W20N Chemical Kinetics

Why Study Reaction Rates?

• Studying reaction rates helps understand reaction mechanisms, such as SN1 and SN2 reactions
• Reaction rates are optimized to improve yield and reduce side-products
• Understanding reaction rates aids in minimizing drug degradation, including predicting and improving shelf-life
• Reaction rates help to understand what drives a reaction forward, such as H2 + ½ O2 → H2O ΔH = -286 kJ/mol

Factors Affecting Reaction Rate

• Physical state impacts reaction rates, with many pharmaceutically relevant reactions occurring in solution
• Concentration influences reaction rates as molecules must come into contact to react
  • Increased concentration leads to an increased frequency of collisions
• Temperature affects reaction rates through increasing frequency of collision
  • Higher temperatures increase the vibrational energy of the bonds
• Catalysts increase the rate of reaction via alternative reaction mechanisms

Collision Theory

• Reaction rate relies on the frequency of reacting molecules colliding with sufficient energy
• Collision rate depends on concentration with increased reaction chances
  • This depends on the reaction order
• For a gas, collision rate increase with pressure with the PV = nRT formula
• Surface area and molecular orientation are collision rate dependent
• Temperature and molecular speed affect the collision rate

Effect of Surface Area

• Collision rate depends on available surface area
• For example, the reaction Mg(s) + 2H+ (aq) -> Mg2+(aq) + H2(g) shows this relationship
  • Only the outside of a substance is available to react

Effect of Molecular Orientation

• Correct orientation is required for a collision to produce a reaction
• Not all collisions result in a reaction
  • Reactions involving more complex reactants are less likely to occur
  • Electrophilic addition, such as HCl and ethene
• Complex reactions may only occurs 1 in 10^5 collisions

Effect of Molecular Speed

• Collision rate depends on the molecular speed
• Temperature impacts speed
• Based on kinetic theory of gases
• The formula Vrms = √3RT/M shows this relationship
• An increase in temperature slightly increases speed and volume

Sufficient Energy

• An energy barrier is associated with the transition state, involving distortion of molecular shape
• Normal energy barrier is typically 50-100 kJ/mol
  • The average energy at 20°C is approximately 4 kJ/mol
• Most molecules exhibit insufficient energy, only about 1 in 10^9

Maxwell-Boltzmann Distribution

• Describes the distribution of molecular speeds in a gas
• Represents the number of molecules with sufficient energy to react
• The number of particles not represented by the area under a curve do not display enough energy
• James Clerk Maxwell developed the distribution

Effect of Temperature on Activation Energy

• Increasing temperature increases the number of particles with sufficient activation energy
• Reaction temperature is average energy over the entire system
• Shall increases allow for a large fraction of particles to be available for a reaction

Arrhenius Equation

• Increasing temperature increases rate by increasing k
• Rate constant (k) can be deduced at varying temperatures
• t50 and t90 can also be determined from experiments
• The Arrhenius equation is ln k₁ = ln A – Ea/RT
• An alternative form connects k to temperature: k = Ae-Ea/RT
  • k: indicates the fraction of energy that is able to react
  • A: frequency factor (pre-exponential factor)
  • Ea: activation energy (probability of a collision resulting in a reaction)
  • R: gas constant (8.3145 J mol-1 deg-1)
  • T: temperature (in Kelvin)

Impacts of Temperature

• A is rate constant if an energy barrier is absent
  • This also applies if T is infinite (or very high)
• e-Ea/RT is the fraction of molecules with sufficient energy to react
• Using 50,000 J/mol as the activation energy
  • With temperatures of 293 and 303°K, the fraction of molecules able to react (e) is almost doubled
  • This is when increased by a 10°C increase in temperature

Catalysts

• Catalysts increase reaction rates without being consumed
  • Such as acid catalyzed hydrolysis of esters and chlorine radicals catalyzing the breakdown of ozone
• Provide a lower activation energy pathway for the reaction
• The activation energy is lower, and increases rate increases as a result

Catalyst Effects and Properties

• Catalysts do not affect the equilibrium position of a reaction
• Catalysts do not make unfavorable reactions favorable
  • Overall ΔG does not change; only speeding up
• Enzymes are proteins that act as biological catalysts such as:
  • Acetylcholinesterase: hydrolyzes acetylcholine in 100 μs

Rate of Reaction

• Describes concentration change over time
• A + B --> C demonstrates this concept
• Decrease the reactant concentration (A or B)
• Increase the product concentration (C)
• The rate is calculated with −ΔA/Δt = −ΔB/Δt = ΔC/Δt is a difference over a finite time
• Changing over infinitesimally small time is demonstrated by: Rate = −dA/dt = −dB/dt = dC/dt

Multi-Step Reactions

• Most reactions are multi step
• Molecularity must be an integer and is not the same as reaction order

Understanding Increases in Concentration

• If the rate is independent of [A], then nothing happens to the rate
• A first order reaction results in the rate = k[A]
  • Doubling [A] doubles k, and tripling [A] triples k
• A second order reaction can be rate = k[A]^2;
  • doubling a results in k quadrupled (2^2 = 4)
  • Tripling a results in k increased 9-fold (3^2 = 9)

Understanding Reaction Order

• Units of k must give M/s when combined with concentration units (M)
• Rate Multiplication is the sum of each of the reactant orders such as; aA + bB + cC ->dD + eE, and rate = k[A]x[B]y[C]z where x is the order of A, not the stoichiometry

