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S T U D Y M A T E R I A L PHASE - I CHEMICAL KINETICS & NUCLEAR CHEMISTRY IIT-JEE CHEMISTRY NARAYANA INSTITUTE OF CORRESPONDENCE COURSES FNS HOUSE, 63 KALU SARAI MARKET SARVAPRIYA VIHAR, NEW DELHI-110016 PH.: (011) 32001131/32/50 FAX : (011) 41828320 Website : w w w . n a r a y a n a i c c . c o m E-mail : i n f o @ n a r a y a n a i c c . c o m

2004 NARAYANA GROUP This study material is a part of NARAYANA INSTITUTE OF CORRESPONDENCE COURSES for IIT-JEE, 2008-09. This is meant for the personal use of those students who are enrolled with NARAYANA INSTITUTE OF CORRESPONDENCE COURSES, FNS House, 63, Kalu Sarai Market, New Delhi-110016, Ph.: 32001131/32/50. All rights to the contents of the Package rest with NARAYANA INSTITUTE. No other Institute or individual is authorized to reproduce, translate or distribute this material in any form, without prior information and written permission of the institute.

PREFACE Dear Student, Heartiest congratulations on making up your mind and deciding to be an engineer to serve the society. As you are planning to take various Engineering Entrance Examinations, we are sure that this STUDY PACKAGE is going to be of immense help to you. At NARAYANA we have taken special care to design this package according to the Latest Pattern of IIT-JEE, which will not only help but also guide you to compete for IIT-JEE, AIEEE & other State Level Engineering Entrance Examinations. The salient features of this package include : ! Power packed division of units and chapters in a scientific way, with a correlation being there. ! Sufficient number of solved examples in Physics, Chemistry & Mathematics in all the chapters to motivate the students attempt all the questions. ! All the chapters are followed by various types of exercises, including Objective - Single Choice Questions, Objective - Multiple Choice Questions, Comprehension Type Questions, Match the Following, Assertion-Reasoning & Subjective Questions. These exercises are followed by answers in the last section of the chapter including Hints & Solutions wherever required. This package will help you to know what to study, how to study, time management, your weaknesses and improve your performance. We, at NARAYANA, strongly believe that quality of our package is such that the students who are not fortunate enough to attend to our Regular Classroom Programs, can still get the best of our quality through these packages. We feel that there is always a scope for improvement. We would welcome your suggestions & feedback. Wish you success in your future endeavours. THE NARAYANA TEAM ACKNOWLEDGEMENT While preparing the study package, it has become a wonderful feeling for the NARAYANA TEAM to get the wholehearted support of our Staff Members including our Designers. They have made our job really easy through their untiring efforts and constant help at every stage. We are thankful to all of them. THE NARAYANA TEAM

C O N T E N T S CONTENTS CHEMICAL KINETICS & NUCLEAR CHEMISTRY 1. Theory 2. Solved Problems (i) Subjective Type Problems (ii) Single Choice Problems (iii) Multiple Choice Problems (iv) Miscellaneous Problems 3. Comprehension Type Problems Matching Type Problems Assertion-Reason Type Problems Assignments (i) Subjective Questions (ii) Single Choice Questions (iii) Multiple Choice Questions (iv) Miscellaneous Questions (v) 4. Comprehension Type Questions Matching Type Questions Assertion-Reason Type Questions Problems Asked in IIT-JEE Answers

CHEMICAL KINETICS & NUCLEAR CHEMISTRY IIT-JEE Syllabus Rates of chemical reactions; Order of reactions; Rate constant; First order reactions; Temperature dependence of rate constant (Arrhenius equation). CONTENTS Rate of reaction Elementary reaction Integrated rate laws Activation energy Kinetics of some complex first order reactions Methods of determining order Nuclear chemistry Kinetics of radioactive disintegration INTRODUCTION Some chemical reaction occurs within few micro seconds or milli seconds due to formation of reaction intermediate (carbocation, carboanion or free radicals). But some reaction occur in few year or months because breaking of strong ionic or metallic bond is a slow process. Under chemical kinetics we would study that reaction which occurs at measurable rate. In Chemical Kinetics we would be able to understand the velocity as well as different factors which would effect the chemical reaction. Under this we will be studying the mechanism of the reaction. Here mechanism of reaction means how reactants are converted into product or in how many intermediate steps reactant is converted into product. And which intermediate step is rate determining step. 1 FNS House, 63, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 Ph.: (011) 32001131/32 Fax : (011) 41828320

