Chemical Kinetics and Nuclear Chemistry Exercise # 4

CHEMICAL KINETICS AND NUCLEAR CHEMISTRY Exercise # 4 1. [Subjective Type Questions] Decomposition of H2O2 is a first order reaction. A solution of H2O2 labelled as 20 volumes was left open. Due to this, some H2O2 decomposed. To determine the new volume strength after 6 hours, 10 mL of this solution was diluted to 100 mL. 10 mL of this diluted solution was titrated against 25 mL of 0.025M KMnO4 solution under acidic conditions. Calculate the rate constant for decomposition of H2O2. [ln 20 = 0.1335] 17.5 2. A quantity of ethyl acetate is mixed with an excess of sodium hydroxide at 25ºC. 100 c.c. of the mixture is immediately titrated against 0.05 N Hydrochloric acid, of which 75 c.c. were required for neutralisation. After 30 minutes, 50 c.c. of the mixture required, similarly, 25 c.c. of the acid. When the original reaction of ester was complete 25 c.c. of the mixture required 6.25 c.c. of the acid. Calculate the second order velocity constant (at time = 0) of the reaction, using concentration in moles per litre and time in minutes. Reaction is first order each w.r.t. NaOH & ester. Indicator chosen for above titration is such that, it gives end point when hydrochloric acid reacts with NaOH only. (log2 = 0.30, log3 = 0.48, ln10 = 2.3) 3. A certain reactant Bn+ is getting converted to B(n+4)+ in solution. The rate constant of this reaction is measured by titrating a volume of the solution with a reducing reagent which only reacts with B n+ and B(n+4)+. In this process, it converts Bn+ to B(n2)+ and B(n+4)+ to B(n1)+. At t=0, the volume of the reagent consumed is 25 ml and at t = 10 min, the volume used up is 32 ml. Calculate the rate constant of the conversion of B n+ to B(n+4)+ assuming it to be a first order reaction. 4. Decomposition of ammonia on platinum surface follow the change, 2NH3 (g)  N2 (g) + 3H2 (g) (a) What does –d [NH3 ] denote ? dt d [N 2 ] d [H 2 ] and denote? dt dt (c) If the decomposition is zero order then what are the rate of production of N2 and H2 if k = 2.5 × 10–4 Ms–1? (b) What does k1 [NH 3 ] d [NH 3 ] = 1+ k [NH ] , what will be the order for decomposition of NH3 if (i) [NH3] is very dt 2 3 very less and (ii) [NH3] is very very high K1 and K2 are constant. (d) If the rate obeys – 5. A 1mL sample of a bacterial culture at 370C is taken, and diluted to 10 L. A 1mL sample of the diluted culture is spread on a culture plate. Ten minutes later, another 1mL sample taken from the original culture diluted and spread in the same way. The two plates are incubated for 24 hours. The first sample exhibits 48 colonies of bacteria, the second 72 colonies. If we assume that each colony originates with a single bacterium, what is the generation time (time required for doubling the population). 6. The acid catalysed hydrolysis of an organic compound A at 300C has a time for half change of 100 minutes, when carried out in a buffer solution at pH 5 and of 10 minutes, when carried out at pH 4. Both times of halfchange are independent of the initial concentration of A. If the rate of reaction is given by values of a and b? 7. d[ A ] = k[A]a[H+]b, what are the dt An organic compound A decomposes by following two parallel first order mechanisms: k1 1 –5 –1 k 2 = 9 and k1 = 1.3 × 10 sec . Calculate the concentration ratio of C to A, if an experiment is allowed to start with only A for one hour. 8. The formation in water of dpotassium chromooxalate from its lform is reversible reaction which is first order in both directions, the racemate being the equilibrium product. A polarimeter experiment at 220C showed that, after 506 sec, 12 mole % of the lisomer was converted to the dform. Find the rate constant for the forward and the reverse reactions. 9. For an isomerisation reaction A B in gaseous phase, the equilibrium constant at 60°C is 3.60. Both forward and backward reactions are of first order. Starting with an initial pressure of P atm, of A, the pressure became 0.25 P atm in 40 minutes. Find the values of individual rate constants for the forward and backward reactions. 