Class Note for ECE 449 at UA
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Date Created: 02/06/15
A I we 449549 ontinnons System mutualitth Chemical Thermodynamics III 0 In this lecture we shall analyze the temperature dependence of chemical reactions Arrhenius law 0 We shall also analyze light dependence of some reactions such as the hydrogenbromine reaction 0 Finally we shall discuss the in uence of external sources of energy such as mechanical energy in a Continuous Stirred Tank Reactor CST R or such as electrical energy in electrolysis November 14 2003 start Presentation ASL I we 449549 Glontinnnns System mutualitth Table of Contents 0 Temperature dependence of chemical reactions Arrhenius law 0 Pressure dependence of chemical reactions Photolysis Electrolysis Stirred reactors November 14 2003 start Presentation A I we 449549 ontinnons System mutualitth Temperature Dependence of Chemical Reaction Systems I 0 It can be observed that the reaction rates of essentially all reactions change in function of the temperature that the reactants are at for example Hydrogen Bromine Reaction x 0000 397 WM V E Boom v 4 v V 3 4mm u 2000 3 a 0000 39 39 400 550 MO 700 300 IDO IDDD 100 lZOD Temperature TEK November 1439 2003 start Presentation I we 449549 Glontinnnns System mutualitth Temperature Dependence of Chemical Reaction Systems 11 0 How can this be explained Most reactions require activation energy to take place Without this activation energy they could not occur because otherwise they would occur rather Violently 0 Thus a reaction such as 0 should probably be written as 0 where M is a catalyst that does not otherwise participate in the reaction It only provides the necessary activation energy for the reaction to take place November 14 2003 start Presentation JAE I ma 449549 Imtinnou System including Temperature Dependence of Chemical Reaction Systems 111 0 Temperature is only a statistical quantity ie the different molecules vary in the amount of energy that they possess Temperature is a measure of the average microscopic kinetic energy Brown s movement that a molecule possesses 0 If two high energized molecules collide they react because they can borrow the necessary activation energy from the microscopic kinetic energy ie from the thermal domain 0 In the case of the Br2 decaying reaction it probably will never occur unless one Br2 molecule collides with another molecule from which it can borrow the necessary activation energy 0 The higher the temperature of the reactants the more highly energized the average molecule will be and the more likely it will overcome the activation energy Thus the reaction rate constants are always functions of temperature November 14 2003 start Presentation 1A I am 449549 outiuuous System mhdmgl Arrhenius Law I 0 We can redraw the previous gure using a double logarithmic scale JigBra Rl cuon Arrhenius discovered that the 39 T 1 temperature dependence for many reactions is approximately linear if depicted using a double logarithmic scale Z mu Constant k1 net 1 a a 42 102 to to Tam erature TK A frequency factor frequency ofco is ions Ea activation energy 10 November 14 2003 start Presentation A I we 449549 ontinnons System mnemgl Arrhenius Law II Notice that although the temperature dependence of chemical reaction rates is physically interpretable Arrhenius law is purely empirical and no physical explanation can be provided that would support the precise nature of the Arrhenius equation Indeed the equation is often modified to Notice that no external energy was added here in order to speed up the reactions The modulation of the reaction rates is purely internal It is caused by the heat stored in the system November 14 2003 Start Presentation ltIJEgt A I we 449549 Glontinnnns System 00010th The HydrogenBromine Reaction The following experimental rates have been found to describe well the hydrogen39bmmme Mama Abs Tempunmr T K Emma cm K mole Inquot 3000 11440 x 10 quot a 1892430 191 4000 19543 x 10 quot ab 139 3910 39 T R T 5000 22102 x 1039 6000 52044 x 1039 k k 189243 0 7000 13007 x 10quot 1 a 1 39 P R T 0000 90m x10 k 0000 23700 x 10 10000 32500 x 10 k2 11000 21ae1x10quot K T 12000 16735 x 10quot 11000 70013 x 10quot k3 1011 cz 14000 usmx 10 R T 15000 00715 x 10quot 6 0 A 4 l quot k 101Mquot M quot1498000 i730 0311 1quot R T 10000 11047 19000 1606 kg 01 150 20000 40411 November 14 2003 Start Presentation ltgt A I we 449549 untinnons System mnemgl Arrhenius Law III We need to ask ourselves one more question If the participating reactants are at different temperature values which value do we use in the Arrhenius equation Remember that temperature is only a statistical quantity It is a measure for the average microscopic kinetic energy contained in a molecule of a substance Consequently if two reactant substances are at different temperature values we can safely use the average value of their temperatures in satisfying the Arrhenius equation November 14 2003 Start Presentation ltIJEgt A I we 449549 Glontinnnns System mutualitth Pressure Dependence of Reaction Rates In the light of what we have learnt about temperature dependence of reaction rates a pressure dependence should also be expected If the pressure of a gas rises this means that more molecules are present per unit volume Consequently the probability of collisions among molecules should increase as well Although a pressure dependence certainly exists it isn t explored much in the chemical engineering literature November 14 2003 Start Presentation ltgt A I we 449549 ontinnons System mutualitth Light Sensitivity of Reaction Rates I 0 Some reaction rates have been found to be sensitive to light ie the reaction rates increase in the presence of light and decrease When the reactants are kept in the dark 0 For example this is most certainly true for the hydrogen bromine reaction 0 The explanation of this phenomenon is simple photons collide With reactants and provide the necessary activation energy for the