NARAYANA Chemistry : Chemical Kinetics & Nuclear Chemistry INSTITUTE OF CORRESPONDENCE COURSES 1. RATE OF REACTION Rate of a reaction is defined as the increase in molar concentration of a product per unit time or decrease in molar concentration of a reactant per unit time. Molar concentration is normally measured in moles per litre, the rate of a reaction is specified in mole per litre per time. 1.1 AVERAGE RATE x is known as average rate, where x is the change in concentration in t t time. As we have discussed in chemical equilibrium rate of change of concentration of reactant decreases as the reaction proceeds. This means that rate of change of concentration is not constant. If the time interval is quite large then average rate will show large deviations from the actual rate. The quantity 1.2 INSTANTANEOUS RATE In order to precisely define rate time interval t is made smaller i.e. instantaneous rate average rate as t approaches zero. [A] d[A] dt t 0 t Consider the hypothetical reaction A 2B 3C D Rate of disappearance of A d[A] dt Rate of disappearance of B d[B] dt Rate of appearance of C d[C] dt Rate of appearance of D d[D] dt But from the stoichiometry it is apparent that when one mole of A is reacted, two moles of B are also consumed. i.e. rate of disappearance of B 2 rate of disappearance of A d[B] d[A] 2 dt dt or d[A] 1 d[B] dt 2 dt 2 FNS House, 63, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 Ph.: (011) 32001131/32 Fax : (011) 41828320

Chemistry : Chemical Kinetics & Nuclear Chemistry NARAYANA INSTITUTE OF CORRESPONDENCE COURSES Similarly we can prove that So, rate of reaction d[A] 1 d[C] dt 3 dt d[A] 1 d[B] 1 d[C] d[D] dt 2 dt 3 dt dt We can also generalize our statement i.e. for a general reaction m1A m2 B n1C n 2 D Rate of reaction 1 d[A] 1 d[B] 1 d[C] 1 d[D] m1 dt m 2 dt n1 dt n 2 dt Illustration 1 : Dinitrogen pentaoxide decomposes as follows: d [ N 2O5 ] 1 N 2O5 2 NO2 O2 . If, K ′[ N 2O5 ] 2 dt d [ NO2 ] K ′′[ N 2O5 ] dt d [O2 ] K ′′′[ N 2O5 ] dt Derive a relation in, K ′, K '' and K ''' Solution : d[N 2O5 ] 1 d[NO 2 ] d[O 2 ] 2 dt 2 dt dt 1 On substituting values, K′[N 2O5 ] K′′[N 2O5 ] 2K′′′[N 2O5 ] 2 ′ ′′ ′ ′′ or 2K K K For the given change EXERCISE 1 1. For the reaction; 4NH3(g) 5O2(g) 4NO(g) 6H2O(g), the rate of reaction in terms of d[NH3 ] , then write rate expression in terms of O2, NO and disappearance of NH3 is dt H2O. 2. For the decomposition reaction: N2O4(g) 2NO2(g); the initial pressure of N2O4 falls from 0.46 atm to 0.28 atm in 30 minute. What is the rate of appearance of NO2? 3. A chemical reaction 2A 4B C; in gaseous phase shows an increase in concentration of B by 5 10–3 M in 10 second. Calculate: a) rate of appearance of B, b) rate of the reaction, c) rate of disappearance of A 3 FNS House, 63, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 Ph.: (011) 32001131/32 Fax : (011) 41828319

