UNIT I CHEMICAL KINETICS Chemical Kinetics Raectant Product @ Chemical —— w ~_@ Concentration D &® @acadpilts @®) @acadpills & @acadpills GD po”detec! PSEUDO FIRST ORDER REAC Cee etna] Cer ea ioral eC olay Cleared a calely a ILO IN ake} REACTION. Tdsy De Sc aac ea te batik. Sean RATE OF CHEMICAL REACTION RATE eae Piracy eoNcOLE CSN am et reed 1 Pearse) Maroons oad Liew ee Beg OF REACTION Ee ere aT eT aati Perr errr Pela RO aeaeC enn HALF LIFE OF A REACTION Peat Mel One Eom ‘Chemical Kinetics the branch of chemistry, which deals with the study of reaction rates and their ‘mechanisms. Rate of a Chemical Reaction: the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time. It can be expressed in terms of: (i) The rate of decrease in concentration of any one of the reactants. concentration of any one of the products. Consider a hypothetical reaction, R -—-> P One mole of the reactant R produces one mole of the product P. If [R]: and [P]: are the concentrations of R and P respectively at time ti and [Rp and [P}p are their concentrations at time t2 then, Ar = 2-11 AIR] = [Rh ~ [Riv A[P]=[Pl— [Ph ‘The square brackets in the above expressions are used to express molar concentration. Rate of disappearance of R = Decrease in concentration of R / Time taken = - R/t (1) Rate of appearance of P = Increase in concentration of P /Time taken = P/t (2) Since, A{R] is a negative quantity (as concentration of reactants is decreasing), it is multiplied with —1 to make the rate of the reaction a positive quantity Equations (1) and (2) given above represent the average rate of a reaction. ra. cacatsits (EB) excatoits ED) @acadoits RD) ecotrt.comAverage rate depends upon the change in concentration of reactants or products and the time taken for that change to occur. (Ref. ncert Fig. 4.1) i | se (m8) oe ae eT Units of rate of a reaction: The units will be mol L's In gaseous reactions, the units of the rate equation will be atm 5. Factors affecting rate of reaction: The important factors are: 1. Concentration of the reacting species. 2. Temperature of the system. 3. Nature of reactant and products. 4. Presence of a catalyst. 5. Surface area 6. Exposure to radiation. Rate Law and Rate Constant: Consider a general reaction: aA + bB —-> eC + dD Where a, b,c and d are the stoichiometric coefficients of reactants and products. The rate expression for this reaction is Rate « [A] [B}” Where exponents x and y may or may not be equal to the stoichiometric coefficients (a & b) of the reactants. Above equation can also be written as Rate = k [AP [BP -d[R] /dr = k{A]* [BP This form of equation is known as differential rate equation, where k is a proportionality constant called rate constant. ‘The equation, Rate = k [A}* [B)’ which relates the rate of a reaction to concentration of reactants rate law or rate expression. Rate law is the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power, which may or may not be same as the stoichiometric coefficient of the reacting species in a balanced chemical equation. For example: 2NO (g) + 02 (g) ---> 2NO2((g) Rate = k [NOF [02] -d[R] /dr = k [NO]? [O2} @acadpilts => @acadpills & @acadpills GD po” alledOrder of reaction: Rate = k [AP [BP x and y indicate the rate is to the change in concentration of A and B. ‘Sum of these exponents, i.e., x + y in above equation gives the overall order of a reaction. where: represent the order with respect to the reactants A and B respectively. Order of reaction is defined as the sum of powers of the concentration of the reactants in the rate law is called the order of that chemical reaction. a reaction can be 0, 1, 2, 3 and even a fraction. ‘A zero-order reaction means that the rate of reaction is independent of the concentration of reactants. Units of rate constant Zero order rate of reaction: mol L'! s! First order rate of reaction: s Second order rate of reaction: L mol s sx andy Molecularity of a reaction: The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction is called molecularity of a reaction. For examples: NH:NO2 -----> No + 2H20 Unimolecular reaction 2HI (g) ---> He (g) +b (@) Bimolecular reaction 2NO (g) + O2 (g) > 2NO2 (g) ‘Trimolecular reaction Important points of distinction between order and molecularity S.No. Order Molecularity 1 | Order is the sum of powers of the Molecularity is the number of reacting concentration terms in the rate law species undergoing simultaneous collision expression. in the elementary or simple reaction. 2 | Order of a reaction is determined ‘Moleculatity isa theoretical concept. experimentally. 