10. Experiment shows that the equilibrium constant of the reaction : C2H5OH + CH3COOH CH3COOC2H5 + H2O is 2.8 at room temperature, and the velocity constant of the forward reaction is 0.002. When a catalyst is added this velocity constant is increased to 0.0045. What is now the velocity constant of the backward reaction? 11. A 1st order chemical reaction was carried out for 1.0 hour in absence of a catalyst and 20% reaction was complete. A catalyst was then added and reaction was allowed to continue for next 30 min when 60% reaction was complete. A second catalyst was then added at this time and reaction was allowed to continue for further 10 min. when 90% reaction was complete. If activation energy of the original path was 80 kJ, determine activation energies of catalyzed pathways. Assume constant temperature throughout to be 300 K. 12. Derive an expression for the velocity of reaction : 2N2O5(g)  4NO2(g) + O2(g) catalyst With the help of following mechanism N 2O 5 K a NO2 + NO3 NO2 + NO3 Kb NO2 + O2 + NO ; NO3 + NO2 ; NO + NO3 K a Kc N2O5 2NO2 13. Mole percentage of A as a function of time in the following reversible first order reaction A Time (hr) 0 1 Infinity Mole % of A 100 75 30 Determine mole percentage of A after four hour from the beginning. B are : 14. The mean life of a first order reaction at 610 K is 127 hours. What fraction of the initial concentration will decompose in 42 hours at 600 K, given that the activation energy is 30 Kcal mol–1 ? 15. Two reaction (i) A  products (ii) B  products, follow first order kinetics. The rate of the reaction (i) is doubled when the temperature is raised from 300 K to 310K. The half life for this reaction at 310K is 30 minutes. At temperature 310 K, B decomposes twice as fast as A. If the energy of activation for the reaction (ii) is half that of reaction (i), calculate the rate constant of the reaction (ii) at 300K. 16. Derive an expression for the velocity of reaction : H2 (g) + Br2 (g)  2HBr (g) With the help of following mechanism k1 Br2 H + Br2 17. 84Po 210 2Br k3 ; HBr + Br ; Br + H2 H + HBr k2 k4 HBr + H H2 ; Br + Br k5 Br2 decays with alpha to 82Pb206 with half life of 138.4 days. If 1.0 gram of Po210 is placed in a sealed tube, how much helium will accumulate in 69.2 days? Express the answer in cm3 at S.T.P. 18. The energy of activation for a reaction is 100 kJ mol–1. Presence of a catalyst lowers the energy of activation by 75%. What will be effect on rate of reaction at 20°C ; other things being equal ? CHEMICAL KINETICS AND NUCLEAR CHEMISTRY 19. A follows parallel path  order reactions giving B and C as : If initial concentration of A is 0.25 M calculate the concentration of C after 5 hrs. of reaction Given : 1 = 1.5 x 10–5 sec–1 ; 2 = 5 x 10–6 sec–1 20. Two reactants A and B separately shows two chemical reactions. Both reactions are made with same initial concentration of each reactant. Reactant A follows first order kinetics whereas reactant B follows second order kinetics. If both have same half lives, compare their rates (a) at the start of reaction (b) after the lapse of one half life. 21. Figure represents the variation of the concentrations of A and B with time for the reaction : A  nB. Calculate the concentration of B at the point of intersection O. A0 B O A Time 22. The net rate of reaction for the change : [Cu(NH3)4]2+ + H2O [Cu(NH3)3H2O]2+ + NH3 is, dx = 2.0 x 10–4 [Cu(NH3)4]2+ – 3.0 x 105 [Cu(NH3)3H2O]2+[NH3] dt Calculate : (i) rate expression for forward and backward reaction. (ii) the ratio of rate constants for forward and backward reaction. (iii) the direction of reaction in which the above reaction will be more predominant. 