NARAYANA Chemistry : Chemical Kinetics & Nuclear Chemistry INSTITUTE OF CORRESPONDENCE COURSES 2. ELEMENTARY REACTION An elementary reaction is a single molecular event, such as collision of molecules resulting in a reaction. The set of elementary reactions whose overall effect is given by the net chemical equation is called reaction mechanism. Let us consider an example for the reaction of nitrogen dioxide with carbon monoxide. NO 2(g) CO(g) NO (g) CO 2(g) [net chemical equation] (i) Suppose this chemical reaction takes place in two steps NO 2(g) NO 2(g) NO3(g) NO (g) [Elementary reaction] (ii) NO3(g) CO (g) NO 2(g) CO 2(g) [Elementary reaction] (iii) Thus net reaction (i) is obtained by the combination of two elementary reaction (ii) and (iii) and NO3 is a reaction intermediate as it is produced and consumed during the course of reaction. 2.1 MOLECULARITY It is defined as the number of molecules taking part on the reactant side of an elementary reaction. A unimolecular reaction is an elementary reaction involves one reactant molecule, a bimolecular reaction is an elementary reaction that involves two reactant molecules. 2.2 DIFFERENTIAL RATE LAW It is a relationship that relates the variation of rate of reaction with the concentration of reactants. Consider the reaction 2A 3B C D as we have seen 1 d[A] d[C] [A]m [B]n 2 dt dt [law of mass action states that rate of reaction is directly proportional to the product of the active masses of reactants raised to some powers] So, d[C] k[A]m [B]n dt k is known as velocity constant or rate constant or specific reaction rate. m is known as order with respect to A, n is known as order with respect to B. Sum m n is known as overall order of the reaction. 2.3 ORDER OF REACTION It is defined as the sum of exponents or powers which are raised to concentration terms in the rate law expression of a reaction. 4 FNS House, 63, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 Ph.: (011) 32001131/32 Fax : (011) 41828320

Chemistry : Chemical Kinetics & Nuclear Chemistry NARAYANA INSTITUTE OF CORRESPONDENCE COURSES Difference between order and Molecularity : Molecularity of a reaction can be used to describe only an elementary process and molecularity can be predicted just be viewing the elementary reaction. Whereas order of a reaction refers to the overall reaction and can be determined experimentally, however for elementary process the order and molecularity are same. Molecularity has got no meaning for an overall reaction and order cannot be predicted from a balanced chemical equation. Note : If a reaction can be written as a combination of several elementary reaction then it’s the slowest step that governs the rate of reaction i.e. the slowest step is the rate determining step. Differential Rate Law : Consider reaction P 2Q R The differential rate law is written as d[P] 1 d[Q] Rate k[P]m [Q]n dt 2 dt Value of m and n can be determined by performing the reaction in laboratory i.e. order w.r.t P is m and order w.r.t. Q is n and overall order will be m n. 4.4 UNITS OF k In general rate law for a nth order reaction can be written as dC kCn dt Where k is rate constant, k is characteristic of a reaction at a given temperature. It changes only when temperature changes and n is the order of reaction. k dC / dt Cn Units of k: (concentration)1–ntime–1 For a zero order reaction (n 0) Units of k mol/L/s For a first order reaction (n 1) Units of k time–1 For a second order reaction (n 2) Units of k (mol/l)–1time–1 l/mol/s 5 FNS House, 63, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 Ph.: (011) 32001131/32 Fax : (011) 41828319