3 | Order of a reaction can be zero, ‘Molecularity of a reaction cannot be zero. Integrated rate equations: Zero order reaction: Zero order reaction means that the rate of the reaction is proportional to zero power of the concentration of reactants. Consider the reaction, Integrating both sides [R]=-kr40 (1) Where, | is the constant of integration Att=0 the concentration of reactant [R] = [RJo Where [Rl is the initial concentration of reactant. [RJo =-kx 0 +11, Substituting the value of I in the equation (1) @acadpilts => @acadpills & @acadpills GD po”‘kt + [R]o [Ro - [R]}/t ‘Variation in the concentration Vs time plot for a zero-order reaction ° > Example of Zero order reaction is the decomposition of gaseous ammonia 2NHG (g) No (g) + 3 Ho(g) Rate = k [NHs]" =k the rate of the reaction is proportional to the First Order Reactions: The rate of the reaction is proportional to the first power of the concentration of the reactant R. For example: R—>P Rate = -d[R] /dt = k[R] d{R] AR]= -k dr, Integrating this equation and we get In [R] =-ke +1) Att=0, In [R}=-kx 0+ 1, T= In [R]Jo, Substituting the value of I in the equation (1) In[R]=-k+ In[Rlo k= (In [Ro - In [R]} /t Remember that, (log a —log b = log(a/b) k= (1A) In {{RlofR]} In {[RJ/[R]Jo} =~ kt, taking antilog both sides [R]=[Rloe We know that, In a= 2.303 log a A= (2.303/t) log {[R]o/[R]} If we plot a graph between log [R]o/[R] Vs t, the slope is k/2.303 for first order reaction ‘Slope = b/2.308 tog URL /IRD > Time —> @acadpiltsFirst order gas phase reaction: A(g) > B(g) + C(g) Total pressure px = pa + pa + pc A(g) => Big) + ce) Att=0 piatm Oatm O atm Attimet (pi-») xatm x atm P= (pir) +x+x=pitx x=(P-P) PA=P—X=pi- Pr- P)= 2p k= (2.303/) log [pi pal k= (2.303) log [p/2p-p)] Half-life of a reaction: The half-life of a reaction is the time in which the concentration of a reactant is, reduced to one half of its initial concentration. It is represented as ty. For a zero-order reaction, rate constant [Rlo- [RI}t v2» [R] = [R]o/2 At K={I[R]o- [Rlo /2}/tv2= [R]o /2 tra tia = [Rho /2k For a first order reaction, rate constant is k= (2.303/) log {{R}o/[R}} At » [R] = [Rlo/2 2.303/ti2) log {[RJo[Ro /2} k= (2.303 /tia) log 2 = (2303/12) 0.3010 ti = 0.693/ k For zero order reaction fi & [R]o. For first order reaction f1 is independent of [Rlb. Collision Theory of Chemical Reactions: Collision frequency: Itis defined as the number of collisions per second per unit volume of the reaction mixture is known as collision frequency (Z). Effective collision: The collisions in which molecules collide with proper orientation, breaking of bonds between reacting species and formation of new bonds to form products are called as effective collisions. Ineffective collision: The collisions in which molecules collide with improper orientation no products are formed are called as ineffective collisions. For example, formation of methanol from Bromoethane depends upon the orientation of reactant molecules. ‘The proper orientation of reactant molecules lead to bond formation whereas improper orientation makes @acadbilts @acadpills )) @acadpills GD po”them simply bounce back and no products are formed. Diagram showing molecules having proper and improper orientation: - cuipr + OH —> cHoH + Be 26 near Su No. 5, Products jon is proportional to the number of collisions per unit volume per second (collision frequency, Z) between the reacting species. the fraction of effective collisions (properly oriented and possessing sufficient energy), f ivc., Rate =- dw/dt= fx Z ‘Temperature Dependence of the Rate of a Reaction: For the effect of temperature on reaction rates is that the rate of a reaction or rate constant becomes almost doubled for every 10° rise in temperature. Increase in the rate of reaction with the rise in temperature is mainly due to the increase in number of effective collisions. ‘The temperature dependence of the rate of a chemical reaction can be accurately explained by Arrhenius equation. Arrhenius equat and calculation of Activation energy: Ae BIRT Where A is the Arrhenius factor or the frequency factor. It is also called pre-exponential factor. It isa constant specific to a particular reaction, R is gas constant and Ea is activation energy measured in joules/mole (J mol 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. It is equal to the difference between the threshold energy needed for the reaction and the average kinetic energy of all the reacting molecules. That is, Activation