Key Points

The rate of a reaction is the change in concentration of a reactant or product per unit time. For a reaction $R \rightarrow P$, the average rate is $r_{\text{av}} = -\frac{\Delta[R]}{\Delta t} = +\frac{\Delta[P]}{\Delta t}$.

The instantaneous rate is the rate of reaction at a particular moment in time. It is determined by the slope of the tangent to the concentration versus time curve at that point, expressed as $r_{\text{inst}} = -\frac{d[R]}{dt}$.

The rate law is an expression that relates the rate of a reaction to the concentration of reactants. For a general reaction $aA + bB \rightarrow \text{Products}$, the rate law is $\text{Rate} = k[A]^x[B]^y$, where k is the rate constant.

The order of a reaction is the sum of the powers of the concentration terms in the experimentally determined rate law. For $\text{Rate} = k[A]^x[B]^y$, the overall order is $x + y$. It can be zero, an integer, or a fraction.

Molecularity is the number of reacting species (atoms, ions, or molecules) that collide simultaneously in an elementary (single-step) reaction. It is a theoretical concept and must be a positive integer (e.g., unimolecular, bimolecular).

Order is an experimental quantity determined from the rate law and can be zero or fractional, while molecularity is a theoretical quantity for elementary reactions and cannot be zero or non-integer. For an elementary reaction, order equals molecularity.

For a zero-order reaction, the rate is independent of concentration ($\text{Rate} = k$). The integrated rate equation is $[R] = -kt + [R]_0$, where $[R]_0$ is the initial concentration.

The half-life ($t_{1/2}$) is the time taken for the reactant concentration to reduce to half its initial value. For a zero-order reaction, it is directly proportional to the initial concentration: $t_{1/2} = \frac{[R]_0}{2k}$.

For a first-order reaction, the rate is proportional to the first power of the concentration ($\text{Rate} = k[R]$). The integrated rate equation is $\ln[R] = -kt + \ln[R]_0$ or $k = \frac{2.303}{t} \log \frac{[R]_0}{[R]}$.

The half-life for a first-order reaction is independent of the initial concentration of the reactant. It is given by the formula $t_{1/2} = \frac{0.693}{k}$.

These are reactions that are not truly first-order but appear to be, because one of the reactants is present in a large excess, so its concentration remains almost constant during the reaction. An example is the acid hydrolysis of an ester.

The effect of temperature on the rate constant is given by the Arrhenius equation: $k = A e^{-E_a/RT}$. Here, $A$ is the pre-exponential factor, $E_a$ is the activation energy, R is the gas constant, and T is the absolute temperature.

Activation energy ($E_a$) is the minimum amount of energy that reacting molecules must possess in order to form the activated complex and convert into products. A lower activation energy leads to a faster reaction rate.

A catalyst increases the rate of a reaction by providing an alternative reaction pathway with a lower activation energy ($E_a$). It does not get consumed in the reaction and does not affect the overall Gibbs energy change ($\Delta G$) or the equilibrium constant.

According to collision theory, a reaction occurs when reactant molecules collide with sufficient kinetic energy (threshold energy) and in the correct orientation. The rate is expressed as $\text{Rate} = P Z_{AB} e^{-E_a/RT}$, where P is the steric factor and $Z_{AB}$ is the collision frequency.