NARAYANA Chemistry : Chemical Kinetics & Nuclear Chemistry INSTITUTE OF CORRESPONDENCE COURSES Illustration 2 :The data given below are for the reaction of NO and Cl2 to form NOCl at 25K [Cl2] [NO] Initial rate 103 (mol litre–1sec–1) 0.05 0.05 1 0.15 0.05 3 0.05 0.15 9 a) What is the order with respect to NO and Cl2 in the reaction? b) Write the rate expression. c) Solution : Calculate the rate constant d) Determine the reaction rate when conc. of Cl2 and NO are 0.2 M and 0.4 M respectively. For the reaction; 2NO Cl2 2NOCl Rate k[Cl2]m[NO]n (1) Where, m and n are order of reaction w.r.t Cl2 and NO, respectively. From the given data: 1 10–3 k[0.05]m [0.05]n (2) 3 10–3 k [0.15]m [0.05]n (3) 9 10–3 k[0.05]m [0.15]n (4) By equations (2) and (3), m 1 By equations (2) and (4) n 1 a) order with respect to NO is 2 and w.r.t. to Cl2 is 1. b) Also, rate expression r k[Cl2]1 [NO2]2 c) And rate constant., k d) Further, r 1 10 3 [Cl2 ][NO]2 [0.05]1[0.05]2 8 litre2 mol–2 sec–1 r k[Cl2]1 [NO]2 8 [0.2]1 [0.4]2 0.256 mol litre–1 sec–1 6 FNS House, 63, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 Ph.: (011) 32001131/32 Fax : (011) 41828320

NARAYANA Chemistry : Chemical Kinetics & Nuclear Chemistry INSTITUTE OF CORRESPONDENCE COURSES EXERCISE 2 : 1. The reaction; 2A B C D 2E; is found to be I order in A II order in B and zero order in C. a) Write the rate expression b) What is the effect on rate on increasing the conc. of A, B and C two times. 2. The reaction; 2NO Br2 2NOBr, is supposed to follow the following mechanism, i) NO Br2 fast NOBr2 slow ii) NOBr2 NO 2NOBr Suggest the rate law expression 3. The thermal decomposition of N2O5 occurs in the following steps: Step I: slow N2O5 NO2 NO3 Step II fast N2O5 NO3 3NO2 O2 �–––––––––– Overall reaction 2N2O5 4NO2 O2- Suggest the rate expression 3. INTEGRATED RATE LAWS The differential rate laws show how the rates of reaction depend on the concentrations of reactants. It is also useful to known how the concentration is depend on time, this information can be obtained from the differential rate law by integration. 3.1 FIRST ORDER REACTION A reaction is said to be first order if its rate is determined by the change of one concentration term only. Consider a first order reaction A Products The differential rate law equation will be d[A] k[A] dt Integrating both sides taking limits [A]0 , which is the concentration at t 0 and [A ]t , the [A ]t concentration at time t [A ]0 t d[A] k dt dt 0 7 FNS House, 63, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 Ph.: (011) 32001131/32 Fax : (011) 41828319

NARAYANA Chemistry : Chemical Kinetics & Nuclear Chemistry INSTITUTE OF CORRESPONDENCE COURSES ln [A]0 [A]0 2.303 kt or k log [A]t t [A ]t A t 0 a t t a–x k 3.2 Products 2.303 a log t a x CHARACTERISTICS OF A FIRST ORDER REACTION A first order reaction must follow above form of rate law for all time instants. This means if we are given value of a i.e. initial concentration and values of x at different time instants i.e. a – x is known to us. If values of K are calculated for different time instants by using above expression, if the reaction is following a first order kinetics then all values of K will approximately be equal to each other. 3.3 HALF LIFE PERIOD It is defined as the time in which half of the reactants are reacted for a first order reaction. k at 2.303 a log t a x t t 1/ 2 ; x k a 2 2.303 a log t1/ 2 a/2 t1/ 2 0.6932 k In fact we can define any life suppose we want to define 7/8 life. k 2.303 a log t a x at t t 718 ; x at k 7a 8 2.303 a log 7a t 718 a 8 t 718 2.303 2.303 log 8 3 log 2 k k t 7 / 8 3 t1/ 2 8 FNS House, 63, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 Ph.: (011) 32001131/32 Fax : (011) 41828320

