PHA 111 Chemical Kinetics PDF

PHA 111 Chemical Kinetics: Rate & Order of Reaction Dr Stephen Childs Senior Lecturer in Pharmaceutical Chemistry [email protected] de 1 PHA 111: Chemical Kinetics  Recommended R...

PHA 111 Chemical Kinetics: Rate & Order of Reaction Dr Stephen Childs Senior Lecturer in Pharmaceutical Chemistry [email protected] de 1 PHA 111: Chemical Kinetics  Recommended Reading Atkins’ Physical Chemistry Chapters 21.2 – 21.5 (9th Edition) de 2 PHA 111: Chemical Kinetics  Why study rates of reaction? To better understand reaction mechanisms eg. SN1 & SN2 To optimise reaction rates Improve yield / reduce side-products To minimise drug degradation Predict / improve shelf-life eg. pH dependant hydrolysis of aspirin to salicylic acid Understand what drives a reaction forward H2 + ½ O2 → H2O ΔH = -286 kJ/mol de 3 PHA 111: Chemical Kinetics  What affects reaction rate? Physical state Many pharmaceutically relevant reaction occur in solution Concentration Molecules must come in contact to react Increased concentration = increased frequency of collisions Temperature Increases frequency of collision Increases the (vibrational) energy of the bonds Catalysts Alternative reaction mechanism de 4 PHA 111: Chemical Kinetics  Collision Theory Rate of reaction will depend on how often reacting molecules collide with sufficient energy to react. Collision rate depends on: – Concentration: chances of collision increased, depends on reaction order! – Pressure : for a gas, rate increases with pressure (same mechanism as concentration) 𝒏 𝒑= 𝒙 𝑹𝑻 𝑽 – Surface area and molecular orientation – Temperature and molecular speed de 5 PHA 111: Chemical Kinetics  Effect of Surface Area Collision rate depends available surface area Mg(s) + 2H+ (aq) -> Mg2+(aq) + H2(g) de 6 PHA 111: Chemical Kinetics  Effect of Molecular Orientation Must have correct orientation – Not all collisions will produce a reaction, – Consider HCl and ethene, (electrophilic addition) – Less likely the more complex the reactants – Only occurs 1 in 105 collisions for complex reactions de 7 PHA 111: Chemical Kinetics  Effect of Molecular Speed Collision rate depends on molecular speed – Temperature affects speed – Based on kinetic theory of gases 3RT Vrms  M – At 5°C Vrms = 240 m/s (120 amu) – At 20°C Vrms = 247 m/s (120 amu) de 8 PHA 111: Chemical Kinetics  Activation Energy H H HH H H OH + C Cl HO C Cl HO C + Cl H H H Energy barrier associated with the transition state – Distortion of molecular shape Sufficient energy – Energy barrier usually 50 – 100 kJ/mol – Average energy at 20°C approx. 4 kJ/mol – Most molecules have insufficient energy – Only about 1 in 109 de 9 PHA 111: Chemical Kinetics  Maxwell-Boltzmann Distribution For gases, the number of molecules with sufficient energy to react can be represented as below: James Clerk Maxwell Ludwig Boltzmann de 10 PHA 111: Chemical Kinetics  Effect of Temperature Increasing Temperature disproportionally increased the number of particles with sufficient activation energy No. of 293 ° K 303 ° K Particles Activation Energy Energy de 11 PHA 111: Chemical Kinetics  Arrhenius Equation Increasing temperature affects rate by increasing k From a small number of experiments we can deduce k at varying temperatures, as well as determining t50 and t90 Arrhenius equation: Alternative form of Arrhenius equation relates k to temperature: k = Ae-Ea/RT – k: kinetic rate constant – A: frequency factor (a.k.a. pre-exponential factor) – Ea: activation energy (probability collision will result in reaction) – R: gas constant (8.3145 J mol-1 deg-1) – T: temperature (in Kelvin) de 12 PHA 111: Chemical Kinetics  Effect of Temperature k = Ae-Ea/RT A is rate constant if energy barrier is absent – Also if T is infinite (or very high) e-Ea/RT is the fraction of molecules with sufficient energy to react Assuming an activation energy or 50,000 J/mol, and temperatures of 293 and 303°K respectively, the fraction of molecules able to react (e) is almost doubled by a 10°C increase in temperature: de 13 PHA 111: Chemical Kinetics  Catalysts Catalysts increase the rate of reaction without being consumed – Acid catalysed hydrolysis of esters – Chlorine radicals catalyse breakdown of ozone Catalysts provide a lower activation energy pathway for the reaction New AE Original AE Energy de 14 PHA 111: Chemical Kinetics  Catalysts Catalysts do not affect the position of equilibrium of a reaction Catalysts do not make unfavourable reactions favourable – Overall DG