Physical chemistr Reaction Kinetics(6) Xuan Cheng Xiamen University
1 Reaction Kinetics (6) Xuan Cheng Xiamen University Physical Chemistry
Ch ical chemistr Reaction Kinetic Theories of reaction rates Hard-Sphere collision Theory of gas-Phase reactions assumptions )The molecules are hard spheres (2) For a reaction to occur between B and C, the two molecules must collide (3)Not all collisions produce reaction. Reaction occurs if and only if the reactive translational kinetic energy along the line of centers of the colliding molecules exceeds a threshold energy ethr (4)The Maxwell-Boltzmann equilibrium distribution of molecular velocities is maintained during the reaction
2 Physical Chemistry Theories of Reaction Rates Hard-Sphere Collision Theory of Gas-Phase Reactions Assumptions (1) The molecules are hard spheres (2) For a reaction to occur between B and C, the two molecules must collide (3) Not all collisions produce reaction. Reaction occurs if and only if the reactive translational kinetic energy along the line of centers of the colliding molecules exceeds a threshold energy thr (4) The Maxwell-Boltzmann equilibrium distribution of molecular velocities is maintained during the reaction Reaction Kinetics
1h ical Chemistr Reaction Kinetic 简单碰撞理论的基本假设 该理论的基本假设(即理论模型) (i)反应物分子可看作简单的硬球,无内部结构和相互作用; (i)反应分子必须通过碰撞才可能发生反应; (ⅲ〕并非所有碰撞都能发生反应,相互碰撞的两个分子—碰撞 分子对的能量达到或超过某一定值c-称为阈能时,反应才能 发生,这样的碰撞叫活化碰撞; (iV)在反应过程中,反应分子的速率分布始终遵守麦克斯韦一 玻耳兹曼( Maxwell-Boltzmann)分布
3 (ii)反应分子必须通过碰撞才可能发生反应； (iii)并非所有碰撞都能发生反应，相互碰撞的两个分子—碰撞 分子对的能量达到或超过某一定值thr—称为阈能时，反应才能 发生，这样的碰撞叫活化碰撞； (iV)在反应过程中，反应分子的速率分布始终遵守麦克斯韦— 玻耳兹曼(Maxwell-Boltzmann)分布。 简单碰撞理论的基本假设 该理论的基本假设(即理论模型）： (i)反应物分子可看作简单的硬球，无内部结构和相互作用； Physical Chemistry Reaction Kinetics
Ch ical chemistr Reaction Kinetic Theories of reaction rates Hard-Sphere Collision Theory of Gas-Phase Reactions The number of B reacting in a bimolecular reaction B+C→ Products EL/RT B Ethr= Naeth (17.3) thr /RT 丿Vadt e The predict rate constant k=BCe - Eier/RT r=kBc NA[B[C」 EL/RT k=<Bce NALBJLC (232) The use of(15.62 )for ZBC k=M八/8R7(111)71/2 e thr/RT forB≠C(23.3) B
4 Physical Chemistry Theories of Reaction Rates Hard-Sphere Collision Theory of Gas-Phase Reactions The number of B reacting in a bimolecular reaction B + C → Products E RT BC thr Z e − / Ethr NA thr = − dt dn V V a J r 1 1 A (17.3) A thr N E RT r ZBCe / − = r = k[B][C] [ ][ ] / N B C Z e k A E RT BC − thr The predict rate constant = (23.2) [ ][ ] / N B C Z e k A E RT BC − thr = The use of (15.62) for ZBC (23.3) E RT B C A B C thr e M M RT k N r r / 1/ 2 2 8 1 1 ( ) − = + + for B C Reaction Kinetics
choical Chemistry Reaction Kinetic Theories of reaction rates Hard-Sphere Collision Theory of Gas-Phase Reactions For the bimolecular reaction 2b-> Products 1 dB 2=B2 E./RT The rate of disappearance of B d[B]-2zBce k 1 d[B/dt E/RT BB N4[BI2 r=kB The use of (15.63 )for ZBB 1/2 aRT E/RT for B=C(23.4) TB
5 Physical Chemistry Theories of Reaction Rates Hard-Sphere Collision Theory of Gas-Phase Reactions For the bimolecular reaction 2B → Products 2 [ ] [ ] 2 1 k B dt d B r = − = A thr N E RT ZBCe dt d B / 2 [ ] − − = 2 2 r = k[B] / 2 [ ] [ ] [ ]/ 2 1 N B Z e B d B dt k A E RT BB − thr = − = The rate of disappearance of B The use of (15.63) for ZBB (23.4) E RT B A B thr e M RT k N d / 1/ 2 2 1/ 2 8 2 1 − = for B = C Reaction Kinetics