NARAYANA Chemistry : Chemical Kinetics & Nuclear Chemistry INSTITUTE OF CORRESPONDENCE COURSES Important thing is that in a first order reaction time required for the completion of a definite fraction is independent of initial concentration of reactants. 3.4 HALF LIFE FOR NTH ORDER REACTION Let A products is following nth order kinetics. i.e. d[A] k[A]n , it can be shown that dt t1/ 2 2n 1 1 k(n 1)a 0n 1 i.e.t1/ 2 1 (n 2) a n0 1 Expression for first order reaction is 2.303 a log t a x 2.303 a 2.303 t log [log a log(a x)] or K a x k 2.303 2.303 t log a log(a x) k k Comparing this equation with Y mx C k So a plot of t vs log (a – x) will be straight line with a intercept of of 2.303 log a and a slope k 2.303 k 2.303 log a K 2.303 K time slope log(a x) 3.5 EXAMPLES OF FIRST ORDER REACTION 3.5.1 Decomposition of H2O2 2H 2O2 2H 2O O2 H 2O2 H 2O O [slow i.e. rate determining step] O O O 2 [fast] 9 FNS House, 63, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 Ph.: (011) 32001131/32 Fax : (011) 41828319

NARAYANA Chemistry : Chemical Kinetics & Nuclear Chemistry INSTITUTE OF CORRESPONDENCE COURSES So Rate [H 2 O2 ]1 or R k[H 2 O2 ] Order 1 Kinetics of this reaction can be studied by withdrawing a definite volume of reaction mixture after regular interval of time and titrating it against KMnO 4 solution in presence of dil. H 2SO4 2KMnO 4 3H 2SO4 K 2SO4 2MnSO 4 3H 2O 5O [H 2O2 O H 2 O O2 ] 5 ��–––––––––––––– 2KMnO 4 3H 2SO 4 5H 2O 2 K 2SO4 2MnSO 4 8H 2O 5O 2 Since H2O2 is undergoing self decomposition so quantity of H2O2 present in a definite volume will also go on decreasing, KMnO4 is reacting with H2O2 so titre value i.e. volume of KMnO4 used will also go on decreasing. Let V0 and Vt be the volumes of KMnO 4 used at zero time and after t time respectively. then V0 a [a initial conc. of H 2O2 ] Vt a x [a –x conc. of H 2O2 after t time] V0 a Vt a x k V 2.303 log 0 t Vt Illustration 3 :From the following data show that the decomposition of hydrogen peroxide in aqueous solution is a first - order reaction. What is the value of the rate constant ? Time in minutes VolumeV/(ml) 0 10 20 30 40 25.0 20.0 15.7 12.5 9.6 where V is the number of ml of potassium permanganate required to decompose a definite volume of hydrogen peroxide solution. Solution : The equation for a first order reaction is 2.303 a k1 log t a-x The volume of KMnO4 used, evidently corresponds to the undecomposed hydrogen peroxide. 10 FNS House, 63, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 Ph.: (011) 32001131/32 Fax : (011) 41828320

NARAYANA Chemistry : Chemical Kinetics & Nuclear Chemistry INSTITUTE OF CORRESPONDENCE COURSES Hence the volume of KMnO4 used, at zero time corresponds to the initial concentration a and the volume used after time t, corresponds to (a - x) at that time. Inserting these values in the above equation, we get 2.303 25 log 0.022287 min-1 0.000314 s-1 when t 10 min. k1 10 20.0 2 .303 25 log 0.023230 min -1 0.0003871 s -1 when t 20 min. k1 10 15.7 2.303 25 when t 30 min. k1 log 0.02369 min -1 0.0003948 s -1 30 12.5 2.303 25 log 0.023897 min -1 0.0003983 s -1 when t 40 min. k1 40 9.6 The constancy of k, shows that the decomposition of H2O2 in aqueous solution is a first order reaction. The average value of the rate constant is 0.0003879 s-1. 3.5.2 Decomposition of NH4NO2 in aqueous solution NH 4 NO 2 N 2 2H 2O Rate [NH 4 NO2 ]1 Rate K[NH 4 NO2 ] order 1 Kinetics of this reaction may be studied by collecting the nitrogen evolved and measuring its volume after regular intervals of time Let Vt and V be the volumes of N 2 liberated after t time and at the end of reaction. NH 4 NO 2 N 2 2H 2O Initial conc. Conc. after t time a a–x 0 x Conc. at t 0 a Vt x V a or V Vt a x V a V Vt a x k 2.303 V log t V Vt 11 FNS House, 63, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 Ph.: (011) 32001131/32 Fax : (011) 41828319

