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Chemical kinetics or dynamics

Chemical kinetics or dynamics. 3 lectures leading to one exam question Texts: “Elements of Physical Chemistry” Atkins & de Paula Specialist text in Hardiman Library “Reaction Kinetics” by Pilling & Seakins, 1995

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Chemical kinetics or dynamics

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  1. Chemical kinetics or dynamics 3 lectures leading to one exam question • Texts: “Elements of Physical Chemistry” Atkins& de Paula • Specialist text in Hardiman Library • “Reaction Kinetics” by Pilling & Seakins, 1995 These notes available On NUI Galway web pages athttp://www.nuigalway.ie/chem/degrees.htm What is kinetics all about?

  2. Academic? Ozone chemistry • Ozone; natural formation (l» 185-240 nm) • O2 + hu ® 2O • O + O2® O3 • Ozone; natural destruction (l» 280-320 nm) Thomas Midgely • O3 + hu ® O + O21922 TEL; 1930 CFCs • O + O3® 2O2 • ‘Man-made’ CCl2F2 + hu ® Cl + CClF2 • Cl + O3® Cl̶ O + O2 • Cl̶ O + O ® Cl + O2 • ----------------------------- • Net result is: O + O3® 2 O2 • 1995 Nobel for chemistry: Crutzen, Molina & Rowland • 1996 CFCs phased out by Montreal protocol of 1987

  3. Thermodynamics Direction of change Kinetics Rate of change Key variable: time What times? 1018 s age of universe 10-15 s atomic nuclei 108 to 10-14 s Ideal theory of kinetics? structure, energy calculate fate Now? compute rates of elementary reactions most rxnsnot elementary reduce observed rxn. to series of elementary rxns. Chemical kinetics

  4. Thermodynamics vs kinetics Kinetics determines the rate at which change occurs

  5. Pressure vs CAD in an engine

  6. Kinetics and equilibrium ⇌ kinetics equilibrium

  7. Hierarchical structure C.K. Westbrook and F.L. Dryer Prog. Energy Combust. Sci., 10 (1984) 1–57.

  8. Reactionmechanism k = A Tn exp(-Ea/RT) Reaction AfnfEaf ArnrEar

  9. Rate of reaction {symbol: R, v, ..} Stoichiometric equation • m A + n B = p X + q Y • Rate =-(1/m) d[A]/dt • =- (1/n) d[B]/dt • =+ (1/p) d[X]/dt • =+ (1/q) d[Y]/dt • Units: (concentration/time) • in SI mol/m3/s, more practically moldm–3 s–1

  10. Rate of reaction {symbol: R,n, ..} 5Br- + BrO3- + 6H+ = 3Br2 + 3H2O Rate?conc/time or in SI mol dm-3 s-1 – (1/5)(d[Br-]/dt) = – (1/6) (d[H+]/dt) = (1/3)(d[Br2]/dt) = (1/3)(d[H2O]/dt) Rate law?Comes from experiment Rate = k [Br-][BrO3-][H+]2 where k is the rate constant (variable units)

  11. Rate Law • How does the rate depend upon [ ]s? • Find out by experiment The Rate Law equation • R = kn [A]a [B]b … (for many reactions) • order, n = a + b + … (dimensionless) • rate constant, kn (units depend on n) • Rate = kn when each [conc] = unity

  12. Experimental rate laws? CO + Cl2®COCl2 • Rate = k [CO][Cl2]1/2 • Order = 1.5 or one-and-a-half order H2 + I2®2HI • Rate = k [H2][I2] • Order = 2 or second order H2 + Br2®2HBr • Rate = k [H2][Br2] / (1 + k’ {[HBr]/[Br2]} ) • Order = undefined or none

  13. Determining the Rate Law • Integration • Trial & error approach • Not suitable for multi-reactant systems • Most accurate • Initial rates • Best for multi-reactant reactions • Lower accuracy • Flooding or Isolation • Composite technique • Uses integration or initial rates methods

  14. Integration of rate laws • Order of reaction For a reaction aA products, the rate law is: rate of change in the concentration of A

  15. First-order reaction

  16. First-order reaction A plot of ln[A] versus t gives a straight line of slope ̶ kAif r = kA[A]1

  17. First-order reaction

  18. A® Passume that -(d[A]/dt) = k [A]1

  19. Integrated rate equationln [A] = -k t + ln [A]0 1st Order reaction Slope = -k

  20. Half life: first-order reaction • The time taken for [A] to drop to half its original value is called the reaction’s half-life, t1/2. Setting [A] = ½[A]0and t = t1/2 in:

  21. Half life: first-order reaction

  22. When is a reaction over? • [A] = [A]0exp{-kt} Technically [A]=0 only after infinite time

  23. Second-order reaction

  24. Second-order reaction A plot of 1/[A] versus t gives a straight line of slope kA if r = kA[A]2

  25. Second order test: A + A®P 2nd Order reaction Slope = k

  26. Half-life: second-order reaction

  27. Kinetics and equilibrium kinetics equilibrium

  28. Initial Rate Method 5 Br- + BrO3- + 6 H+® 3 Br2 + 3 H2O General example: A + B +…® P + Q + … • Rate law: rate = k [A]a[B]b…?? log R0 = alog[A]0 + (log k+ blog[B]0 +…) y = mx + c • Do series of expts. in which all [B]0, etc are constant and only [A]0 is varied; measure R0 • Plot log R0 (Y-axis) versus log [A]0 (X-axis) • Slope Þ a

