04/11/2012 03:26 Molecular reaction dynamics Collision Theory 6/2/2008 04/11/2012 03:26 Course Outline (2 lectures/w and 2Tutorial/w) Microscopic theories of reaction rates: Collision and transition state theories Elementary reactions Rates and mechanisms of chemical reactions (reactions rates and equilibria, enzyme catalysed reactions) Electromotive force and electrochemical cells Electrolytes in solutions The Debye-Huckel theory of interionic interaction and ionic activity coefficient CH 344: CHEMICAL KINETICS AND ELECTROCHEMISTRY (2 units) Dr. E.B. Mubofu and G. Kinunda 04/11/2012 03:26 ASSESSMENT MODE: 1. Set of questions to be distributed for the tutorials 2. There will be 2 tests, each carry 20 Marks 3. Final examination: 60 Marks Section A: 30 Marks Section B: 30 Marks, 3 Questions answer 2 References: 1. P.W. Atkins Physical chemistry (5th, 6th or 7th ed.) 2. G.M. Barrow Physical chemistry 3rd ed. 1973 or later ed. 3. B. G. Segal Chemistry experiment and theory, 1985 4. Any advanced physical chemistry book 04/11/2012 03:26 Molecular reaction dynamics Collision Theory 6/2/2008 04/11/2012 03:26 The pharmacokinetics of artensunate is that following oral administtration .. reaches Cmax within 45 to 90 minutes. The product is effective against malaria by the same mechanism of action. 04/11/2012 03:26 You may recall that thermodynamics can predict whether or not a reaction will proceed but cannot tell us how fast or slow will the reaction occur! NOW Chemical kinetics deals with the understanding of the factors that affect the rate of a chemical reaction and elucidates information about the mechanism of the reaction (A reaction mechanism is a series of steps that defines the order in which bonds are broken and new ones are formed, until the final product is obtained) chemical reaction kinetics is concerned with the rates at which chemical reactions occur NB: Generally, a rate is a change in some quantity wrt time 04/11/2012 03:26 Nature of reactants: Each reaction proceeds at its own rate. Changing the nature of reactants will, in general, change the rate of the reaction The concentration of reactants: For a chemical reaction to occur, the reactants must come close together and collide. Because collisions are more frequent when concentrations increase, then the reaction rates increase as the concentration of the reactants increase The temperature: In general, increasing the temperature increases the rate of the reaction. The rate of most reactions increases by a factor of 2 or 3 for a 10oC rise in temperature! The nature of the solvent:Although not all reactions occur in solution, but for those carried in solution, changing the solvent will generally change the rate of the reaction The presence of the catalyst What factors affect the rate of a chemical reaction? 04/11/2012 03:26 Molecular reaction dynamics Why do reactions occur? How?! i.e pathways and rate/speed This is the heart and the cornerstone of chemistry (why?) because here we examine the details of what happens to molecules at the climax of reactions and hence we can establish mechanisms of reactions The simplest quantitative account of reaction rates at microscopic level is in terms of collision theory which can be used only for discussion of reactions between simple species in the gaseous phase 04/11/2012 03:26 04/11/2012 03:26 Collision Theory of bimolecular gas reaction Generally, a theory is an explanation for something which happens AND Collision Theory is a theory that assumes that, in order for a reaction to occur, reactant molecules must COLLIDE with an ENERGY GREATER than some minimal value and with a PROPER ORIENTATION 04/11/2012 03:26 Collision Theory In other words, collision theory maintains that the rate constant for a reaction is the product of three factors. 1. Z, the collision frequency 2. f, the fraction of collisions with sufficient energy to react 3. p, the fraction of collisions with the proper orientation to react 4. Mathematically, 04/11/2012 03:26 Collision frequency Z is only slightly temperature dependent. This is illustrated using the kinetic theory of gases, which shows the relationship between the velocity of gas molecules and their absolute temperature. or 04/11/2012 03:26 c o \T/M This implies that the higher the temperature, the higher the root mean square speed of the molecules, and at a given temperature heavy molecules travel more slowly than light molecules 04/11/2012 03:26 - A collision will only be successful only if the kinetic energy exceeds a minimum energy value, acof the reaction THUS - The rate constant should also be proportional to a Boltzmann factor of the form RTEae, so we can anticipate that k2 o o(\T/M)e-Ea/RT 04/11/2012 03:26 - Moreover, not every collision will lead to reaction even if the energy requirement is satisfied, because the reactants may need to collide in a certain orientation. The steric requirement suggests that another factor, p, should be introduced, and thus k2 o op(\T/M)e-Ea/RT - Indeed this is what is predicted by the collision theory! It reflects that for a successful reaction/effective collision:- k2 o encounter rate x minimum energy x steric requirement 04/11/2012 03:26 Collision Theory-Collision energy That is, f, the fraction of molecules with sufficient threshold energy turns out to be very temperature dependent. This is the primary factor relating temperature increases to observed rate increases. 04/11/2012 03:26 Collision Theory and reaction rates The reaction rate dependence on the fraction of collisions with the proper orientation, p, is independent of temperature changes So, with changes in temperature, Z and p remain fairly constant. We can thus use that fact to derive a mathematical relationship between the rate constant, k, and the absolute temperature. 04/11/2012 03:26 The Arrhenius Equation If we were to combine the relatively constant terms, Z and p, into one constant, and call it A. We obtain the Arrhenius equation: The Arrhenius equation expresses the dependence of the rate constant on absolute temperature and activation energy. 04/11/2012 03:26 The Arrhenius Equation It is useful to recast the Arrhenius equation in logarithmic form. We can relate this equation to the (somewhat rearranged) general formula for a straight line. y = b + m x A plot of ln k versus (1/T) should yield a straight line with a slope of (-Ea/R) and an intercept of ln A. 04/11/2012 03:26 The Arrhenius Equation A more useful form of the equation emerges if we look at two points on the line this equation describes that is, (k1, (1/T1)) and (k2, (1/T2)). With this form of the equation, given the activation energy and the rate constant k1 at a given temperature T1, we can find the rate constant k2 at any other temperature, T2. 04/11/2012 03:26 Now, let us compare k2 = NAop(\T/M)e-Ea/RT with 04/11/2012 03:26 Note: The above equation has the Arrhenius form k2 =Ae-Ea/RT AND We therefore identify the activation energy with the minimum kinetic energy along the line of approach that is needed for a reaction and That the pre-exponential factor A is a measure of the rate of collisions occurring in gas 04/11/2012 03:26 04/11/2012 03:26 Collision rates in gases-The collision frequency z NOTE: o= Collision cross-section =td2 (Fig below), and d = 1/2(dA + dB) 04/11/2012 03:26 END END END 04/11/2012 03:26 CH344 13/2/2008 04/11/2012 03:26 04/11/2012 03:26 04/11/2012 03:26 A Simple approach to calculate the collision frequency Z of the molecules we consider the following hypothetical collision tube Fig. 1 A: Freeze the positions of all molecules except one B: Note what happen when the mobile molecule travels through the gas with a mean speed C for a time At C: Upon travelling, the molecule sweeps out a collision tube of cross-sectional area o = td2 and length CAt and thus volume = oCAt dddddd