Study notes on CHEMICAL KINETICS., Study notes of Chemistry

Download Study notes on CHEMICAL KINETICS. and more Study notes Chemistry in PDF only on Docsity! Chemical Kinetics 455 The branch of physical chemistry which deals with the rate at which the chemical reactions occur, the mechanism by which the chemical reactions take place and the influence of various factors such as concentration, temperature, pressure, catalyst etc., on the reaction rates is called the chemical kinetics. Types of chemical reactions On the basis of reaction rates, the chemical reactions have been classified into the following three types, (1) Very fast or instantaneous reactions : These reactions occur at a very fast rate generally these reactions involve ionic species and known as ionic reactions. It is almost impossible to determine the rates of these reactions. Examples (i) 3 (PPt.) 3 NaNOAgClNaClAgNO  (Precipitation reaction) (ii) OHNaClNaOHHCl 2 (Salt)(base)(acid)  (Neutralization reaction) (2) Moderate reaction : These reactions proceed with a measurable rates at normal temperature and it is these reactions are studied in chemical kinetics. Mostly these reactions are molecular in nature. Examples (i) Decomposition of 22OH : 2222 22 OOHOH  (ii) Decomposition of 52ON : 24252 22 OONON  (3) Very slow reactions : These reactions are extremely slow and take months together to show any measurable change. Examples (i) Rusting of iron : (Rust) oxideferric Hydrated 232232 . OxHOFeOxHOFe  (ii) OHOH 2 re temperatuRoom 22 22   Rate of a reaction The rate (speed or velocity) of a reaction is the change in concentration in per unit time. t x   or            12 12 tt xx dt dx where x or dx is the concentration change, i.e., )( 12 xx  in the time interval t or dt, i.e., )( 12 tt  . Concentration is generally expressed in active mass, i.e., mole L–1  The rate measured over a long time interval is called average rate and the rate measured for an infinitesimally small time interval is called instantaneous rate and Instantaneous rate 0trate) (Average   For the reaction dDcCbBaA  Rate of disappearance of a reactant is negative  dt Ad ][ Rate of disappearance of A  dt Bd ][ Rate of disappearance of B Rate of formation of a product is positive  dt Cd ][ Rate of formation of C Chemical Kinetics Chapter 11 456 Chemical Kinetics  dt Dd ][ Rate of formation of D  In terms of stoichiometric coefficient rate may be expressed as dt Dd ddt Cd cdt Bd bdt Ad adt dx ][1][1][1][1   The rate of reaction is always positive.  The rate of chemical reaction decreases as the reaction proceeds.  Unit of rate of a reaction = of time Unit conc.of Unit =mole L–1 time –1 In term of gaseous reaction the unit is atm time-1 and Rate in atm time-1= Rate in mole RTtimeL  11 Factors affecting rate of a reaction The rate of a chemical reaction depends on the following things (1) Nature of reactants (i) Physical state of reactants : This has considerable effect over rate of reaction. reactionof rate Decreasing state Solidstate Liquid satae Gaseous    (ii) Physical size of the reactants : Among the solids, rate increases with decrease in particle size of the solid. (iii) Chemical nature of the reactants (a) Reactions involving polar and ionic substances including the proton transfer reactions are usually very fast. On the other hand, the reaction in which bonds is rearranged, or electrons transferred are slow. (b) Oxidation-reduction reactions, which involve transfer of electrons, are also slow as compared to the ionic substance. (c) Substitution reactions are relatively much slower. (2) Effect of temperature : The rate of chemical reaction generally increases on increasing the temperature. The rate of a reaction becomes almost double or tripled for every Co10 rise in temperature. Temperature coefficient of a reaction is defined as the ratio of rate constants at two temperatures differing by (generally 25°C and 35°C) 10°C.  C C o o o k k Ctk Ck 25 35 o at )10(t at tcoefficien eTemperatur    (3) Concentration of reactants : The rate of a chemical reaction is directly proportional to the concentration of the reactants means rate of reaction decreases with decrease in concentration. (4) Presence of catalyst : The function of a catalyst is to lower down the activation energy. The greater the decrease in the activation energy caused by the catalyst, higher will be the reaction rate. (5) Effect of sunlight : There are many chemical reactions whose rate are influenced by radiations particularly by ultraviolet and visible light. Such reactions are called photochemical reactions. For example, Photosynthesis, Photography, Blue printing, Photochemical synthesis of compounds etc. The radiant energy initiates the chemical reaction by supplying the necessary activation energy required for the reaction. Law of mass action and Rate constant The rate at which a substance reacts is directly proportional to its active mass and the rate at which a reaction proceeds is proportional to the product of the active masses of the reacting substances.  For a reaction,  bBaA product Rate ba BA dt dx ][][       ; ba BAk dt dx ][][      Where k is called rate constant or velocity constant. When litremolBA /1][][  , then k dt dx  Thus, rate constant k is also called specific reaction rate.  The value of rate constant depends on, nature of reactant, temperature and catalyst. It is independent of concentration of the reactants.  