NARAYANA Chemistry : Chemical Kinetics & Nuclear Chemistry INSTITUTE OF CORRESPONDENCE COURSES Note: t indicates that sufficient time is provided to the reaction i.e., the reaction has practically gone to completion. Illustration 4 : From the following data for the decomposition of diazobenzene chloride, show that the reaction is of first order: Time (min) 20 50 70 Volume of N2 (mL) 10 25 33 162 C6H5N2Cl C6H5Cl N2 Solution : initial concentration a Concentration of after time t (a – x) x At time, i.e., when the reaction is complete, the whole of C6H5N2Cl converts into N2. Hence volume of N2 at time corresponds to the initial concentration ‘a’ while volumes of N2 at different time intervals correspond to x as shown above. 2.303 162 log For t 20 min, k1 0.0032min 1 20 162 10 2.303 162 log 0.0033min 1 For t 50 min, k1 50 162 25 2.303 162 log For t 70 min, k1 0.0032min 1 70 162 33 The constant of k1 shows that the decomposition of C6H5N2Cl; is a first order reaction. 3.5.3 Conversion of N-Chloroacetinalide into p-chloro acetanialide O O Cl N H CH3 N CH3 rearrangement isomerism N-chloro-N-phenylacetamide Cl N-(4-chlorophenyl)acetamide Rate [N-chloroacetinalide]1 order 1 Kinetics of this reaction may be studied by withdrawing a definite volume of the reaction mixture after regular intervals of time, adding excess of KI and titrating the liberated I2 against standard sodium thiosulphate solution. N-chloroacetinalide reacts with KI and liberates I2 but p-chloroacetinalide does not. I2 2Na 2S2O3 Na 2S4O6 2NaI 12 FNS House, 63, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 Ph.: (011) 32001131/32 Fax : (011) 41828320

NARAYANA Chemistry : Chemical Kinetics & Nuclear Chemistry INSTITUTE OF CORRESPONDENCE COURSES N-chloroacetinalide P chloroacetinalide a 0 a–x x t 0 t t Let V0 and Vt be the volumes of sodium thiosulphate used at t 0 and t t respectively, then V0 a Vt a x V0 a Vt a x k Illustration V 2.303 log 0 t Vt 5 : Acetochloracetanilide (N-chloroacetanilide) is converted into pchloroacetanilide, it is followed by the addition of KI which acts only on the former compound. The progress of reactionis studied by titrating the iodine liberated with standard hypo solution and the following results are obtained. Time (hour) 0 1 2 6 ml of hypo solution 45 32 22.5 5.7 Show that the reaction is unimolecualr. Calculate the velocity constant of the reaction and also determine the fraction of N-chloroacetanilide which has reacted in three hours. Solution : The velocity constant of the first order reaction is given by k 2.303 a log t a x Here the initial concentration ‘a’ corresponds to the volume of hypo used against liberated iodine at time 0, a 45, (a – x) corresponds to the volume of hypo used for titrations at different intervals of time, i.e. when t 1 hour, (a – x) 32, and so on. Substituting the values in the above equation, (i) When t 1 hour, (a – x) 32 k (ii) When t 2 hours, (a – x) 22.5 k (iii) When 2.303 45 log 0.3411 1 32 2.303 45 log 0.3468 t 22.5 t 6 hours, (a – x) 5.7 13 FNS House, 63, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 Ph.: (011) 32001131/32 Fax : (011) 41828319