23. The catalytic decomposition of formic acid may take place in two ways : (i) HCOOH(g)  H2O(g) + CO(g) (ii) HCOOH(g)  H2(g) + CO2(g) The rate constant and activation energy for reaction (i) are 2.79 x 10–3 min–1 at 237°C and 12.0 kcal mol–1 respectively. These values for reaction (ii) are 1.52 x 10–4 min–1 at 237°C and 24.5 kcal mol–1 respectively. Find out the temperature at which equimolar quantities of H2O, CO, CO2 and H2 are formed. (R = 2 cal) ? 24. The progress of the reaction, A nB with time is presented in the figure. Determine : conc./mol litre-1 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 (i) the value of n B A 1 2 3 4 5 6 7 8 (ii) the equilibrium constant K and (iii) the initial rate of conversion of A. –d[A] = k [A] [OH–]. If initial concentrations dt of [A] and [OH¯] are 0.002 M and 0.3 M respectively and if it takes 30 sec for 1% A to react at 25°C, calculate the rate constant for the reaction. 25. The reaction, A + OH¯  Products, obeys rate law expression as, 26. Catalytic decomposition of nitrous oxide by gold at 900°C at an initial pressure of 200 mm was 50% in 53 minute and 73% in 100 minute. (a) What is order of reaction ? (b) Calculate velocity constant. (c) How much will it decompose in 100 minutes at the same temperature but at an initial pressure of 600 mm ? 27. The gas phase decomposition of dimethyl ether follows first order kinetics, CH3OCH3(g)  CH4(g) + H2(g) + CO(g) The reaction is carried out in a constant volume container at 500°C and has a half life of 14.5 minute. Initially only dimethyl ether is present at a pressure of 0.40 atmosphre. What is the total pressure of the system after 12 minute ? Assume ideal gas behaviour. The half time of first order decomposition of nitramide is 2.1 hour at 15°C. NH2NO2(aq)  N2O(g) + H2O(). If 6.2 g of NH2NO2 is allowed to decompose, calculate : (i) time taken for NH2NO2 to decomposition 99% (ii) volume of dry N2O produced at this point measured at STP. 28. 29. The reaction : CH3COF + H2O  CH3COOH + HF has been studied under the following initial conditions : Case-I Case-II CH 2O  1.00 M CH 2O  0.02 M C CH3COF  0.01 M C CH3COF  0.80 M Concentrations were monitored as a function of time and are given below : Case-I Case-II t/min CCH3COF /M t/min CH2O /M 0 0.01000 0 0.0200 10 0.00857 10 0.0176 20 0.00735 20 0.0156 40 0.00540 40 0.0122 Determine the order of the reaction and the rate constant for the reaction. 30. Show that for a first order reaction, time required for 99.0% completion is twice for the time required for the completion of 90% of the reaction. 31. At 100°C, a gaseous reaction, A  B + 2C, is observed to be of  order. On starting with pure A, at the end of 14 minute, the total pressure was found to be 264 mm of Hg. After a long time the total pressure of the system was 450 mm of Hg. Calculate (a) initial pressure of A (b) rate constant of reaction (c) half life period of reaction. 32. The conversion of trypsinogen (A) and trypsin (B) is an autocatalytic reaction, A  B, where B catalyses the reaction. The rate equation is dx = K . x . y, where x and y are concentration of tripsinogen at time t. Integrate this dt 2.303 y . x0 equation for initial concentration of x0 and y0 for A and B. Show that, Kt = x  y log x . y . 0 0 0 CHEMICAL KINETICS AND NUCLEAR CHEMISTRY 33. The rate constant for the II order neutralization of 2-nitropropane by aqueous alkali obeys the equation log10 K = 3163 + 12 T T is temperature in Kelvin. Time and concentration were in minute and mol litre–1 respectively. Calculate half life at 43.3°C and for an initial concentration of 0.001 mol litre–1 for each of the reactant. 34. In the decomposition of H2O2 at 300 K, the energy of activation was found to be 18 kcal/mol while it decreases to 6 kcal/mol when the decomposition was carried out in the presence of a catalyst at 300 K. How many times is the catalysed reaction faster than uncatalysed one ? 35. The rate of decomposition of a substance increases by a factor 2.25 for 1.5 times increase in concentration of substance at same temperature. Find out order of reaction. 