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Reaction Kinetics (6)

Physical Chemistry. Reaction Kinetics (6). Xuan Cheng Xiamen University. Physical Chemistry. Reaction Kinetics. Theories of Reaction Rates. Hard-Sphere Collision Theory of Gas-Phase Reactions. Assumptions. The molecules are hard spheres

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Reaction Kinetics (6)

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  1. Physical Chemistry Reaction Kinetics (6) Xuan Cheng Xiamen University

  2. Physical Chemistry Reaction Kinetics Theories of Reaction Rates Hard-Sphere Collision Theory of Gas-Phase Reactions Assumptions • The molecules are hard spheres • For a reaction to occur between B and C, the two molecules must collide • 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 • The Maxwell-Boltzmann equilibrium distribution of molecular velocities is maintained during the reaction

  3. Physical Chemistry Reaction Kinetics 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； (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。

  4. Physical Chemistry (17.3) (23.2) for B  C (23.3) Reaction Kinetics Theories of Reaction Rates Hard-Sphere Collision Theory of Gas-Phase Reactions The number of B reacting in a bimolecular reaction B + C  Products The predict rate constant The use of (15.62) for ZBC

  5. Physical Chemistry for B = C (23.4) Reaction Kinetics Theories of Reaction Rates Hard-Sphere Collision Theory of Gas-Phase Reactions For the bimolecular reaction 2B  Products The rate of disappearance of B The use of (15.63) for ZBB

  6. Physical Chemistry (17.68) for B = C (23.4) (23.5) for B  C (23.3) Reaction Kinetics Theories of Reaction Rates Hard-Sphere Collision Theory of Gas-Phase Reactions

  7. Physical Chemistry for B  C (23.6) (17.69) (23.5) for B  C (23.3) Reaction Kinetics Theories of Reaction Rates Hard-Sphere Collision Theory of Gas-Phase Reactions 1/2RT is small 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)

  8. Physical Chemistry k0 1011dm3 · mol-1 · s-1 k0 (theo) k0 (cal) T E K kJ· mol-1 Reaction measured cal. 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 CHO CHO + Reaction Kinetics A comparison of theoretic calculation and experimental measurement

  9. Physical Chemistry Reaction Kinetics 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 single quantum-mechanical entity supermolecule Only exists during collision

  10. Physical Chemistry Reaction Kinetics Potential-Energy Surfaces Morse potential Energy 当r>r0时,有引力,即化学键力。 当r<r0时，有斥力。 =0时的能级为振动基态能级， E0为零点能。 D0为把基态分子离解为孤立原子所需的能量，它的值可从光谱数据得到。

  11. Physical Chemistry A Rab  C Rbc B Reaction Kinetics Potential-Energy Surfaces For a reaction If  < 180o Potential is a function of Rab and Rbc only.

  12. Physical Chemistry Reaction Kinetics Potential-Energy Surfaces 图中R点是反应物BC分子的基态,随着A原子的靠近,势能沿着RT线升高，到达T点形成活化络合物。 随着C原子的离去，势能沿着TP线下降，到P点是生成物AB分子的稳态。 A-----B-----C D点是完全离解为A,B,C原子时的势能；OEP一侧,是原子间的相斥能,也很高。 A-------B---C A---B-------C

  13. Physical Chemistry Reaction Kinetics Transition-State Theory Transition-State Theory (TST) Activation-Complex Theory (ACT) The potential-energy surface for a reaction has a reaction region and a product region that are separated by a barrier. TST chooses a boundary surface located between the reactant and product regions and assumes that all supermolecules that cross this boundary surface (critical dividing surface) become products. The critical dividing surface (Fig. 23.7) is taken to pass through the saddle point of the potential-energy surface. saddle point The maximum point on the minimum-energy path

  14. Physical Chemistry Reaction Kinetics Transition-State Theory Transition-State Theory (TST) Assumptions (1) all supermolecules that cross the critical dividing surface from the reactant side become products. Once a supermolecule crosses the critical surface it is a downhill journey to products. (2) during the reaction the Boltzmann distribution of energy is maintained for the reactant molecules. (3) the supermolecules crossing the critical surface from the reactant side have a Boltzmann distribution of energy corresponding to the temperature of the reacting system.

