the formula $\text{Rate} = k[\text{concentration}]^n$. For a first-order reaction where $n=1$, dividing the rate by the concentration yields units of M sec-1 divided by M, which simplifies to sec-1. For a zero-order reaction where $n=0$, the concentration term effectively becomes one, meaning the rate constant shares the same units as the rate, which is M sec-1.

The differential rate law expresses the speed of a chemical reaction by equating the rate of consumption of reactants and the rate of formation of products, divided by their respective stoichiometric coefficients. For the reaction $\mathrm{H}_2 + \mathrm{I}_2 \rightarrow 2\mathrm{HI}$, the relationship is defined as $-\frac{d[\mathrm{H}_2]}{dt} = -\frac{d[\mathrm{I}_2]}{dt} = \frac{1}{2} \frac{d[\mathrm{HI}]}{dt}$. Multiplying this entire equality by 2 removes the fraction and results in the rearranged expression $-2 \frac{d[\mathrm{H}_2]}{dt} = -2 \frac{d[\mathrm{I}_2]}{dt} = \frac{d[\mathrm{HI}]}{dt}$.