Rate Laws

• The rate law illustrates the change in reactant concentration as a function of time, represented with a linear curve

Rate Order Calculation Example

• The overall rate order and reaction order can be computed
• F₂ + 2ClO₂ → 2ClO₂F exemplifies calculation of rate orders
• Doubling [F₂] doubles the rate
  • [F₂] must be 1st order
• Doubling [ClO₂] doubles the rate
  • [ClO₂] must also be 1st order
• Overall order is 1+1 = 2nd order
• The rate law is k [F₂] [ClO₂]

Rate Order Examples

• The rate can be calculated from experimental data on reactants and products
• A complex reaction can be broken down into its reactants, where the overall reaction order can be calculated, such as the formula; BrO3¯ + 5Br¯ + 6H+ → 3 Br2 + 3H2O
• Doubling [BrO3-] doubles the rate, indicating it must be 1st order
• Doubling [Br-] doubles the rate, signifying 1st order reaction
• Doubling [H+] quadruples the rate, meaning the rate reaction is 2nd order

Rate Law Examples

• If the reaction between A + B is measured: rate = k[A][B]
  • The reaction is first order w.r.t. A and B, so the overall rate is second order
• rate = k[B]^2; the reaction w.r.t A is zero and w.r.t B is second order reaction - The overall rate is second order
• If rate = k[A]; the order w.r.t A is first and the order w.r.t B is zero - The overall order is 1

SN1 Reaction

• SN1 reaction: tert-Butyl chloride and hydroxyl anion
  • Rate = k[(CH3)3CBr]
    • The rate is only dependent on (CH3)3CBr
    • OH has no affect on rate of the reaction
• Step 1 - (rate determining) unimolecular
• Step 2 - Fast (does not affect overall rate of reaction)

SN2 Reaction

• SN2 reaction: Chloromethane and hydroxyl anion
  • Rate = k[(CH3)3CBr][OH-] means both components affect the rate of reaction
• Bimolecular

Determining Mechanisms

• For a reaction between A + B, rate =k[A][B] the mean both contribute rate
• If the slow step is first in the mechanism
  • The orders tell you what is taking part in that step, so both (A +B) must take part
• Must be mechanism 2 (Cant be 1, as B isn’t in the slow step!)
• If the rate step is not first; must derive a rate equation

Alternate Rate Mechanisms

• Using Kc = [X] / [A][B] helps determine the rate constant for all components present
• Rate = K₁[A]^2[B] is only when the slow process is not followed first

Integrated Rate Laws

• Integrated rate laws help find the concentration of a reactant at any given time
• It also helps determine how long it will take for a reactant to fall to a given concentration
• Rate and the integration law can be determined for these products in; - 0th Order K[A]⁰ : [A]t = -kt + [A]0 - 1st Order K[A]¹ : ln[A]t = -kt + ln[A]0 - 2nd Order K[A]² : 1/[A]t = kt + 1/[A]0
• Each integrated rate law can be incorporated in y=mx+c
• The x term is always time

Reaction Order

• These orders can be compared to create a straight line

Natural Logarithms

• Natural logarithms help determine changes over time

Second Order Reactions

• In the case of A + A → Product
• With the steps of integrating rate law : R = −Δ[𝐴]/Δ[𝑡] = 𝑘 [𝐴]2
• Fractional loss depends on [A] 0 (initial concentration)
  • Including environmentally harmful products which persist due to long half lives at low concentrations
• Time to fall (half life): −𝑡1/2 = 1/[𝐴]0 𝑘
• Time to fall (shelf life?): −𝑡90 = 1/9[𝐴]0 𝑘

Second Order Reactions with Different Concentration

• The integrated rate law is; 1 [𝐵]𝑡 [𝐴]𝑡 [𝐴]0 −[𝐵]0 𝑙𝑛 [𝐵]0

• This law does not allow determination of half life

First Order Reactions

• Where A+B→C , the formulas 𝑡1/2 = ln(100/50)/𝑘 = 0.693/𝑘 helps show time to fall initial

Pseudo First Order Reactions

• Describes base hydrolysis of benzocaine 𝑅𝑎𝑡𝑒 = 𝑘 𝐴 [𝐵]0 ,where the conc of benzocaine only matters to rate changes
• 1st order can be referred to as pseudo first order
• This is also demonstrated in hydrolysis with ampicillin is In( 1/0)/k

Calculating Hydrolysis of Ampicillin

• Desrcibes a pseudo first order with an a formula of 𝟐𝟏𝟒 𝒉𝒐𝒖𝒓𝒔 = 𝟗 𝒅𝒂𝒚𝒔 𝒂𝒕 5°C
• The time to fall equation 𝒕𝟗𝟓 = 𝒍𝒏( 100/95)/ 2.4 x10^-3

Zero Order Integrated Rate Law Derivation

• Shows an intergraded rate laws and rate formula of −Δ[A] / Δt

Zero Order Half Life

• tₔₒ = 0.5(Ao)/(Km )
• Zero Order integrated rate law determines reaction rate which are directly proportional with substrate concentration

Hydrolysis of Bupivacaine

• Presents data as the initial Value is In (A-t/Ao)=kt
• Zero Order Shelf Life - For half life; x = 0.5t=0.5[A]0/k

Prediction of Degradation

• Utilizes this integrated rate laws to determine a value for Ln to find the rate to find the half life and shelf life
• 𝒕𝟗𝟎 = % of shelf life