NARAYANA Chemistry : Chemical Kinetics & Nuclear Chemistry INSTITUTE OF CORRESPONDENCE COURSES k 2.303 45 log 0.3443 6 5.7 Since the value of K in all the three cases is nearly same, the reaction must be unimolecular. Calculation of fraction that has reacted in 3 hours Let the amount reacted in 3 hours x moles Given a 45, t 3 hours, (a – x) 45 – x Substituting these values in the reaction k 2.303 a log t a x 0.300 2.303 45 log t (45 x) 45 – x 16.03 x 28.97 Hence fraction of N-chloroacetanilide reacted in 3 hours 3.6 28.97 0.643 45 PSEUDO FIRST ORDER REACTION If molecularity of a reaction is 2 but order is 1 then the reaction is known as pseudo firstorder reaction or pseudo unimolecular reaction. Hydrolysis of tertiary butyl bromide : (CH3 )3 CBr OH (CH3 )3 OH Br This reaction takes place in two steps. CH3 i) CH3 slow Br H 3C H3C CH3 CH3 ii) Br - CH3 CH3 fast H3C OH - H3C CH3 OH CH3 Since slowest step is rate determining step. Rate [(CH3 )3 CBr]1[OH ]0 K[(CH3 )3 CBr] Molecularity 2 14 FNS House, 63, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 Ph.: (011) 32001131/32 Fax : (011) 41828320

NARAYANA Chemistry : Chemical Kinetics & Nuclear Chemistry INSTITUTE OF CORRESPONDENCE COURSES Order 1 So the reaction is pseudo unimolecular 3.6.1 Hydrolysis of Ester catalysed by an acid H CH3COOC 2H 5 H 2O CH3COOH C6 H5OH Rate [CH 3COOC 2 H 5 ][H 2O] Since water is in large excess so its concentration almost remains constant Rate [CH 3COOC 2 H 5 ]1 Rate k[CH 3COOC 2 H 5 ] order 1 Molecularity 2 So the reaction is pseudo unimolecualr reaction. Kinetics of this reaction can be studied by withdrawing a definite volume of reaction mixture after regular intervals of time and titrating against NaOH solution. This reaction mixture is chilled during titration by adding ice cold water. Chilling checks hydrolysis of ester during titration. Chilling also checks reaction of ester with NaOH (second order and biomolecular). Let V0 , Vt and V be the volumes of NaOH used at 0 time, t time and at the end of reaction respectively. The volume of NaOH used at 0 time ( V0 ) corresponds to the concentration of catalyst and volume of NaOH used after t time (Vt ) corresponds to the concentration of catalyst and acetic acid formed. H CH3COOC 2H 5 H 2O CH3COOH C2 H5OH t 0 a 0 t t a–x x t 0 a Vt V0 x [x conc. of CH3 COOH formed after t time] V V0 a (V V0 ) (Vt V0 ) a x V Vt a x V V0 a V Vt a x k V V0 2.303 log t V Vt 15 FNS House, 63, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 Ph.: (011) 32001131/32 Fax : (011) 41828319

NARAYANA Chemistry : Chemical Kinetics & Nuclear Chemistry INSTITUTE OF CORRESPONDENCE COURSES Illustration 6 :5 ml of ethylacetate was added to a flask containing 100 ml of 0.1 N HCl placed in a thermostat maintained at 30 C. 5 ml of the reaction mixture was withdrawn at different intervals of time and after chilling, titrated against a standard alkali. The following data were obtained : Time (minutes) 0 75 119 183 ml of alkali used 9.62 12.10 13.10 14.75 21.05 Show that hydrolysis of ethyl acetate is a first order reaction. Solution : The hydrolysis of ethy acetate will be a first order reaction if the above data confirm to the equation. k1 2.303 V V0 log t V Vt Where V0, Vt and V represent the volumes of alkali used at the commencement of the reaction, after time t and at the end of the reaction respectively, Hence V - V0 21.05 - 9.62 11.43 Time V - Vt 2.303 V V0 log k1 t V Vt 75 min 21.05 - 12.10 8.95 2.303 11.43 log 0.003259 min -1 75 8.95 119 min 21.05 - 13.10 7.95 2.303 11.43 log 0.003264 min -1 119 7.95 83 min 21.05 - 14.75 6.30 2.303 11.43 log 0.003254 min -1 183 6.30 A constant value of k shows that hydrolysis of ethyl acetate is a first order reaction 3.6.2 Inversion of Cane Sugar H C12 H 22O11 H 2O C6 H12O6 C6 H12O6 Cane sugar glu cose fructose Rate [C12 O22 O11 ][H 2 O] Since water is solvent its concentration is constant. So Rate K[C12 H22O11 ] Molecularity 2 Order 1 So the reaction is pseudo unimolecular 16 FNS House, 63, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 Ph.: (011) 32001131/32 Fax : (011) 41828320