  15. Physical Chemistry Reaction Kinetics Transition-State Theory Transition-State Theory (TST) Assumptions Not all supermolecules cross the dividing surface at precisely the saddle point of the potential-energy surface. Activated complex Potential-energy Any supermolecule whose nuclear configuration corresponds to any point on the dividing surface or to any point within a short distance beyond the dividing surface. Minimum-energy path

  16. Physical Chemistry Reaction Kinetics 碰撞理论的优缺点 优点： 碰撞理论为我们描述了一幅虽然粗糙但十分明确的反应图像，在反应速率理论的发展中起了很大作用。 对阿仑尼乌斯公式中的指数项、指前因子和阈能都提出了较明确的物理意义，认为指数项相当于有效碰撞分数，指前因子A相当于碰撞频率。 它解释了一部分实验事实，理论所计算的速率系数k值与较简单的反应的实验值相符。 缺点：但模型过于简单，所以要引入概率因子，且概率因子的值很难具体计算。阈能还必须从实验活化能求得，所以碰撞理论还是半经验的。

  17. Physical Chemistry Reaction Kinetics 过渡态理论的优缺点 优点： 1.形象地描绘了基元反应进展的过程； 2.原则上可以从原子结构的光谱数据和势能面计算宏观反应的速率常数； 3.对阿仑尼乌斯的指前因子作了理论说明，认为它与反应的活化熵有关； 4.形象地说明了反应为什么需要活化能以及反应遵循的能量最低原理。 缺点：引进的平衡假设和速决步假设并不能符合所有的实验事实；对复杂的多原子反应，绘制势能面有困难，使理论的应用受到一定的限制。

  18. Physical Chemistry (23.8) (23.9) The quantity differs from the classical barrier b, because of the zero-point vibrational species of , B, C, … Reaction Kinetics Transition-State Theory For ideal-gas reactions Denoting an activated complex by (forward direction) Equation (22.129) gives

  19. Physical Chemistry (23.10) Ideal gas (22.128) Reaction Kinetics Transition-State Theory For ideal-gas reactions Division of each N in (23.9) by NAV converts it to a molar concentration equilibrium constant The activated complexes are in equilibrium with reactants The activated complexes are not in a true chemical-reaction equilibrium with the reacting system, are assumed to be in thermal equilibrium with the reacting system  populated according to Boltzmann distribution appropriate to the system temperature

  20. Physical Chemistry The partition function of the activated complex is given by (22.110) (23.12) (23.13) (23.14) (23.15) (23.16) Reaction Kinetics Transition-State Theory For ideal-gas reactions

  21. Physical Chemistry (23.17) (23.18) Ideal gas (23.19) Reaction Kinetics Transition-State Theory For ideal-gas reactions The probability density of g(vrc) for vrcis TST expression for the rate constant of an ideal-gas elementary reaction

  22. Physical Chemistry Ideal gas (23.19’) Reaction Kinetics Transition-State Theory For ideal-gas reactions Eyring equation  is transmission coefficient (0 <  < 1), in many cases   1 Relation between TST and Hard-Sphere Collision Theory For the bimolecular reaction B + C  Products (B  C)

  23. Physical Chemistry Ideal gas (23.19) for B  C (23.20) for B = C (23.4) for B  C (23.3) Reaction Kinetics Transition-State Theory Relation between TST and Hard-Sphere Collision Theory Substitution in equation (23.19) (for B  C) TST reduces to the hard-sphere collision theory when the structure of the molecules is ignored.

  24. Physical Chemistry (23.21) (23.22) (23.23) Reaction Kinetics Transition-State Theory Temperature dependence of the rate constant C and m are constants Taking the log of (23.21) and differentiating

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