Chemical Kinetics

Chemical kinetics is the study of how fast reactions go and what controls their speed. The rate of a reaction is the change in concentration of a reactant or product per unit time. For a reaction $\text{A} \rightarrow \text{B}$, the rate can be expressed as the rate of disappearance of A ($-\dfrac{d[A]}{dt}$) or the rate of appearance of B ($+\dfrac{d[B]}{dt}$). For a general reaction the rate is divided by each stoichiometric coefficient so that one value describes the whole reaction — a point NEET tests with the 'rate in terms of each species' question.

We distinguish the average rate (change over a measurable time interval) from the instantaneous rate (the rate at a particular instant, the slope of the concentration–time curve at that point). Rates are usually expressed in $\text{mol L}^{-1}\,\text{s}^{-1}$.

The rate depends on several factors: the concentration of reactants (more concentrated usually means faster), temperature (higher temperature speeds reactions sharply), the presence of a catalyst, the surface area of solids, and (for photochemical reactions) light. The quantitative dependence on concentration is captured by the rate law — a relationship determined experimentally, not from the balanced equation.

For a reaction $a\text{A} + b\text{B} \rightarrow$ products, the rate law takes the form $\text{rate} = k[A]^x[B]^y$, where $k$ is the rate constant and $x, y$ are the orders with respect to A and B. Crucially, $x$ and $y$ are found by experiment and need not equal the stoichiometric coefficients $a$ and $b$. The rate constant $k$ is independent of concentration but depends strongly on temperature; its units change with the overall order, which is another reliable NEET question.

Two terms describe how reactions depend on the species involved, and NEET frequently tests the distinction. The order of a reaction is the sum of the powers of the concentration terms in the experimentally determined rate law. It tells us how the rate responds to concentration and can be zero, a whole number, or even fractional. The molecularity, by contrast, is the number of reacting species that come together in a single elementary step; it is a theoretical quantity, always a positive whole number (1, 2, or rarely 3), and is defined only for elementary reactions.

The key differences: order is experimental and applies to the overall reaction, while molecularity is theoretical and applies only to a single step; order can be zero or fractional, but molecularity cannot. For a multi-step reaction, the overall order is governed by the slowest step, the rate-determining step — its molecularity often equals the overall order. Confusing these two is one of the most common NEET errors.

The units of the rate constant $k$ depend on the overall order, and reading them off is a guaranteed exam point. For a zero-order reaction, $k$ has units of $\text{mol L}^{-1}\,\text{s}^{-1}$; for first order, $\text{s}^{-1}$; for second order, $\text{L mol}^{-1}\,\text{s}^{-1}$. The general rule is units of $k = (\text{mol L}^{-1})^{1-\text{order}}\,\text{s}^{-1}$. You can therefore identify the order of a reaction simply from the units of its rate constant — and vice versa.

Order is found experimentally by methods such as the initial-rates method (measuring how the initial rate changes when one reactant's concentration is varied) or by fitting concentration–time data to integrated rate equations (the next topic). Once the order is known, the rate constant can be calculated, and the reaction's behaviour fully predicted. Being clear on order versus molecularity, and matching $k$'s units to the order, equips you for most conceptual NEET questions in kinetics.

The rate law tells us the rate at an instant; integrated rate equations tell us how concentration changes with time, which is what we actually measure. Each order has its own integrated form, and NEET problems usually plug values into the first-order equation.

For a zero-order reaction, the rate is independent of concentration, so $[A] = [A]_0 - kt$. A plot of $[A]$ against time is a straight line with slope $-k$. The half-life is $t_{1/2} = \dfrac{[A]_0}{2k}$, which depends on the initial concentration. Zero-order behaviour is seen in some surface-catalysed and photochemical reactions.

For a first-order reaction, the integrated equation is $k = \dfrac{2.303}{t}\log\dfrac{[A]_0}{[A]}$, and a plot of $\log[A]$ against time is a straight line with slope $-\dfrac{k}{2.303}$. The most important result is the half-life: $t_{1/2} = \dfrac{0.693}{k}$, which is independent of the initial concentration. This is why radioactive decay — a first-order process — has a constant half-life regardless of how much sample remains, a fact NEET often connects to nuclear chemistry and carbon dating.

The difference in half-life behaviour is a favourite NEET discriminator: for first order the half-life is fixed, so the amount remaining after $n$ half-lives is $[A]_0/2^n$; for zero order the half-life shrinks as the reaction proceeds. Being fluent with $k = \dfrac{2.303}{t}\log\dfrac{[A]_0}{[A]}$ and $t_{1/2} = \dfrac{0.693}{k}$, and knowing which graph is linear for each order, handles essentially all the quantitative kinetics questions in this chapter.

Reaction rates rise sharply with temperature — as a rough rule of thumb, the rate roughly doubles for every $10\ \text{K}$ increase. This strong dependence is explained quantitatively by the Arrhenius equation: $k = A\, e^{-E_a/RT}$, where $k$ is the rate constant, $A$ the frequency (pre-exponential) factor, $E_a$ the activation energy, $R$ the gas constant and $T$ the absolute temperature. The equation is central to NEET kinetics.

The activation energy $E_a$ is the minimum energy that colliding molecules must possess for a reaction to occur — the energy barrier between reactants and products. A higher $E_a$ means a slower reaction (fewer molecules can surmount the barrier), while a lower $E_a$ means a faster one. Taking logarithms gives the linear form $\ln k = \ln A - \dfrac{E_a}{RT}$, so a plot of $\ln k$ against $1/T$ is a straight line of slope $-E_a/R$, from which $E_a$ can be found — a standard NEET graph question.

Comparing rate constants at two temperatures gives the useful two-point form $\log\dfrac{k_2}{k_1} = \dfrac{E_a}{2.303\,R}\left(\dfrac{1}{T_1} - \dfrac{1}{T_2}\right)$, which lets you calculate $E_a$ from $k$ at two temperatures, or predict $k$ at a new temperature. The deeper picture comes from collision theory: molecules must collide with energy at least equal to $E_a$ and with the correct orientation; only such 'effective collisions' lead to product. The fraction of molecules exceeding $E_a$ rises rapidly with temperature, explaining the Arrhenius behaviour.

A catalyst increases the rate by providing an alternative pathway with a lower activation energy, so a larger fraction of collisions are effective. Importantly, a catalyst speeds up the forward and reverse reactions equally — it does not change the enthalpy change $\Delta H$ of the reaction or shift the position of equilibrium; it only helps the system reach equilibrium faster. This ties kinetics back to thermodynamics and equilibrium, and is a perennial NEET assertion-reason theme.