NARAYANA Chemistry : Chemical Kinetics & Nuclear Chemistry INSTITUTE OF CORRESPONDENCE COURSES If some inert liquid is used as solvent then concentration of water can be changed and rate changes on changing the concentration of water. The reaction then becomes second order. Rate of this reaction is also proportional to the concentration of catalyst H . But concentration of catalyst remains constant during the reaction. If we change concentration of water as well as that of H then reaction becomes 3rd order. Rate [C12 H 22 O11 ][H 2 O][H ] But under ordinary conditions H 2O and H are constant so, Rate [C12 H 22 O11 ] The initial solution of cane sugar is destrorotatory but the product mixture is laevorotatory. Since the reaction involves inversion in the sign of rotation, ths is known as inversion of cane sugar. H C12 H 22O11 H 2O C6H12O6 C6 H12O6 Dextrorotatory Dextrorotatory Laevorotatory 92 Specific rotation 52.5 laevorotatory Fructose Laevo rotatory Glucose Prism dextro rotatory Cane sugar dextro rotatory Kinetics of this reaction can be studied by taking cane sugar solution in a polarimeter and measuring the angles of rotation after regular intervals of time. Let r0 , rt and r be the angles of rotation at 0 time, after t time and at the end of reaction. 0 r rt r0 -90 90 180 So, r0 rt x (i) r0 r a (ii) 17 FNS House, 63, Kalu Sarai Market, Sarvapriya Vihar, New Delhi-110016 Ph.: (011) 32001131/32 Fax : (011) 41828319

NARAYANA Chemistry : Chemical Kinetics & Nuclear Chemistry INSTITUTE OF CORRESPONDENCE COURSES (r0 r ) (r0 rt ) a x or rt r a x r0 r a rt r a x k r r 2.303 log 0 t rt r Illustration 7 :The optical rotations of sucrose in 0.5 N HCl at 35 C at various time intervals are given below. Show that the reaction is of first order : Time (minutes) Rotation (degree) Solution : 0 10 20 30 40 32.4 28.8 25.5 22.4 19.6 -11.1 The inversion of sucrose will be first order reaction if the above data confirm to 2.303 r r log 0 the equation , k 1 t rt r Where r0, rt and r represent optical rotations at the commencement of the reaction after time t and at the completion of the reaction respectively n the case a0 r0 - r 32.4 - (-11.1) 43.5 The value of k at different times is calculated as follows : Time rt rt - r k 10 min 28.8 39.9 2.303 43.5 log 0.008625 min-1 10 39.9 20 min 25.5 36.6 2.303 43.5 log 0.008625 min-1 20 36.6 0 min 22.4 33.5 2.303 43.5 log 0.008694 min-1 30 33.5 40 min 19.6 30.7 2.303 43.5 log 0.008717 min-1 40 30.7 The constancy of k1 indicates that the inversion of sucrose is a first - order reaction. 18 FNS House, 63, Kalu Sarai

CHEMICAL KINETICS & NUCLEAR CHEMISTRY 1. Theory 2. Solved Problems (i) Subjective Type Problems (ii) Single Choice Problems (iii) Multiple Choice Problems (iv) Miscellaneous Problems Comprehension Type Problems Matching Type Problems Assertion-Reason Type Problems 3. Assignments (i) Subjective Questions (ii) Single Choice Questions

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