does not change Enzymes are proteins which act as biological catalysts Acetylcholinesterase hydrolyses acetylcholine in 100 ms de 15 PHA 111: Chemical Kinetics  Rate of Reaction Following concentration as a function of time A+B→C Decrease in reactant concentration (A or B) Increase in product concentration (C) Difference over a finite time Want change over infinitesimally small time: de 16 PHA 111: Chemical Kinetics  Measuring Rate of Reaction de 17 PHA 111: Chemical Kinetics  Chemical Reactions Most reactions are multi-step i) 2NO2 (g) 2NO (g) O2 (g) ii) 2NO2 (g) NO3 (g) NO (g) iii) NO3 (g) NO (g) O2 (g) Molecularity Number of molecules involved in each elementary reaction step Can be obtained from the stoichiometry 1 species = unimolecular 2 species = bimolecular 3 species = termolecular Molecularity must be an integer Not the same as reaction order! de 18 PHA 111: Chemical Kinetics  Rate of Reaction What happens when we increase [A] ? Nothing happens: Rate independent of [A] Rate = k[A] Double [A], k is double Triple [A], k is tripled Rate = k[A]2 [A] is double, k is quadrupled (22 = 4) [A] is tripled, k is increased nine-fold (32 = 9) de 19 PHA 111: Chemical Kinetics  Reaction Order (i) Rate constant (k) Rate Multiplication Reaction Order units 1 0 M/s 2 1 1/s 4 2 1/(M*s) Units of k must give M/s when combined with concentration units (M) The rate law is the sum of each of the reactant orders. If aA +bB + cC → dD + eE rate = k[A]x[B]y[C]z where x is the order of A, not the stoichiometry! de 20 PHA 111: Chemical Kinetics  Reaction Order de 21 PHA 111: Chemical Kinetics  Reaction Order (ii) Calculate the reaction order for each reactant, and the overall reaction order for the following reaction: F₂ + 2ClO₂ → 2ClO₂F Experiment Initial Rate [Fl₂] (M) [ClO₂] (M) No. (M/s) 1 0.10 0.010 0.0012 2 0.10 0.040 0.0048 3 0.20 0.010 0.0024 Doubling [F₂] doubles the rate – therefore must be 1st order Doubling [ClO₂] doubles the rate – therefore must also be 1st order Overall order is 1+1 = 2nd order de 22 Therefore PHAthe 111:rate Chemical law Kinetics is k [F₂] [ClO₂]  Reaction Order Example Calculate the reaction order for each reactant, and the overall reaction order for the following reaction: BrO3- + 5Br- + 6H+ → 3 Br2 + 3H2O Experimen [BrO3-] [Br-] (M) [H+ ] (M) Initial Rate (M/s) t No. (M) 1 0.10 0.10 0.10 8.0 x 10-4 2 0.20 0.10 0.10 1.6 x 10-3 3 0.20 0.20 0.10 3.2 x 10-3 4 0.10 0.10 0.20 3.2 x 10-3 Doubling [BrO3-] doubles the rate – therefore must be 1st order Doubling [Br-] doubles the rate – therefore must also be 1st order Doubling [H+] quadruples the rate – therefore must de 23 also be PHA 2nd 111: orderChemical Kinetics  Rate Law Examples The reaction between A + B is measured in the lab: rate = k[A][B] Order or reaction w.r.t. A is first Order or reaction w.r.t. B is first Overall order is 2 rate = k[B]2 Order or reaction w.r.t. A is zero Order or reaction w.r.t. B is second Overall order is 2 rate = k[A] Order or reaction w.r.t. A is first Order or reaction w.r.t. B is zero Overall order is 1 de 24 PHA 111: Chemical Kinetics  Reaction Mechanisms SN1 reaction: tert-Butyl chloride and hydroxyl anion Rate = k[(CH3)3CBr] Rate order of (CH3)3CBr? Rate order of OH? (knowing these might let us determine the mechanism!) Step 1 - (rate determining) unimolecular Step 2 - Fast Me Me (does Cl not affect Me overall Me rate of Step 1 C reaction) C Cl Me Me Me Me Me Me OH Step 2 C C OH Me Me de 25 PHA 111: Chemical Kinetics  Reaction Mechanisms SN2 reaction: Chloromethane and hydroxyl anion Rate = k[(CH3)3CBr][OH-] Rate order of (CH3)3CBr? Rate order of OH? Bimolecular H H H Cl H H C C Cl H OH OH de 26 PHA 111: Chemical Kinetics  Determining Mechanisms For a reaction between A + B, rate =k[A] [B] Which mechanism is correct? slow slow 1) A C D 2) A B D E fast B C E If the slow step is first in the mechanism the orders tell you what is taking part in that step. First order w.r.t. A and B, so both must take part. Must be mechanism 2 (Cant be 1, as B isn’t in the slow de 27 step!) PHA 111: Chemical Kinetics  Determining Mechanisms What if the slow step is not first in the mechanism? fast A B X slow A X C Rate = k[A][X] But we don’t start with X so we can’t measure it! We need to derive a new rate equation based on the [ 𝑋] equilibrium: 𝐾 𝑐 = [ 𝐴 ] [ 𝐵] 𝑅𝑎𝑡𝑒=𝑘 [ 𝐴 ]. 𝐾 [ A][ B] Re-arrange and substitute into𝑐 initial rate expression: 𝑅𝑎𝑡𝑒=𝐾 1 [ 𝐴]2 [ B] Combine the constants to get the new rate expression: de 28 PHA 111: Chemical Kinetics