Chemistry: Class 121 — Chapter 3: Chemical Kinetics

• Average Rate ($r_{av}$): Depends on the change in concentration of reactants or products over a finite time interval $\Delta t$.
• Instantaneous Rate ($r_{inst}$): The rate of reaction at a specific instant of time, obtained when the time interval $\Delta t$ approaches zero.

Units of Rate: Expressed in $\text{mol L}^{-1} \text{s}^{-1}$ (or $\text{atm s}^{-1}$ for gaseous reactions where concentration is expressed in terms of partial pressures).

When the stoichiometric coefficients of reactants and products are not equal to one, the rate of consumption of reactants or formation of products is divided by their respective stoichiometric coefficients to obtain a uniform rate of reaction.

The rate law is the mathematical expression in which reaction rate is given in terms of molar concentration of reactants, with each term raised to some power which may or may not be equal to the stoichiometric coefficient of the reacting species in a balanced chemical equation.

Where $k$ is a proportionality constant called the rate constant, and exponents $x$ and $y$ must be determined experimentally.

The order of a reaction is defined as the sum of the powers of the concentration of the reactants in the rate law expression. It can be $0, 1, 2, 3,$ or even a fraction.

• Zero Order: The rate of reaction is independent of the concentration of reactants.
• First Order: The rate depends on the first power of reactant concentration.

Units of Rate Constant ($k$) for Different Orders:

• Zero Order: $\text{mol L}^{-1} \text{s}^{-1}$
• First Order: $\text{s}^{-1}$
• Second Order: $\text{L mol}^{-1} \text{s}^{-1}$

The molecularity of a reaction is the number of reacting species (atoms, ions, or molecules) taking part in an elementary reaction, which must collide simultaneously to bring about a chemical reaction.

• Unimolecular: One reacting species (e.g., decomposition of ammonium nitrite).
• Bimolecular: Two reacting species colliding simultaneously (e.g., dissociation of hydrogen iodide).
• Trimolecular: Three reacting species colliding simultaneously (rare and slow).

Key Differences between Order and Molecularity:

1. Order is an experimental quantity (can be zero or fractional); molecularity is a theoretical concept applicable only to elementary reactions (cannot be zero or non-integer).
2. For complex reactions, order is determined by the slowest step, known as the rate determining step, while molecularity has no meaning for the overall complex reaction.

For a zero-order reaction $R \rightarrow P$, the rate is proportional to the zero power of reactant concentration.

A plot of $[R]$ vs $t$ gives a straight line with slope $= -k$ and intercept $= [R]_0$.

For a first-order reaction $R \rightarrow P$, the rate is proportional to the first power of reactant concentration.

A plot of $\ln [R]$ vs $t$ yields a straight line with slope $= -k$ and intercept $= \ln [R]_0$. A plot of $\log \frac{[R]_0}{[R]}$ vs $t$ yields a slope $= \frac{k}{2.303}$.

The half-life ($t_{1/2}$) of a reaction is the time in which the concentration of a reactant is reduced to one-half of its initial concentration.

• For a Zero Order Reaction: $$t_{1/2} = \frac{[R]_0}{2k}$$ (directly proportional to initial concentration).
• For a First Order Reaction: $$t_{1/2} = \frac{0.693}{k}$$ (independent of initial concentration).

Reactions which are higher-order chemically but behave as first-order due to one of the reactants being present in large excess (such that its concentration remains virtually constant).

• Hydrolysis of Ethyl Acetate: Water is in large excess, so the rate depends only on ethyl acetate concentration.
• Inversion of Cane Sugar: $$C_{12}H_{22}O_{11} + H_2O \xrightarrow{H^+} C_6H_{12}O_6 + C_6H_{12}O_6$$

Where:

• $A$ is the Arrhenius factor, frequency factor, or pre-exponential factor.
• $E_a$ is the activation energy (measured in $\text{J mol}^{-1}$).
• $R$ is the gas constant, and $T$ is the absolute temperature.

Taking natural logarithms:

According to Arrhenius, reactants must form an unstable intermediate called an activated complex before converting to products. The energy required to form this complex is the activation energy ($E_a$).

A catalyst increases the rate of a reaction by providing an alternate pathway with a lower activation energy barrier.

• It does not alter the Gibbs energy ($\Delta G$) of a reaction.
• It catalyses spontaneous reactions but cannot force non-spontaneous reactions to occur.
• It helps attain equilibrium faster but does not change the equilibrium constant.

• Reactant molecules are assumed to be hard spheres, and reactions occur when they collide.
• Collision Frequency ($Z$): The number of collisions per second per unit volume of the reaction mixture.
• Effective Collisions: Only collisions with sufficient kinetic energy (threshold energy) and proper orientation lead to product formation.
• Steric Factor ($P$): A probability factor introduced to account for the requirement of proper molecular orientation during collision.