Chapter 3: Chemical Kinetics | Summary

The rate of a chemical reaction depends on several experimental conditions: concentration of reactants (or pressure in case of gases), temperature, and presence of a catalyst. The mathematical relationship between rate and concentration is called the rate law or rate expression. It must always be determined experimentally and cannot be predicted from the balanced chemical equation alone.

The rate law for a general reaction aA + bB → cC + dD is expressed as Rate = k[A]ˣ[B]ʸ, where x and y are experimentally determined exponents that may or may not equal the stoichiometric coefficients. The proportionality constant k is called the rate constant, which is specific to a reaction at a given temperature.

The order of a reaction is the sum of the powers of concentration terms in the rate law expression. It can be 0, 1, 2, 3, or even a fraction. A zero order reaction means the rate is independent of reactant concentration. Order is an experimentally determined quantity applicable to both elementary and complex reactions.

Molecularity is defined only for elementary reactions and refers to the number of reacting species (atoms, ions, or molecules) that must collide simultaneously for the reaction to occur. It can only be 1 (unimolecular), 2 (bimolecular), or 3 (trimolecular). For complex reactions, the rate is determined by the slowest step, called the rate-determining step, and the molecularity of that step equals the overall order of the reaction.

Integrated rate equations relate concentration directly to time, making it easier to determine rate constants experimentally. For a zero order reaction (R → P), the integrated equation is [R] = [R]₀ – kt. Plotting [R] vs t gives a straight line with slope = –k. Zero order reactions occur under special conditions such as enzyme-catalysed reactions and surface reactions (e.g., decomposition of NH₃ on hot Pt surface at high pressure).

For a first order reaction, the integrated rate equation is ln[R] = –kt + ln[R]₀, or equivalently k = (2.303/t) log([R]₀/[R]). A plot of ln[R] vs t gives a straight line with slope = –k. Examples include hydrogenation of ethene, radioactive decay, and decomposition of N₂O₅. Pseudo first order reactions like hydrolysis of ethyl acetate and inversion of cane sugar behaveas first order due to one reactant (water) being in large excess.

Half-life (t₁/₂) is the time required for the concentration of a reactant to decrease to half its initial value. For a zero order reaction, t₁/₂ = [R]₀/2k, showing that it is directly proportional to the initial concentration. For a first order reaction, t₁/₂ = 0.693/k, which is independent of the initial concentration — a characteristic feature of first order reactions.

The independence of half-life from initial concentration for first order reactions is highly significant. It means that the half-life remains constant throughout the reaction, regardless of how much reactant remains. This property is used extensively in radioactive decay calculations and in pharmacokinetics.

Most chemical reactions are accelerated by an increase in temperature. It has been found that for every 10°C rise in temperature, the rate constant nearly doubles. The quantitative relationship between rate constant and temperature is given by the Arrhenius equation: k = Ae^(–Ea/RT), where A is the frequency factor (pre-exponential factor), Ea is the activation energy, R is the gas constant, and T is the absolute temperature.

Taking the natural logarithm: ln k = –Ea/RT + ln A. A plot of ln k vs 1/T gives a straight line with slope = –Ea/R and intercept = ln A. The factor e^(–Ea/RT) represents the fraction of molecules with kinetic energy equal to or greater than the activation energy. The Maxwell-Boltzmann distribution curve shows that raising temperature increases the fraction of molecules with energy ≥ Ea, thereby increasing the rate.

A catalyst is a substance that increases the rate of a reaction without itself undergoing any permanent chemical change. It works by providing an alternate reaction pathway with a lower activation energy. According to the intermediate complex theory, the catalyst forms a temporary bond with reactants to give an intermediate complex, which then decomposes to yield products and regenerates the catalyst.

A catalyst does not alter the Gibbs energy (ΔG) or the equilibrium constant of a reaction. It catalyses both forward and backward reactions equally, so the equilibrium state remains unchanged but is attained faster. A substance that decreases the rate of a reaction is called an inhibitor, not a catalyst.

Collision theory, developed by Max Trautz and William Lewis in 1916–18, is based on the kinetic theory of gases. It postulates that reactant molecules are hard spheres and reactions occur when they collide. The number of collisions per second per unit volume is the collision frequency (Z). For a bimolecular reaction A + B → Products, rate = Z_AB × e^(–Ea/RT).

Not all collisions lead to product formation. Only effective collisions — those with sufficient kinetic energy (≥ threshold energy) and proper molecular orientation — result in reaction. To account for orientation, a steric factor P is introduced: Rate = PZ_AB × e^(–Ea/RT). Collision theory accurately predicts rate constants for simple molecules but shows deviations for complex molecules, as it ignores structural aspects.

Chemical kinetics provides a comprehensive framework for understanding how fast chemical reactions proceed and what variables control their speed. The key takeaways include: rate laws must be determined experimentally; order and molecularity are distinct concepts; integrated rate equations for zero and first order reactions allow calculation of rate constants from concentration-time data; half-life of first order reactions is independent of initial concentration; and the Arrhenius equation quantitatively links temperature, activation energy, and rate constant.

For CBSE board examinations, this chapter is highly important as it combines conceptual understanding with numerical problem-solving. Students must be proficient in writing rate expressions, calculating rate constants from integrated equations, determining half-lives, applying the Arrhenius equation to find Ea and A, and distinguishing between order and molecularity. Questions from collision theory and pseudo first order reactions are also frequently asked.