第 2 章 均相反应动力学基础

1. 第2章 均相反应动力学基础

2. 均相反应的基本概念（1） • 均相反应：参与反应的各物质处于同一相内 • 均相反应动力学：研究各种因素如温度、压力、催化剂、反应物组成等对反应速率、反应产物分布的影响，并确定表达这些影响因素与反应速率之间定量关系的速率方程。 均相反应动力学是解决工业均相反应器选型、操作与设计计算的理论基础。

3. 反应速率表示方法 • The Rate Expressions • 均相反应速率定义：单位时间内，单位体积反应混合物中某一组分i的反应量（或生成量）。

4. The Rate Expressions • Suppose a single-phase reaction A P The most useful measure of rate for A is then The minus sign means disappearing

5. 例如，有一简单反应 A P

6. Caution 1 & 2 • (-rA) 为一整体符号，恒为正值 • Suppose a single-phase reaction aA+bB pP+sS The rates of all materials are related by

7. Caution 3 • According to the rate equation

8. Caution 4 • In a constant-volume system the measure of reaction rate of component i becomes • Or For the ideal gases where

9. Caution 5 • The rate of reaction in its various forms is defined as follows • Based on unit volume of reaction fluid

10. Based on unit mass of solid in fluid-solid systems • Based on unit interfacial surface in two-fluid systems or based on unit surface of solid in gas-solid systems

11. Based on unit volume of solid in gas-solid systems • Based on unit volume of reactor

12. In homogenous systems, the volume of fluid in the reactor is often identical to the volume of reactor. In such case V and VR are identical and are used interchangeable. • In heterogeneous systems all above definitions of reaction rate encountered, the definition used in any particular situation often being a matter of convenience.

13. These intensive definitions of reaction rate are related by W——固体（催化剂）的重量 S——相界面面积 VP——固相（催化剂）占体积； V——液相占体积； VR­­——反应器的有效体积，VR＝VP＋V。

14. The conversion 转化率 • Suppose that NA0 is initial amount of A in reactor at time t=0, and that NA the amount present at time t. then the conversion of A in the constant volume system is given by

15. 微分上式 for the constant volume system 式中CA0——A的初始浓度。

16. Kinetics of Homogeneous Reaction • 均相反应：反应物系中，所有反应物及生成物（包括催化剂在内）都处于同一相中。 • 影响反应速率的参数：浓度、温度、催化剂等，因此，反应速率与上述这些参数成函数关系。

17. Suppose a homogeneous irreversible reaction The rate of progress of the reaction can be approximated by an expression of the following type

18. n= α+β（n为总反应级数） • Where α,β are not necessarily related to the stoichiometric coefficients. We call the powers to which the concentrations are raised the order of the reaction. Thus, the reaction is αth order with respect to A βth order with respect to B nth order overall

19. 反应的级数：动力学方程中浓度项的幂数，（如，），由实验确定的常数。反应的级数：动力学方程中浓度项的幂数，（如，），由实验确定的常数。 • 基元反应级数，等于计量系数值， =a， =b • 非基元反应，应通过实验来确定 • 级数的大小反映了该物料浓度对反应速率影响的程度。级数越高，表明该物料浓度的变化对反应速率的影响越显著，如是负值，表明抑制反应，使反应速率下降。

20. 反应速率常数 kRate Constant k • When the rate expression for a homogenous chemical reaction is written in the form in book, the dimensions of the rate constant k for nth-order reaction are [time]-1[concentration]1-n which for a first-order reaction becomes simply (time)-1

21. 反应速率常数值的大小决定了反应速率的高低和反应进行的难易程度反应速率常数值的大小决定了反应速率的高低和反应进行的难易程度 • 不同反应有不同的速率常数， • 对于同一反应，k随温度、浓度和催化剂的变化而变化。其中，温度是影响反应速率的主要因素之一。

22. Arrhenius’ Law • For many reactions, and particularly elementary reaction, the rate expression can be written as a product of a temperature-dependent term and a composition-dependent term, or (-rA)=f1(temperature) · f2(composition) =k·f2(composition)

23. For such reaction the temperature-dependent term, the reaction rate constant, has been found in practically all cases to be well represented by Arrhenius’ Law: k=k0e-E/RT Where: k0 frequency or pre-exponential factor E Activation energy At two different temperatures, Arrhenius’ Law indicates that

24. Activation energy and temperature dependency • From Arrhenius’ Law a plot of ln k vs 1/T gives a straight line, with large slope for large E and small slope for small E • Reactions with high activation energies are very temperature-sensitive; reaction with low energies are relatively temperature-insensitive. • Any given reaction is much temperature-sensitive at a low temperature than at a high temperature. • From the Arrhenius’ Law, the value of frequency factor k0 does not affect the temperature sensitive.

