Chemical Kinetics: Mechanisms | General Chemistry 2

Collision Theory:

Collision theory is a fundamental concept in chemical kinetics that explains how and why chemical reactions occur. According to this theory, reactions occur when reacting molecules collide with sufficient energy and proper orientation.
 

Activation energy E_a (in J.mol^-1):

The activation energy is the minimum energy that colliding molecules must possess for a reaction to occur is called the activation energy. If the kinetic energy of the molecules is less than the activation energy, the molecules will collide but not react.
 

The reactants must also be oriented in a specific way when they collide to facilitate the breaking and forming of bonds. Even if the energy is sufficient, incorrect orientation can result in no reaction.

The Arrhenius equation:

The Arrhenius equation is a key formula in chemical kinetics that quantifies the effect of temperature on the rate of a chemical reaction. It also provides insight into the activation energy and the frequency of molecular collisions that lead to a reaction. The Arrhenius equation is expressed as:
 

The frequency factor (A) represents the frequency of collisions between reactant molecules and how likely these collisions are to be oriented in a way that leads to a reaction. The frequency factor is a constant that depends on the specific reaction.

Applications of the Arrhenius equation:

• Predicting temperature effects: The Arrhenius equation is used to predict how changes in temperature affect the rate of a reaction. According to the equation, the rate constant k increases exponentially as the temperature increases. This is because higher temperatures provide more energy to the molecules, increasing the fraction of molecules that have energy equal to or greater than the activation energy.
• Determining activation energy (E_a) and frequency factor (A): By measuring the rate constant k at different temperatures and plotting lnk versus $\frac{1}{\mathrm{T}}$(a plot called an Arrhenius plot), a straight line is obtained with a slope of - $\frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{R}}$ and an intercept of lnA.

Reaction mechanism:

A reaction mechanism is a step-by-step sequence of elementary reactions by which an overall chemical change occurs. Understanding the mechanism of a reaction provides insight into the individual steps involved, the order in which bonds are broken and formed, and the role of intermediates and transition states.

Elementary reaction:

An elementary reaction is a reaction that occurs in a single collision of the reactant molecules, meaning it occurs in a single step. The reaction order of an elementary reaction is equal to the stoichiometric coefficients of the reactants.
 

The formation of NO₂ can be divided in 2 elementary steps:

• Step (1): 2 NO → N₂O₂
• Step (2): N₂O₂ + O₂ → 2 NO₂
• Overall reaction (1) + (2): 2 NO + O₂ → 2 NO₂

Reversible reaction:

A reversible reaction is a reaction in which products can react to reform reactants. This type of reaction proceeds in both the forward and reverse directions. At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction.
 

The reaction 2 NO $\rightleftharpoons$ N₂O₄ is reversible.
At equilibrium: k₁ [NO]² = k_-1 [N₂O₄]

Intermediate vs. catalyst:

• Intermediate: A species that is produced in one step and consumed in a subsequent step. Intermediates do not appear in the overall balanced equation.
• Catalyst: A species that is first consumed and later regenerated. Catalysts do not appear in the overall balanced equation but play a crucial role in altering the reaction mechanism by providing an alternative pathway with a lower activation energy.

• Step (1): 2 NO → N₂O₂
• Step (2): N₂O₂ + O₂ → 2 NO₂
• Overall reaction (1) + (2): 2 NO + O₂ → 2 NO₂

In this example, N₂O₂ is an intermediate: it is produced in step (1) and consumed in step (2).

Rate laws for elementary reactions:

The rate law for an elementary reaction can be directly written from the stoichiometric coefficients of the reactants in the balanced equation as the exponent in the rate law. For example:

• For a unimolecular reaction (one molecule decomposes) A → Products, the rate law is first-order:
  Rate = k [A]
• For a bimolecular reaction (two molecules collide) A + B → Products, the rate law is second-order:
  Rate = k [A][B]

Consider the following bimolecular elementary reaction: NO + O₃ → NO₂ + O₂. Since this is an elementary reaction, the rate law can be written directly from the reaction equation:

Rate = k [NO][O₃]

Rate-determining step:

The rate-determining step is the step in a reaction mechanism that is much slower than all the other steps. Since this step is the slowest, it controls the overall rate of the reaction. The rate law for the overall reaction is directly determined by the rate law of this rate-determining step.
 

Consider a reaction mechanism:

• Step (1): 2 NO₂ → NO + NO₃   (slow)
• Step (2): NO₃ + CO → NO₂ + CO₂   (fast)

Overall reaction: NO₂ + CO → NO + CO₂

In this example, the first step is the rate-determining step, as it is much slower than the second step. Therefore, the rate law for the overall reaction is determined by the first step: Rate = k [NO₂]² 

Catalysis:

Catalysis is the process by which a catalyst increases the reaction rate. The are different types of catalysis depending on the phase of the catalyst and the reactants:

• Homogeneous catalysis: the catalyst and the reactants exist in the same phase, typically in a liquid or gas phase. The catalyst interacts uniformly with the reactants to form intermediates, which then decompose to yield the products while regenerating the catalyst.
• Heterogeneous catalysis: the catalyst and the reactants exist in different phases, usually with the catalyst being a solid and the reactants in a liquid or gas phase. The reaction typically occurs on the surface of the solid catalyst, where reactants are adsorbed, react, and then desorb as products. Heterogeneous catalysis is the most important type of catalysis in industrial chemistry.

• Homogeneous catalysis: Acid catalysis in esterification reactions, where a proton (H⁺) catalyzes the reaction between an alcohol and a carboxylic acid to form an ester.
• Heterogeneous catalysis: The catalytic converter in cars, where solid platinum or palladium catalysts convert harmful gases like carbon monoxide (CO) into less harmful substances like carbon dioxide (CO₂).

Catalyst:

A catalyst is a substance that increases the rate of a chemical reaction without being consumed in the process.  It achieves this by lowering the activation energy barrier, making it easier for the reaction to proceed. Catalysts do not alter the equilibrium position of the reaction; they simply allow the system to reach equilibrium faster.
 

Enzymes:

Enzymes are biological catalysts that increase the rate of biochemical reactions in living organisms. They are highly specific, typically catalyzing only one type of reaction or acting on specific substrates. Enzymes operate under mild conditions (e.g., physiological temperature and pH) and follow complex mechanisms involving the formation of enzyme-substrate complexes.