Unit of rate constant 1 1 sec mol litre          n 1 1 sec litre mol          n Where n order of reaction. Rate law : Molecularity and Order of a reaction Molecularity is the sum of the number of molecules of reactants involved in the balanced chemical equation. Molecularity of a complete reaction has no significance and overall kinetics of the reaction depends upon the rate determining step. Slowest step is the rate- determining step. This was proposed by Van't Hoff. Example : OHNNONH 2224 2 (Unimolecular) 223 ONOONO  (Bimolecular) Reaction path with catalyst Ea Ea Reaction path Without catalyst Energy of Reaction Reactants Products P o te n ti a l E n e rg y A catalyst changes the reaction path Chemical Kinetics 459 (3) Graphical method : A graphical method based on the respective rate laws, can also be used. (i) If the plot of )log( xa  Vs t is a straight line, the reaction follows first order. (ii) If the plot of )( 1 xa  Vs t is a straight line, the reaction follows second order. (iii) If the plot of 2)( 1 xa  Vs t is a straight line, the reaction follows third order. (iv) In general, for a reaction of nth order, a graph of 1)( 1  nxa Vs t must be a straight line. Plots from integrated rate equations Plots of rate Vs concentrations [Rate = k(conc.)n ] (4) Van't Haff differential method : The rate of reaction varies as the nth power of the concentration Where ''n is the order of the reaction. Thus for two different initial concentrations 1C and 2C equation, can be written in the form, nkC dt dC 1 1   and nkC dt dC 2 2   Taking logarithms, 11010 1 10 logloglog Cnk dt dC        …..(i) and 21010 2 10 logloglog Cnk dt dC        …..(ii) Subtracting equation (ii) from (i), 210110 2 10 1 10 loglog loglog CC dt dC dt dC n                 …..(iii) dt dC1 and dt dC 2 are determined from concentration Vs time graphs and the value of ''n can be determined. (5) Ostwald's isolation method (Initial rate method) This method can be used irrespective of the number of reactants involved e.g., consider the reaction, Products321  CnBnAn . This method consists in finding the initial rate of the reaction taking known concentrations of the different reactants (A, B, C). Suppose it is observed as follows, (i) Keeping the concentrations of B and C constant, if concentration of A is doubled, the rate of reaction becomes four times. This means that, Rate 2][A i.e., order with respect to A is 2 (ii) Keeping the concentrations of A and C constant, if concentration of B is doubled, the rate of reaction is also doubled. This means that, Rate  [B] i.e., order with respect to B is 1 (iii) Keeping the concentrations of A and B constant, if concentration of C is doubled, the rate of reaction remains unaffected. This means that rate is independent of the concentration of C i.e., order with respect to C is zero. Hence the overall rate law expression will be, Rate = k[A]2 [B] [C]0  Overall order of reaction = 2 + 1 + 0 = 3. Theories of reaction rate (1) Collision theory (i) The basic requirement for a reaction to occur is that the reacting species must collide with one another. This is the basis of collision theory for reactions. (ii) The number of collisions that takes place per second per unit volume of the reaction mixture is known as collision frequency (Z). The value of collision frequency is very high of the order of 2825 10 to10 in case of binary collisions. (iii) Every collision does not bring a chemical change. The collisions that actually produce the product are effective collisions. The effective collisions, which bring chemical change, are few in comparison to the total number of collisions. The collisions that do not form a product are ineffective elastic collisions, i.e., molecules just collide and disperse in different directions with different velocities. C o n c . [A ]  t Zero order lo g . [A ]  t 1st order ][ 1 A t 2nd order 2][ 1 A 3rd order t R a te  Conc. Zero order R a te  R a te  (Conc.) 2 2nd order (Conc.) 3 3rd order R a te  Conc. 1st order Fraction of molecules capable of bringing effective collisions Distribution of energies at a definite temperature Energy E F ra c ti o n o f m o le c u le s 460 Chemical Kinetics (iv) For a collision to be effective, the following two barriers are to be cleared, (a) Energy barrier : “The minimum amount of energy which the colliding molecules must possess as to make the chemical reaction to occur, is known as threshold energy”.  In the graph 'E' corresponds to minimum or threshold energy for effective collision.  There is an energy barrier for each reaction. The reacting species must be provided with sufficient energy to cross the energy barrier. (b) Orientation barrier : The colliding molecules should also have proper orientation so that the old bonds may break and new bonds are formed. For example, ).()()( 4222 gONgNOgNO  During this reaction, the products are formed only when the colliding molecules have proper orientation at the time of collisions. These are called effective collisions. (v) Thus, the main points of collision theory are as follows, (a) For a reaction to occur, there must be collisions between the reacting species. (b) Only a certain fraction of the total number of collisions is effective in forming the products. (c) For effective collisions, the molecules should possess sufficient energy as well as orientation. (vi) The fraction of effective collisions, under ordinary conditions may vary from nearly zero to about one for ordinary reactions. Thus, the rate of reaction is proportional to : (a) The number of collisions per unit volume per second (Collision frequency, Z) between the reacting species (b) The fraction of effective collisions (Properly oriented and possessing sufficient energy), f i.e., Zf dt dx   Rate Where f is fraction of effective collision and Z is the collision frequency. (vii) The physical meaning of the activation energy is that it is the minimum relative kinetic energy which the reactant molecules must possess for changing into the products molecules during their collision. This means that the fraction of successful collision is equal to RTEae / called Boltzmann factor. (viii) It may be noted that besides the requirement of sufficient energy, the molecules must be properly oriented in space also for a collision to be successful. Thus, if ABZ is the collision frequency, P is the orientation factor (Steric factor) then, RTE AB aePZk / .   . If we compare this equation with Arrhenius equation. RTEaeAk /  We know that pre-exponential form 'A' in Arrhenius equation is, ABPZA  . Concept of activation energy The excess energy (Over and above the average energy of the reactants) which must be supplied to the reactants to undergo chemical reactions is called activation energy )( aE , ts)tanac(Reenergy)(Threshold EEEa  Activation energy = Threshold energy – Average kinetic energy of the reacting molecules. (a) Zero activation energy = Fraction of effective collision (f) will be very large = Very fast reaction (Instantaneous reaction). (b) Low activation energies = Fraction of effective collision (f) will be large = Fast reactions. (c) High activation energies = Fraction of effective collision (f) will be small = Slow reaction. The activation energy )( aE depends upon the nature of chemical bonds undergoing rupture and is independent of enthalpies of reactants and products. According to the concept of activation energy, the reactants do not change directly into the products. The reactant first absorb energy equal to activation energy and form activated complex. At this state, the molecules must have energy at least equal to the threshold energy. This means that the reaction involves some energy barrier which must be overcome before products are formed. The energy barrier is known as activation energy barrier. Products (Ep) E Reactants (Er) Et Progress of reaction Energy of the reaction Ea Er Ep Energy barrier (activation energy) Activated complex Threshold energy (Et) Properly oriented collisions form products approach O N O NO2 + O N O NO2 Product Collision Molecule s Bond Formatio n O N O O N O N2O4 O O O O N N Collisions not properly oriented Molecule s Separate No product O N O O N O NO2 NO2 Molecule s approach Collision O N O N O O NO2 + NO2 O N O N O O Fig. 11.1 Chemical Kinetics 461 (2) Transition state theory (i) According to transition state theory the activated complex is supposed to be in equilibrium with the reactant molecules. (ii) Once the transition state is formed it can either return to the initial reactants or proceeds to form the products. (iii) Assuming that once formed the transition state proceeds to products we can say that rate is proportional to concentration of transition state. Mathematically, Rate  Transition state Rate= Constant × Transition state (iv) The activation energy for the forward reaction, )( f aE and the activation energy for the reverse reaction )( r aE are related to the enthalpy )( H of the reaction by the equation r a f a EEH  . (a) For endothermic reactions, ,0H so that f a r a EE  (b) For exothermic reaction, ,0H so that f a r a EE  . Arrhenius equation Arrhenius proposed a quantitative relationship between rate constant and temperature as, RTEaeAk /  …..(i) The equation is called Arrhenius equation. In which constant A is known as frequency factor. This factor is related to number of binary molecular collision per second per litre. aE is the activation energy. T is the absolute temperature and R is the gas constant Both A and aE are collectively known as Arrhenius parameters. Taking logarithm equation (i) may be written as, RT E Ak a 303.2 loglog  …..(ii) The value of activation energy )( aE increases, the value of k decreases and therefore, the reaction rate decreases. When log k plotted against T/1 , we get a straight line. The intercept of this line is equal to log A and slope equal to R Ea 303.2  . Therefore slope303.2  REa . Rate constants for the reaction at two different temperatures 1T and 2T ,        211 2 11 303.2 log TTR E k k a …..(iii) where 1k and 2k are rate constant at temperatures 1T and 2T respectively )( 12 TT  . Mechanism of the reaction (1) Reaction involving first order consecutive reactions (i) In such reactions, the reactions form a stable intermediate compound before they are finally converted into the products. (ii) For example, reactants (R) are first converted to intermediate (I) which is then converted to product (P) as PIR kk  21 Therefore, the reaction takes place in two steps, both of which are first order i.e., Step I : IR k  1 ; Step II : PI k  2 This means that I is produced by step I and consumed by step II. In these reactions, each stage will have its own rate and rate constant the reactant concentration will always decrease and product concentration will always increase as shown in fig. (2) Reaction involving slow step : When a reaction occurs by a sequence of steps and one of the step is slow, then the rate determining step is the slow step. For example in the reaction IR k  1 ; PI k  2 , if 21 kk  then I is converted into products as soon as it is formed, we can say that ][ ][][ 1 Rk dt Pd dt Rd   (3) Parallel reactions : In such type of reactions the reactants are more reactive, which may have different orders of the reactions taking place simultaneously. For example, in a system containing lo g k 1/T R Ea 303.2  Slope Time C o n c e n tr a ti o n Concentration profile of reactants (R), intermediate (I) and products (P) as a function of time R P I