25. 等温恒容过程 反应动力学方程的建立 • 实验得到不同反应时间的各物料浓度数据 • 或者测定压力、密度、折射率等换算成各物料的浓度 • 数据处理，有积分法和微分法

26. 单一反应 The Single Reactions一级反应(不可逆单分子一级反应）Irreversible Unimolecular-Type First-Order Reaction • Consider the reaction AP at constant- volume and constant-temperature processes, the first-order rate equation is For this reaction. Separating and integrating we obtain xA=(CA0-CA)/CA0

27. A plot of ln(1/1-XA) or ln(CA0/CA) vs. t, as shown on the right, gives a straight line through the origin for this form of rate of equation.

28. 二级反应Irreversible Bimolecular-Type Second-Order Reaction • Consider the reaction A+AP with corresponding rate equation Which on integration yields

29. Consider the reaction A+BP . The definition second-order differential equation becomes Noting that the amounts of A and B that have reacted at any time t are equal and given by CA0xA, we may write above equation in terms of xA as Letting M=CB0/CA0 be the initial molar ratio of reaction, we obtain

30. Which on separation and formal integration becomes After breakdown into partial fractions, integration and rearrangement, the final result in a number of different form is

31. The figures show two equivalent ways of obtaining a linear plot between the concentration function and time for this second-order rate law.

32. n级反应Irreversible nth-order Reaction • Consider the reaction nAP. When the mechanism of reaction is not known, we often attempt to fit the data with nth-order rate equation of the form Which on separation and integration yields

33. The order n cannot be found explicitly from the equation, so a trial-and error solution must be made. This is not too difficult, however. Just select a value for n and calculate k. The value of n which minimizes the variation in k is the desired value of n.

34. 气相反应A3P 为一级反应，速度常数k=0.5min-1，反应在恒容间歇式反应器中进行，求1min后体系的总压，进料状况如下： • a) 纯A，0.1Mpa； • b) 纯A，1Mpa； • c) 10%的A和90%的I（惰性气体）混合物，1MPa • 解：

35. 对比（1）、（2），得

36. 当t=0，=0 积分（3）， 得

37. 等温恒容不可逆反应的速率方程积分式

38. 可逆反应Reversible Reaction • 可逆反应是指正方向、逆方向同时以显著速度进行的反应，也叫对峙反应。 • First-order Reversible reaction Let us consider the opposed unimolecular-typed reaction KC= K = k1/k2 equilibrium constant Starting with a concentration ratio M=CR0/CA0 the rate equation is

39. Now at equilibrium dCA/dt =0. Hence we find the equilibrium constant of A at equilibrium conditions to be

40. Combining the above equations we obtain, in terms of the equilibrium conversion This may be looked on as pseudo first-order irreversible reaction which on integration gives

41. A plot of –ln(1-xA/xAe) vs. t, as shown in the Fig., gives a straight line

42. 二级可逆反应Second-order Reversible Reaction • For the bimolecular-type second-order reaction With the restriction that CA0=CB0 and CR0=CS0, the integrated rate equation for A and B is as follows A plot can then be used to test the adequacy of this kinetics

43. 等温恒容可逆反应速率方程积分式（产物起始浓度为0）等温恒容可逆反应速率方程积分式（产物起始浓度为0）

44. 动力学的实验和数据处理Kinetics Experiment and its DataAnalysis • A rate equation characterizes the rate reaction, and its form may either be suggested by theoretical consideration or simply the result of an empirical curve-fitting procedure. In any case, the value of the constants of the equation can only be found by experiment; predictive methods are inadequate at present.

45. The determination of the rate equation is usually a two-step procedure; first the concentration dependency is found at fixed temperature and then the temperature dependence of the rate constants is found, yielding the complete rate equation .

46. Equipment by which empirical information is obtained can be divided into two types, the batch and flow reactors. The batch reactor（釜式反应器 或间歇式反应器） is simply a container to hold the contents while they react.

47. The experimental batch reactor is usually operated isothermally and at constant volume because it is easy to interpret the results of such runs. This reactor is a relatively simple device adaptable to small- scale laboratory set-ups（装置）, and it needs but little auxiliary（辅助设施） equipment or instrumentation. Thus, it is used whenever possible for obtaining homogenous kinetic data.

48. The flow reactor(连续式反应器) is used primarily in the study of the kinetics of heterogeneous(非均相) reactions. Planning of experiments and interpretation of data obtained in flow reactors are considered in later chapters.

49. There are two procedures for analyzing kinetic data, the integral and the differential methods(积分法和微分法).

50. 用积分法分析实验数据Analyzing the experiment data by integral method • In the integral method of analysis we guess a particular form of rate equation and, after appropriate integration and mathematical manipulation, predict that the plot of a certain concentration function versus time should yield a straight line. The data are plotted, and if a reasonably good straight line is obtained, then the rate equation is said to satisfactorily fit the data