Chemical Kinetics

Chemical Kinetics

Introduction

• Chemical kinetics studies reaction rates, the effects of reaction conditions, and reaction mechanisms.
• Kinetics provides a framework for reaction chemistry, leading to the exploration of reaction equilibria.
• Equilibrium is related to but distinct from kinetics.
• Spontaneous reactions (e.g., ATP utilization) release energy, but equilibrium doesn't indicate reaction rate.
• Conditions like temperature can alter ATP synthesis and utilization rates.
• Hyperthermia and hypothermia symptoms relate to changes in metabolism from temperature-dependent reaction kinetics.
• Multistep biochemical reactions (substrate-level and oxidative phosphorylation) have kinetic limitations in intermediate steps.

Reaction spontaneity

• Reactions can be spontaneous or non-spontaneous, determined by the change in Gibbs free energy ($\Delta G$).
• Even spontaneous reactions can be slow without enzymes or catalysts.
• Enzymes can be saturated, leading to a maximal turnover rate.

Reaction Mechanisms

• Balanced reaction equations are rarely accurate representations of actual chemical process steps.
• Most reactions proceed through multiple steps, forming a reaction mechanism.
• Knowing the mechanism helps explain reaction rate, equilibrium position, and thermodynamic characteristics.
• Consider: $A_2 + 2B \rightarrow 2AB$
• This equation may imply a single-step mechanism, but it could be multi-step.
• Step 1: $A<em>2 + B \rightarrow A</em>2B$ (slow)
• Step 2: $A_2B + B \rightarrow 2AB$ (fast)
• The sum of these steps gives the overall reaction.
• $A_2B$ is a reaction intermediate, often difficult to detect due to rapid consumption.
• Proposed mechanisms with intermediates can be supported by kinetic experiments.
• The slowest step in a mechanism is the rate-determining step, acting as a kinetic bottleneck.

Molecular Basis of Chemical Reactions

• Defining precise interactions between reactants is crucial to understanding the reaction rate.

Collision Theory of Chemical Kinetics

• Molecules must collide for a reaction to occur.
• The reaction rate is proportional to the number of collisions per second between reactant molecules.
• Not all collisions result in a reaction; effective collisions require correct orientation and sufficient energy to break existing bonds and form new ones.
• Activation Energy ($E_a$): The minimum energy of collision necessary for a reaction to take place.
• Only a fraction of colliding particles have enough kinetic energy to exceed the activation energy, making only a fraction of collisions effective.
• The reaction rate is expressed as: $rate = z \cdot f$, where $z$ is the total number of collisions per second and $f$ is the fraction of effective collisions.

Arrhenius Equation

• A more quantitative analysis is provided by the Arrhenius equation: $k = A \cdot e^{\frac{-E_a}{RT}}$
  • $k$ = rate constant of a reaction
  • $A$ = frequency factor (attempt frequency)
  • $E_a$ = activation energy of the reaction
  • $R$ = ideal gas constant
  • $T$ = temperature (in Kelvins)
• Frequency Factor ($A$): Measures how often molecules collide with units of $s^{-1}$.
• The relationship between variables is more important than calculation.
• As $A$ increases, $k$ increases (direct relationship).
• If $T$ increases to infinity, the exponent's magnitude becomes less than one, moving from a more negative value towards zero making the rate constant increase.
• Reaction rate increases with temperature.
• Increasing the number of molecules in a vessel increases $A$, increasing opportunities for collision.

Transition State Theory

• When molecules collide with energy ≥ $E_a$, they form a transition state (activated complex) where old bonds weaken and new bonds form.
• The transition state then dissociates into products.
• For the reaction $A_2 + 2B \rightarrow 2AB$, the reaction coordinate traces the reaction from reactants to products.
• The transition state (denoted by $\ddagger$) has greater energy than both reactants and products.
• The energy required to reach the transition state is the activation energy.
• Once formed, the activated complex can dissociate into products or revert to reactants.
• Transition states are theoretical constructs at the point of maximum energy, unlike reaction intermediates which have finite lifetimes.

Free Energy Diagram

• Illustrates the relationship between energy and the reaction progress.
• Key features:
  • Relative energies of products and reactants.
  • Free energy change of the reaction ($\Delta G_{rxn}$): difference between the free energy of the products and reactants.
  • Negative $\Delta G_{rxn}$: exergonic reaction (energy released).
  • Positive $\Delta G_{rxn}$: endergonic reaction (energy absorbed).
  • Transition state at the peak of the energy diagram.
  • Activation energy of the forward reaction: difference in free energy between the transition state and the reactants.
  • Activation energy of the reverse reaction: difference in free energy between the transition state and the products.

Example

• Formation of $HCl$ from $H<em>2$ and $Cl</em>2$:
  • $H<em>2(g) + Cl</em>2(g) \rightarrow 2HCl(g)$
• The reaction is exergonic; the free energy of the products is less than the free energy of the reactants.
• Energy is released, and the free energy change is negative.

Factors Affecting Reaction Rate

• Conditions that can alter experimental rates:

Reaction Concentrations

• Greater reactant concentration leads to more effective collisions per unit time, increasing the frequency factor ($A$).
• Reaction rate increases for all but zero-order reactions.
• For gaseous reactions, partial pressures serve as a measure of concentration.

Temperature

• Reaction rate increases with temperature for nearly all reactions.
• Temperature measures the average kinetic energy of particles.
• Increasing temperature increases the proportion of reactants with enough energy to surpass $E_a$, increasing the reaction rate.
• All reactions are temperature-dependent and have an optimal temperature for activity.
• A 10°C increase in temperature approximately doubles the reaction rate (generally true for biological systems but not always for other systems).
• At excessively high temperatures, catalysts may denature, and the reaction rate plummets.
• Enzymatic reactions have optimal temperatures (e.g., 35°C - 40°C) and fall sharply when denaturation occurs.

Medium

• The rate is also affected by the medium. Polar solvents are preferred, as their dipoles tend to weaken bonds of the reactants for a faster reaction.
• Some reactions prefer aqueous environments, and others prefer non-aqueous solvents (DMSO or ethanol).
• The physical state (liquid, solid, or gas) significantly affects the reaction.
• Polar solvents are generally preferred because they tend to polarize and weaken reactant bonds, facilitating faster reactions.

Catalysts

• Substances that increase the reaction rate without being consumed.
• Catalysts interact with reactants through adsorption or intermediate formation, stabilizing them to reduce the activation energy ($E_a$).
• Catalysts return to their original chemical state after product formation.
• Catalysts may increase collision frequency, change reactant orientation, donate electron density, or reduce intermolecular bonding.
  • Homogeneous catalysts: Present in the same phase as the reactants.
  • Heterogeneous catalysts: Present in a distinct phase.
• Catalysts decrease $E_a$ for both forward and reverse reactions but do not impact the free energies of the reactants or the products or the difference between them.
• Catalysts change only the rates of reactions and, in fact, change the forward rate and the reverse rate by the same factor.
• Catalysts have no impact on the equilibrium position or the measurement of $K_{eq}$.
• Catalysts will not transform a non-spontaneous reaction into a spontaneous one; they only accelerate spontaneous reactions toward equilibrium.