  29. Example: R0 = k [NO]a[H2]b 2 NO + 2H2®N2 + 2H2O • Expt. [NO]0 [H2]0R0 • 1 25 10 2.4×10-3 • 2 25 5 1.2×10-3 • 3 12.5 10 0.6×10-3 Deduce orders wrt NO and H2 and calculate k. • Compare experiments #1 and #2 Þ b • Compare experiments #1 and #3 Þ a Now, solve for k from k = R0 / ([NO]a[H2]b)

  30. How to measure initial rate? • Key:- (d[A]/dt) » - (d[A]/dt) » (d[P]/dt) A + B + … ® P + Q + … t=0 100 100 ® 0 0 mol m-3 10s 99 99 ® 1 1 ditto • Rate? - (100-99)/10 = -0.10 mol m-3 s-1 +(0-1)/10 = -0.10 mol m-3 s-1 • Conclusion? Use product analysis for best accuracy.

  31. Isolation / flooding IO3- + 8 I- + 6 H+® 3 I3- + 3 H2O • Rate = k [IO3-]a[I-]b[H+]g… • Add excess iodate to reaction mix • Hence [IO3-] is effectively constant • Rate = k¢[I-]b[H+]g… • Add excess acid • Therefore [H+] is effectively constant • Rate » k² [I-]a • Use integral or initial rate methods as desired

  32. Rate law for elementary reaction • Law of Mass Action applies: • rate of rxnµproduct of active masses of reactants • “active mass” molar concentration raised to power of number of species • Examples: • A ® P + Q rate = k1 [A]1 • A + B ® C + D rate = k2 [A]1 [B]1 • 2A + B ® E + F + G rate = k3 [A]2 [B]1

  33. Molecularity of elementary reactions? • Unimolecular (decay) A ® P –(d[A]/dt) = k1 [A] • Bimolecular (collision) A + B ® P –(d[A]/dt) = k2 [A] [B] • Termolecular (collision) A + B + C ® P –(d[A]/dt) = k3 [A] [B] [C] • No other are feasible! Statistically highly unlikely.

  34. Experimental rate law: –(d[CO]/dt) = k [CO] [Cl2]1/2 Conclusion?: reaction does not proceed as written “Elementary” reactions; rxns. that proceed as written at the molecular level. Cl2®Cl + Cl(1) Cl + CO ®COCl(2) COCl + Cl2® COCl2 + Cl(3) Cl + Cl® Cl2(4) Steps 1 thru 4 comprise the “mechanism” of the reaction. decay collisional collisional collisional CO + Cl2XCOCl2

  35. - (d[CO]/dt) = k2 [Cl] [CO] If steps 2 & 3 are slow in comparison to 1 & 4 then, Cl2⇌2Cl or K= [Cl]2 / [Cl2] So[Cl] =ÖK × [Cl2]1/2 Hence: • - (d[CO] / dt) = k2 × ÖK × [CO][Cl2]1/2 Predict that: observed k = k2 × ÖK • Therefore mechanism confirmed (?)

  36. H2 + I2® 2 HI • Predict: + (1/2) (d[HI]/dt) = k [H2] [I2] • But if via: • I2® 2 I • I + I + H2® 2 HI rate = k2 [I]2 [H2] • I + I ® I2 Assume, as before, that 1 & 3 are fast cf. to 2 Then: I2⇌2 IorK = [I]2 / [I2] • Rate =k2 [I]2 [H2] = k2 K [I2] [H2] (identical) Check?I2 + hn® 2 I (light of 578 nm)

  37. Problem • In the decomposition of azomethane, A, at a pressure of 21.8 kPa & a temperature of 576 K the following concentrations were recorded as a function of time, t: Time, t /mins 0 30 60 90 120 [A] / mmol dm-3 8.70 6.52 4.89 3.67 2.75 • Show that the reaction is 1st order in azomethane & determine the rate constant at this temperature.

  38. Recognise that this is a rate law question dealing with the integral method. - (d[A]/dt) = k [A]? = k [A]1 Re-arrange & integrate (bookwork) • Test: ln [A] = - k t + ln [A]0 Complete table: Time, t /mins 0 30 60 90 120 ln [A] 2.16 1.88 1.59 1.30 1.01 • Plot ln [A] along y-axis; t along x-axis • Is it linear? Yes. Conclusion follows. Calc. slope as: -0.00959 so k = + 9.6×10-3 min-1

  39. More recent questions … • Write down the rate of rxn for the rxn: C3H8 + 5 O2 = 3 CO2 + 4 H2O • for both products & reactants [8 marks] For a 2nd order rxn the rate law can be written: - (d[A]/dt) = k [A]2 What are the units of k ? [5 marks] • Why is the elementary rxn NO2 + NO2 N2O4 referred to as a bimolecular rxn? [3 marks]

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