energy = Threshold energy - Average kinetic energy of the reacting molecules Ea = Ea (threshold — Ea (reactants) Low Activation energy: Fast reactions High Activation energy: Slow reactions It-can be understood clearly using the following simple reaction: Hb (g) +b (g) ———>2HI (g) Hor Heep Hod J+ ]2b ia oe Holo Heed Hot Intermediate @acadpills & @acadpills GD po”According to Arrhenius, this reaction can take place only when a molecule of hydrogen and a molecule of iodine collide to form an unstable intermediate. The energy required to form this intermediate, called activated complex, is known as activation energy (Ea). keAe Rit ‘Taking logarithm both side Ink=-3r+InA The plot of In k Vs 1/T giv a straight line. Slope =~ Ea /R and intercept = In A. So we can calculate Ea and A using these values. E, Ink= Rr * Ina Converting to common logarith 2.303log k = 2.303log A — Eall log k = log A ~ Ea/2.303 RT Let k1 and k2 are the rate constants for the reaction at two different temperatures Tl and T2 respectively. log ki = log A — Ea/2.303 RT: ...(i) log ko = log A ~Ea/2.303 RT2....(ii) Subtracting eq. (i) from (ii) log ko - log ki = Ew/2.303 R [1/T: — 1/72] k, E, [3 =F | ky * 2303R| TT, InX = 2.303 log X Assignments: QI. Which of the following observations is incorrect about the order of a reaction? (a) Order of a reaction is always a whole number (b) The stoichiometric coefficient of the reactants doesn’t affect the order (©) Order of reaction is the sum of power to express the rate of reaction to the concentration terms of the reactants, (d) Order can only be assessed experimentally Ans. (a) Q2. In the reaction 2A + B — AB, if the concentration of A is doubled and that of B is halved, then the rate of the reaction will (a) decrease 2 times (b) increase 4 times (©) increase 2 times (@) remain the same Ans. (€) Q3. when the rate of the reaction is equal to the rate constant, the order of the reaction is (a) zero order (b) first order (©) second order (@) third onder excons, @D) @acadpills c& @acadpills GD po”Ans. (a) Q4. A substance *A’ decomposes by a first-order reaction starting initially with [A] = 2.00M and after 200min, [A] becomes 0.15M. For this reaction t)2 is (a) 53.72 min (b) 50.49 min (c) 48.45 min (d) 46.45 mii Ans. (a) Q5. A catalyst alters, which of the following in a chemical reaction? (a) Entropy (b) Enthalpy (©) Internal energy (d) Activation energy Ans. (d) (Q6. Express the rate of the following reaction: 5 Br- (aq) + BrOx (ag) + 6 H* (aq) > 3 Bro (aq) + 3 FO (1) Q7. For the reaction R-—>P, the concentration of a reactant changes from 0.03M to 0.02M in 25 minutes. Calculate the average rate of reaction using units of time both in minutes and seconds. Ans. Average rate = 4x 10% mol L"' min Rate = 6.67 x 10° mol Ls Q8. Calculate the overall order of a reaction which has the rate expression: (a) Rate = k [A}!2 [B}>? (b) Rat fay? (Br Ans. (a) Second order (b) half order. Q9. Identify the reaction order from each of the following rate constants. (@ k= 2.3 x 105 Lmor! s+ Gi) k=3 x 10454 Ans. (i) Second order reaction i) first order reaction. Q10. For a reaction, A + B ——>Produet; the rate law is given by, r= k [A]! [BP. Whaat is the order of the reaction? Ans. Order = 2.5 QI1. The initial concentration of N2Os in the following first order reaction N20s(g) —> 2. NO> (g) + 1/202 (g) was 1.24 x 10” mol L* at 318 K. The concentration of NoOs after 60 minutes was 0.20 x 10? mol L. Calculate the rate constant of the reaction at 318 K. Answer: 0.0304 min"! excons, @D) @acadpills c& @acadpills GD po”QI2. Show that in a first order reaction, time required for completion of 99.9% is 10 times of half-life (12) of the reaction, 1=6.909/k For half-life of the reaction tia = 0.693/k Viir=10 QI3. The rate constant for a first order reaction is 60 s'. How much time will it take to reduce the initial concentration of the reactant to its 1/16" value? Ans, t= 2.303/k (log(Alo/[A]} 2.303/60 (log (a/a/16)} 0.038 logl6 0.038 x 1.204 0.046 seconds QI4. A first order reaction takes 40 min for 30% decomposition, Calculate ti Ans. k = 2.303/t {log(Alo/TA]} 2.303/40 {log (a/0.70a)} = 2.303/40 {0.1549} k=8.92 x 107 mint .693/k 0.693/8.92 x 10° min" 77.7 min, oy he QIS. The rate of the chemical reaction doubles for an increase of 10K in absolute temperature from 298K. Calculate E: Ans, log ko - log ki = Ea/2.303 R [1/T1 ~ 1/Ta} logka/ky = Ea/2.303 R [1/T; — 1/T2} log? = (Ba/2.303 x 8.314) [1/298 — 1/308} Ea = log? x 2.303 x 8.314 x 298 x 308 10 Ba= 52.898 kb @acadpilts excons, @D)