UNIVERSITY OF MALTA DEPARTMENT OF CHEMISTRY. CH237  Chemical Thermodynamics and Kinetics. Tutorial Sheet VIII


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1 UNIVERSITY OF MALTA DEPARTMENT OF CHEMISTRY CH237  Chemicl Thermodynmics nd Kinetics Tutoril Sheet VIII 1 () (i) The rte of the rection A + 2B 3C + D ws reported s 1.0 mol L 1 s 1. Stte the rtes of formtion nd consumption of the prticipnts. (ii) The rte of formtion of C in the rection 2A+B > 2C+3D is 1.0 mol L 1 s 1. Stte the rection rte, nd the rtes of formtion or consumption of A, B, nd D. (iii) The rte lw for the rection in (i) ws found to be v = k[a][b]. Wht re the units of k? Express the rte lw in terms of the rtes of formtion nd consumption of: () A, (b) C. (iv) The rte lw for the rection in (ii) ws reported s d[c]/ = k[a][b][c]. () Express the rte lw in terms of the rection rte. (b) Wht re the units for k in ech cse? (b) (i) At 518 C, the rte of decomposition of smple of gseous cetldehyde (ethnl), initilly t pressure of 363 Torr, ws 1.07 Torr s 1 when 5.0 per cent hd rected nd 0.76 Torr s 1 when 20.0% hd rected. Determine the order of the rection. (ii) Repet the clcultion if you where told tht t the sme temperture, the hlflife for the this rection initilly t 363 Torr ws 410 s whilst when the pressure ws 169 Torr, the hlflife ws 880 s. (c) The rte constnt for the firstorder decomposition of N 2 O 5 in the rection 2N 2 O 5 (g) > 4NO 2 (g) + O 2 (g) is k = 3.38 x 105 s 1 t 25 C. Wht is the hlflife of N 2 O 5? Wht will be the pressure, initilly 500 Torr, () 10s, (b) 10 min fter initition of the rection? (d) A secondorder rection of the type A + B P ws crried out in solution tht ws initilly mol L 1 in A mol L 1 in B. After 1.0 h the concentrtion of A hd fllen to mol L 1. () Clculte the rte constnt. (b) Wht is the hlf life of the rectnts? (e) The secondorder rte constnt for the rection: CH 3 COOC 2 H 5 (q) + OH  (q) CH 3 COO  (q) + CH 3 CH 2 OH(q) is 0.11 L mol 1 s 1. Wht is the concentrtion of ester fter () 10s, (b) 10 min tht the ethyl cette is dded to sodium hydroxide given tht the initil concentrtions re [NOH] = M nd [CH 3 COOC 2 H 5 ] = moll 1? (f) (i) A rection 2A P hs secondorder rte lw with k = 3.05 x 10 4 L mol 1 s 1. Clculte Pge 1
2 the time required for the concentrtion of A to chnge from mol L 1 to mol L 1. (ii) A rection 2A P hs thirdorder rte lw with k = 3.05 x 10 4 L 2 mol 2 s 2. Clculte the time required for the concentrtion of A to chnge from mol L 1 to mol L 1. (g) The rte constnt for the decomposition of two different substnces re: () 2.80 x 103 L mol 1 s 1 t 30 C nd 1.38 x 102 L mol 1 s 1 t 50 C, nd (b) 1.70 x 102 L mol 1 s 1 t 24 o C nd 2.01 L mol 1 s 1 t 37 o C. Evlute the Arrhenius prmeters for these rections. (h) The rection mechnism A 2! 2A (fst) A + B P (slow) involves n intermedite A. Deduce the rte lw for the rection. (g) Consider the following mechnism for renturtion of double helix from its strnds A nd B: A + B!"unstble helix (fst) unstble helix stble double helix (slow) Derive the rte eqution for the formtion of the double helix nd express the rte constnt of the renturtion rection in terms of the rte constnts of the individul steps. (h) (i) (j) The equilibrium A!B is firstorder in both directions. Derive n expression for the concentrtion of A s function of time when the initil molr concentrtions of A nd B re [A] 0 nd [B] 0. Wht is the finl composition of the system? Derive n integrted expression for secondorder rte lw v = k[a][b] for rection of stoichiometry 2A + 3B P. Derive the integrted form of thirdorder rte lw v = k[a] 2 [B] in which the stoichiometry is 2A + B P nd the rectnts re initilly present in () their stoichiometric proportions, (b) with B present initilly in twice the mount. (k) (i) Set up the rte equtions for the rection mechnism: A k B kb #!!!!!!" #!!!!!!" C b (ii) Show tht the mechnism in (i) is equivlent to: k eff A#!!!!!!" C" k ' eff under specil circumstnces. (l) Derive n eqution for the stedystte rte of the sequence of rections A!B!C!D, with [A] mintined t fixed vlue nd the product D removed s soon s it is formed. Pge 2