Ch ical chemistr Reaction Kinetic Theories of reaction rates Hard-Sphere Collision Theory of Gas-Phase reactions l/2 k=Nar(rB+C aRt E/RT forB≠C(23.3) 1/2 2(8Rr 1/2 VATdB MB e Ethr/RT for B=C(23. 4) Ink= const +-Int--inr RT Ea=Rtt Ea= rr2 dhn k (17.68) a- ethr +-Rt (235)
6 Physical Chemistry Theories of Reaction Rates Hard-Sphere Collision Theory of Gas-Phase Reactions (23.4) E RT B A B thr e M RT k N d / 1/ 2 2 1/ 2 8 2 1 − = for B = C (23.3) E RT B C A B C thr e M M RT k N r r / 1/ 2 2 8 1 1 ( ) − = + + for B C RT E k const T thr = + ln − 2 1 ln dT d k Ea RT 2 ln (17.68) = + 2 2 2 1 RT E E RT T thr a Ea Ethr RT 2 1 = + (23.5) Reaction Kinetics
Ch ical chemistr Reaction Kinetic Theories of reaction rates Hard-Sphere collision Theory of Gas-Phase reactions aRT k=NaI(rB+rO thr/ for B≠C(233) U/2RT is small ea >>rt Ea= Ethr+RT (23.5) En≈En E a=kert (17.69) 1/2 A=M1n八8RT(11 1/2 forB≠C(23.6) The hard-sphere threshold energy is nearly the same as the activation energy. The simple collision theory gives only the pre-exponential factor A(but not for the calculation of ethr)
7 Physical Chemistry Theories of Reaction Rates Hard-Sphere Collision Theory of Gas-Phase Reactions RT Ea A ke (17.69) Ea Ethr RT 2 1 = + (23.5) (23.6) 1/ 2 1/ 2 2 8 1 1 ( ) − = + + e M M RT A N r r B C A B C for B C (23.3) E RT B C A B C thr e M M RT k N r r / 1/ 2 2 8 1 1 ( ) − = + + for B C 1/2RT is small Ea Ethr The hard-sphere threshold energy is nearly the same as the activation energy. The simple collision theory gives only the pre-exponential factor A (but not for the calculation of Ethr) Ea RT 2 1 Reaction Kinetics
Chical chemistr Reaction Kinetico a comparison of theoretic calculation and experimental measurement E ko(theo Reaction 10uldm3·mol1·s-l K|kJ·mol ca measured ca K+Br2→KBr+Br6000 10 2.1 4.8 CH3+ CH3 2Hb3000 0.24 1.10.22 2NOC→→2NO+Cl24701020.0940.590.16 CHO cHo 500831.5×10-5305×10-6 H2+C,H4→→CH。8001801.24×10-57317×10-6
8 K + Br2 KBr + Br 600 0 10 2.1 4.8 CH3 + CH3 C2H6 300 0 0.24 1.1 0.22 2NOCl 2NO + Cl2 470 102 0.094 0.59 0.16 500 83 1.5×10 -5 3.0 5×10- 6 H2 + C2H4 C2H6 800 180 1.24×10 -5 7.3 1.7×10- 6 Reaction T E K kJ· mol-1 k0 (theo) k0 (cal) k0 1011dm3 · mol-1 · s-1 measured cal. A comparison of theoretic calculation and experimental measurement + CHO CHO Physical Chemistry Reaction Kinetics
Ch ical chemistr Reaction Kinetic Potential-Energy surfaces The hard-sphere collision theory does not give accurate rate constants In chemical reactions. bonds are being formed and broken Intramolecular forces Forces acting on atoms in the molecules Intermolecular forces Consider two molecules to form a d supermolecule single quantum-mechanical entit Only exists during collision
9 Physical Chemistry Potential-Energy Surfaces The hard-sphere collision theory does not give accurate rate constants. In chemical reactions, bonds are being formed and broken. Forces acting on atoms in the molecules Intramolecular forces Intermolecular forces Consider two molecules to form a single quantum-mechanical entity supermolecule Only exists during collision Reaction Kinetics
choical Chemistry Reaction Kinetic Potential-Energy Surfaces Morse potential Energy En(r)=delexp-2a(r-ro)-2expfa(r-no)) 当r>ro时有引力,即化学键力。 当r<r时,有斥力 v=0时的能级为振动基态能级 E为零点能。 D D为把基态分子离解为孤立 原子所需的能量,它的值可 双原子分子的莫尔斯势能曲线 从光谱数据得到
10 Physical Chemistry Potential-Energy Surfaces Morse potential Energy =0时的能级为振动基态能级， E0为零点能。 当rr0时,有引力,即化学键力。 p e 0 0 E r D a r r a r r ( ) [exp{ 2 ( )} 2exp{ ( )}] = − − − − − Reaction Kinetics