36. A substance A is mixed with equal quantities of the substance B and C. At the end of 1000 second, half of the amount of A has reacted. What fraction of A will be left unreacted at the end of 2000 second. If the reaction is (a) zero order with respect to A ? (b) II order with respect to A ? 37. Acetone on heating gives CO and other hydrocarbons at 600°C. The reaction obeys Ist order kinetics with respect to acetone concentration. The half life period is 81 sec. Calculate the time in which acetone taken in a container at 600° reduces its pressure from 0.5 atm to 0.4 atm. The specific rate constant of the decomposition of N2O5 is 0.008 min–1. The volume of O2 collected after 20 minute is 16 mL. Find the volume that would be collected at the end of reaction. NO2 formed is dissolved in CCl4. 38. 39. For a homogenous gaseous reaction, A  B + C + D, the initial pressure was P0 while pressure after time t was P. Derive an expression for rate constant K in terms of P0 and t. 40. In a II order reaction, when the concentration of both the reactants are equal, the reaction is completed 20% in 500 sec. How long it would take for the reaction to go to 60% completion ? 41. Half-life period for decomposition of NH3 over tungsten wire are given below : Initial Pressure in min 50 100 200 T1/2 3.52 1.82 0.93 Calculate order of reaction. 42. A flask contains a mixture of compounds A and B. Both compounds decompose by first-order kinetics. The halflives are 54.0 min for A and 18.0 min for B. If the concentrations of A and B are equal initially, how long will it take for the concentration of A to be four times that of B ? 43. Compounds A and B react to form C and D in a reaction that was found to be second-order overall and second-order in A. The rate constant at 30°C is 0.622 L mol –1 min –1 . What is the half-life of A when 4.10 × 10–2 M of A is mixed with excess B ? 44. Acetoacetic acid, CH3COCH2COOH, in acid solution decomposes to CO2 and acetone by a firstorder reaction. From the following data find the halflife time for this reaction at 370C. A solution containing 6 mmol sodium acetoacetate was rapidly brought into about 0.2M HCl so that the total volume was 200ml. After 220 min. at 370C, a sample of 10 ml was taken out and immediately put into an excess of NaOH, which put an end to the decomposition. The acetone that had formed was blown away by bubbling air. The sample was again acidified and boiled; all the remaining acetoacetic acid was then transformed to acetone, which was distilled with water vapour. To this distillate, NaOH and 10.00 ml 50 mM I2 solution were added, transforming all acetone to iodoform CH3COCH3 + 3I2 + 4OH  CHI3 + CH3COO + 3I + 3H2O After acidification the remaining iodine was decolorize by 4.5 ml thiosulfate solution. Ten ml 50 mM I2 solution was decolourized by 10 ml of the same thiosulfate solution. At pH = 0 to 3 the reaction rate is independent of pH. 45. A 22.4 litre flask contains 0.76 mm of ozone at 25°C. Calculate : (i) the concentration of oxygen atom needed so that the reaction, O + O3  2O2 having rate constant equal to 1.5 x 107 litre mol–1 sec–1 can proceed with a rate of 0.15 mol litre–1 sec–1. (ii) the rate of formation of oxygen under this condition. 46. A vessel contains dimethyl ether at a pressure of 0.4 mm. Dimethyl ether decomposes as : CH3OCH3(g)  CH4(g) + CO(g) + H2(g). The rate constant of decomposition is 4.78 x 10–3 min–1. Calculate the ratio of initial rate of diffusion to rate of diffusion after 4.5 hours of initiation of decomposition. Assume the composition of gas present and gas diffused to be same. 47. A certain reaction A + B  Product is first-order w.r.t. each reactant with k = 5.0 × 10–3 M–1 s–1. Calculate the concentration of A remaining after 100 s if the initial concentration of A was 0.1 M and that of B was 6.0 M. State any approximation made in obtaining your result.