Biological Chemistry - Reaction Kinetics

Biological Chemistry - Lecture 4: Reaction Kinetics

REACTION KINETICS

• The field of kinetics deals with the speed or rate at which chemical reactions proceed.

  • The rate of reaction is defined as the rate of change of concentration of reactants and products.

  • Key concerns in reaction kinetics include:

  • How rates of chemical reactions are measured.

  • How reactions and rates can be predicted.

  • How reaction rate data can be used to deduce probable reaction mechanisms.

REACTION MECHANISM

• Definition: A reaction mechanism is the detailed step-by-step description of a chemical reaction. It represents a hypothesis developed to account for observable facts in chemical reactions.

• Importance of understanding reaction mechanisms:

  • They help to create a framework for a reaction.

  • Understanding mechanisms allows for recognition of patterns in reactions.

ENERGY OF ACTIVATION

• For a reaction to occur, particles (atoms and molecules) must collide.

• Effective Collision: A collision is effective when it meets two criteria:

  • Sufficient energy (act or Ea).

  • Proper orientation of the colliding particles.

• Energy of Activation (Eact / Ea):

  • This is the minimum energy required for a collision to result in a reaction.

  • The source of activation energy is the kinetic energy of the moving particles.

  • Most collisions provide less than the minimum energy, hence reactions may not occur.

PROFILE OF A CHEMICAL REACTION

• Changes in energy during a reaction can be represented graphically. Two primary types of reactions include:

  • Exothermic Reaction: During this type of reaction, heat is generated and released.

  • Endothermic Reaction: During this type of reaction, heat is absorbed.

EXOTHERMIC REACTION

• Characteristics:**:

  • An example is the reaction between CO and NO2 in the gas phase, where the overall energy results in a net release of energy.

  • The process proceeds through an unstable state known as the activated complex or transition state.

  • This complex exists momentarily before breaking down into the products.

• Example of an exothermic reaction:

  • CH4 + 2 O2 → CO2 + 2 H2O + Heat

  • CaCl2(s) + 2 H2O(g) → Ca(OH)2(aq) + 2 HCl(g) + Heat

ENDOTHERMIC REACTION

• Characteristics: Heat is absorbed during endothermic reactions.

• Examples include:

  • Photosynthesis: 6 CO2 + 6 H2O + Heat → C6H12O6 + 6 O2

  • Cooking an egg: Heat is absorbed from the pan to cook the egg.

  • Dissolving ammonium nitrate: NH4NO3(s) + Heat → NH4+(aq) + NO3-(aq) (Flask feels cold).

ENTHALPY CHANGE

• Enthalpy Change (ΔH): The sign indicates the heat change when reactants are converted to products.

  • Positive ΔH indicates heat is absorbed.

  • Negative ΔH indicates heat is released.

FACTORS AFFECTING THE RATE OF REACTION

• Reactions occur when two reactant molecules effectively collide with enough energy and proper orientation. Key factors include:

  • Structure of the reacting species.

  • Concentration of the reactants.

  • Temperature.

  • Physical state of the reactants (solid, liquid, gas).

  • Presence of a catalyst.

STRUCTURE OF REACTING SPECIES

• Proper geometry for collision is essential.

• Electrostatic forces (attraction/repulsion) significantly influence reaction rates.

• Size and shape of molecules (especially bulky groups) may hinder effective collisions.

PHYSICAL STATE OF REACTANTS

• The physical state (solid, liquid, gas) affects reaction rates due to bond energies and molecular mobility.

• Reactions occur faster in gases due to increased mobility, then liquids, and slowest in solids.

CATALYSTS

• Catalysts increase reaction rates without undergoing change themselves.

• They lower the activation energy and provide effective surfaces for reactions.

CONCENTRATION OF REACTANTS

• An increase in the concentration of reactants generally increases the rate of reaction due to a greater number of effective collisions.

TEMPERATURE

• For each increase of 100 °C in temperature, the rate of reaction often doubles due to more molecules having sufficient energy to react.