reaction to take place 0 In the hydrogenbromine reaction it is the decaying reaction of the bromine gas that is in uenced by collisions With photons November 14 2003 start Presentation EA I we 449549 Glontinnnns System mutualitth Light Sensitivity of Reaction Rates 11 0 However in this case there is external energy namely optical energy that is added to the system 0 Thus contrary to the previously discussed types of reaction rate dependencies here the bond graph Will need to change since external energy is added to the system h iPl39anckAfeonstant g h v may go We choose November 14 2003 start Presentation IA l we 449549 ontinnoux system mmml Light Sensitivity of Reaction Rates III 0 The photons add energy to the microscopic kinetic motion of the molecules ie the optical energy is adding energy to the thermal side 0 Consequently the Gibbs equation is modified as follows The additional entropy is entered at reaction k1 since this is the reaction that is in uenced by the photon ux Yet this is arbitrary since the photons collide with all molecules November 14 2003 start Presentation AL I it 449549 untinuonx System mnaml Light Sensitivity of Reaction Rates IV 0 Furthermore the reaction rates need to be modified At room temperature kl is almost equal to 0 but kl is not November 14 2003 start Presentation A we 449549 untinnons System mutualitth Electrolysis I 0 Chemical reactions can also be in uenced by applying an electrical field In a solution molecules are often ionized 1e gt they either lack or have a surplus of negatively charged electrons charged 0 For example individual ions salts dissolve in aqueous solutions Hpen m 39 Hgo 61 Ions are thus either positively or negatively into 0 Since ions are electrically charged they can be physically separated from each other by applying an electrical field November 14 2003 start Presentation ltIJEgt we 449549 Glontinnnns System mutualitth A Electrolysis II 0 In water there exists an equilibrium between water molecules and positively and negatively charged ions 0 If the pH value of the water is changed by adding a drop of either an acid such as sulphuric acid H2S04 or alkali such as potash lye KOH the number of ions in the solution will be drastically enhanced If two metal plates are dipped into the water and an electric field is created by connecting a voltage source to these two plates the negatively charged ions will migrate towards the anode whereas the positively charged ions will migrate towards the cathode November 14 2003 Start Presentation ltmgt A I we 449549 untinnons System mutualitth Electrolysis III 0 In the electrolysis of water the following reactions take place 4H3O 14e 2112 4H20 4011 1519 21129 ar 02 4e 2 1120 Q 1130 011 Hsor OilquotEL 21120 Reactions k2 and k3 are fast equilibrium reactions 0 The surplus electrons from the second reaction kl wander from the anode through the voltage source back to the cathode where they are recycled in the rst reaction November 14 2003 start Presentation EAL em 449549 Glontinnnns System mutualitth Electrolysis IV 0 It may be interesting to look at the reaction rate equations 0 Since the meeting of the 4 ions at the electrode is not stochastic but driven by the electric field the corresponding reaction rate does not go with the fourth power of the molar mass of these ions 0 A certain minimal voltage no is needed to polarize the ions before they start migrating to the electrodes 0 Thus we can write Vkm 39 0quot 39ug 39 quotH30 November 14 2003 start Presentation Au em 449549 ontinnons System manslitml Electrolysis V 0 Thus the set of reaction rate equations can be written as November 14 2003 start Presentation Ask me 449549 Glontinnnns System mutualitth Electrolysis VI 0 This can be rewritten as Since the two ions are always created in pairs November 14 2003 start Presentation lt19 10 A I we 449549 ontinnons System whalingl Electrolysis VII Nmatrix November 14 2003 Start Presentation As I we 449549 Glontinnnns System whalingl Electrolysis VIII 0 We need to ask ourselves what happens with the external electrical power that is introduced into the system 0 The power supply sees a resistor that consumes the power ui Resistors usually generate heat In fact there really is no choice in the matter The power that is introduced has to be accounted for in the Gibbs equation which is used to determine the entropy ow 0 Thus the resistor indeed heats up the system November 14 2003 Start Presentation lt19 11 A I we 449549 untinnons System mutualitth Stirred Reactors I 0 Until now we always assumed that the reactants are ideally mixed 0 In gas reactions this assumption holds true quite well In liquid reactions the same cannot be said The more highly Viscous a liquid is the less likely it is homogeneous We may need to stir in order to mix the reactants well 0 Nothing really happens to the reaction equations since these were created under the assumption of an ideal mixture 0 Yet the stirring causes Viscous friction which creates heat November 14 2003 start Presentation ltIJEgt EASE I we 449549 Glontinnnns System mutualitth Stirred Reactors II 0 The entire power of stirring except for what is stored in the mechanical inertia of the paddle gets converted to heat 0 It is most convenient to add this entropy at the component side more precisely at the 0juncti0ns next to the CF elds and simply split it among the reactants in proportion to their relative mass November 14 2003 Start Presentation ltgt 12 A em 449549 ontinnons System whalingl References Cellier FE 1991 Continuous System Modeling SpringerVerlag New York Chapter 9 Brooks BA and FE Cellier 1993 Modeling of a Distillation Column Using Bond Graphs Proc ICBGM 93 Intl Conf on Bond Graph Modeling and Simulation La Jolla CA pp 315 7 320 Brooks BA 1993 Modeling of a Distillation Column using Bond Gray1s MS Thesis Dept of Electrical amp Computer Engineering University of Arizona November 14 2003 Start Presentation 13
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