3 (m) For the consecutive rection A I P, the figure below shows [I] plotted ginst time for k =10k b. For [A] 0 = 1.0 moll 1 nd k = 1.0 min 1, plot [I] ginst t for k /k b = 5, 1, nd 0.5. For ech cse determine the time t which [I] reches mximum. 2. () (i) Prove tht the rte of product P formtion for n enzymectlyzed rection proceeding through the MichelisMenten mechnism: S + E!" ES E + P k S + E ES SE S + E k b SE P is given by: d[p] = k[ E] 0 E nd S represent the enzyme nd substrte respectively, [E] 0 is the initil concentrtion of the enzyme, nd: Pge 3
4 kb[s] k = K M + [S] where K M is the Michelis constnt, given by: k + kb K M = ' k (ii) Show tht if rection follows the MichelisMenten mechnism, then there is liner reltionship between 1/k nd 1/[S] (xxis) with grdient of K M / k b nd intercept of 1/k b. Wht do we cll this plot? (iii) Obtin n expression the rte of formtion of product nd find its limiting behviour for lrge nd smll concentrtions of substrte for the MichelisMenten mechnism. (iv) The enzymectlysed conversion of substrte t 25 C hs Michelis constnt of mol L 1. The rte of the rection is 1.15 x 103 mol L 1 s 1 when the substrte concentrtion is mol L 1. Wht is the mximum velocity of this enzymolysis? (v) The enzymectlysed conversion of substrte t 25 C hs Michelis constnt of mol L 1.The rte of the rection is 2.45 x 104 mol L 1 s 1 when the substrte concentrtion is mol L 1. Wht is the mximum velocity of this enzymolysis? (vi) Mny enzymectlysed rections re consistent with modified version of the MichelisMenten mechnism in which the second step (i.e. ES E + P) is lso reversible. For this mechnism obtin n expression the rte of formtion of product nd find its limiting behviour for lrge nd smll concentrtions of substrte. (b) Rections such s the isomeristion of cyclopropne (rectnt, A) to propene (product, P) proceeds ccording to the LindemnnHinshelwood (LH) mechnism cn. According to this mechnism, the rection tkes off by hving molecule A getting energeticlly through collision with nother A molecule: d[ A ] A + A A + A = k A (1) [ ] 2 The energized molecule A might loose is excess energy either by: (1) Collision with nother A molecule (forming no products), i.e.: d[ A ] A + A A + A = A A (2) [ ][ ] (2) Shking itself prt forming the product (the unimoleculr step), i.e.: d[ A ] d[ P] A P = kb[ A ] = (3) Show tht under different sets of conditions, the rte of product formtion cn be either first order in [A] or second order in [A], or more specificlly tht: Pge 4
5 kkb d[p] kobs = high [A] = kobs[ A ] where kobs = k[a] low [A] Show lso how this switch in the rte cn be demonstrted by plot log k obs vs. log [A]. (ii) The effective rte constnt for gseous rection which hs LindemnnHinshelwood mechnism is 2.50 x 104 s l t 1.30 kp nd 2.10x l05 s 1 t 12 P. Clculte the rte constnt for the ctivtion step in the mechnism. (iii) Cyclopropne isomerizes into propene when heted to 500 o C in the gs phse. The extent of conversion for vrious initil pressures hs been followed by gs chromtogrphy by llowing the rection to proceed for time with vrious initil pressures: p o /Torr t /s p /Torr where p o is the initil pressure nd p is the finl pressure of cyclopropne. Wht re the order nd rte constnt for the rection under these conditions? Pge 5
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