ARRHENIUS THEORY

• Involves the collision of particles, where only a fraction of molecular collisions lead to reactions.

• The rate of most chemical reactions is approximately doubled for each 100 °C rise in temperature.

• Arrhenius Equation: The relationship between reaction rate constant (k) and temperature is given by: $k = Ae^{-E_a/RT}$

  • Where:

  • $k$ = rate constant

  • $E_a$ = activation energy

  • $R$ = universal gas constant (8.314 J/mol·K)

  • $T$ = absolute temperature (in Kelvin)

ARRHENIUS EQUATION CONT'D

• If collision orientations are accounted for, the equation becomes: $k = zpe^{-E_a/RT}$

  • Where $A = zp$ is the product of collision frequency (z) and steric factor (p).

• A logarithmic representation may be structured as: $ext{Log}<em>{10} ext{(k)} = - rac{E</em>a}{2.303R} imes rac{1}{T} + ext{log}_{10}A$

  • Slope of this graph gives the value of activation energy.

EXAMPLE

• Given activation energy of 100 kJ/mol and A as 10 M^-1 s^-1, find the rate constant at 300 K using the Arrhenius equation.

EYRING EQUATION

• Developed from transition state theory, it describes changes in the rate of a chemical reaction with temperature: $rac{In(k)}{T} = - rac{AH}{RT} + In\bigg( rac{K_B}{h} + rac{AS}{R}$

  • Where:

  • $AH$ = enthalpy of activation

  • $h$ = Planck's constant

  • $K_B$ = Boltzmann constant

THE RATE LAW

• According to the law of mass action, the rate of a reaction is proportional to the active masses of each of the reactants at constant temperature.

• Active mass = concentration raised to an appropriate power.

• For a reaction of the form:
  $mA + nB <br>ightarrow ext{Products}$

• The rate of reaction can be expressed as:
  $r riangleq k[A]^{m}[B]^{n}$

• Additionally, the overall order of reaction is derived from the sum of the exponents m and n.

REVERSIBLE REACTIONS & CHEMICAL EQUILIBRIUM

• Many reactions are reversible and can proceed in both directions:
  $A + B ⇌ C + D$

• As products are formed, the forward and reverse reactions establish an equilibrium where: $r<em>1 = r</em>2$

  • At equilibrium: $k<em>1[A]^{m}[B]^{n} = k</em>2[C]^{p}[D]^{q}$

  • The equilibrium constant (K) is given by:
    $K = rac{[C]^{p}[D]^{q}}{[A]^{m}[B]^{n}}$

CHAIN REACTIONS

• Chain reactions are spontaneous reactions that continue in an endless series once initiated.

• The three main steps include:

  • Chain Initiating Step: Energy absorption leading to radical generation.

  • Chain Propagating Step: Consumption of radicals generating new radicals.

  • Chain Terminating Step: Loss of radicals from the mixture by combining them.

ORDER OF REACTION

• Order of reaction signifies the dependence of rate on reactant concentrations and is expressible as an integer or fraction.

FIRST ORDER REACTION

• A reaction is first order if the rate is proportional to the concentration of one substance:
  $rac{d[N<em>2O</em>5]}{dt} = k[N<em>2O</em>5]$

SECOND ORDER REACTION

• If the rate depends on the concentrations of two reactants or the square of a single reactant, it is second order:
  $rac{d[N<em>2O</em>5]}{dt} = k[N<em>2O</em>5]^{2}$

ZERO ORDER REACTION

• For reactions where the rate remains constant regardless of concentration changes, it is classified as zero order:
  $rac{d[A]}{dt} = k$

MOLECULARITY

• Molecularity refers to the number of reactant molecules involved in the rate-determining step of a reaction.

• May be unimolecular (1), bimolecular (2), or termolecular (3), but never greater than 3 due to collision limitations.

• Simple reactions usually have a molecularity equal to the order of reaction for reaction steps occurring in one step.