KINETICS TAKE HOME EXAM (DEADLINE January 1,2018) (graphical solutions) 1. The rate of decomposition of dimethyl ether (CH3OCH3) in the gas phase has been determined by Hinshelwood and Askey(1927) by measuring the increase in pressure ( P) accompanying decomposition in a constant-volume batch reactor at a given temperature. The reaction is complicate somewhat by the appearance of formaldehyde as an intermedi ate product at the conditions studied, but we assume here that the reaction goes to completi on according to 3 3 → 4 + 2 + , or A M+H+C. in one experiment at 504C, in which the initial pressure (Po = pao, pure ether being present initially) was 41.6 kPa, the f ollowing values of P were obtained: t/s t/s P = (Ptotal-pao) / kPa P = (Ptotal-pao) / kPa 0 0 1195 33.3 207 7.5 1587 41.6 390 12.8 2240 53.6 481 15.5 2660 58.3 665 20.8 3155 62.3 777 23.5 82.5 916 26.7 Test the reaction if it is zero, first-order, and second-order reaction. Show initial calculations and show complete tabulations for graphs like Ptotal, Pa,Ln Pa, 1/Pa etc. 2. Ethyl acetate reacts with sodium hydroxide in aqueous solution to produce sodium acetate and ethyl alcohol: CH3COOC2H5(A) + NaOH→ CH3COONa + C2H5OH. This saponifi cation reaction can be followed by withdrawing samples from a Batch reactor at various times, adding excess standard acid to quench the reaction by neutralizing the unreacted hydroxide, and titrating the excess acid with base. In a particular experiment at 16C, samples of 100 cm3 were withdrawn at various times; the concentration of acid used (HCl) was 0.0416 moles/liter. The following results were obtained (Vt is the volume of acid solution requi red to neutralize unreacted NaOH at time t) (glassto ne, 1946, p. 1058) t/s 0 224 377 629 816 Vt/cm3 62.09 54.33 50.60 46.28 43.87 33.06 Using this information, obtain the rate law for the reaction. Test the reaction if it is zero, first- order, and secondorder reaction. Show initial calculations and show complete tabulations for graphs. 3. The rate of decomposition of nitrogen peroxide (N2O5) in the inert solvent CCl4 can be foll owed by measuring the volume of oxygen evolved at a give n temperature and pressure, since the unreacted N2O5 and the other products of decomposition remain in solution. Some results at 45C from a BR are as follows (Eyring and Daniels, 1930): t/s 162 409 1721 3400 O2 evolved/ cm3 3.41 7.78 23.00 29.33 32.60 What is the order of the decomposition of nitrogen pentoxide (N2O5N2O4+1/2 O2)? Assume the reaction goes to completion. 4. The hydrolysis of ethyl nitrobenzoate by hydroxyl ions NO2C6H4COOC2H5 + OH- NO2C6H4COO- + C2H5OH proceeds as follows at 15C when the initial concentration of both reactants are 0.05m/L (constant-volume batch reactor): t/s 120 180 240 330 530 600 % hydrolyzed
32.95
41.75
48.80
58.05
69.0
70.4
Use (a) the differential method and (b) the integral method to determine the reaction order and the value of the rate constant. For the differential method, you have to get the value of (-ra or -dCa/dt) and plot it against the average concentration between intervals. For letter (b) , you have to plot when n=0, n=1, and n=2. 5. A reaction → + i s carried out in a batch reactor (costant volume). The expe riment was started with several i nitial concentrations and when half of the concentration was reached, the corresponding time was measured. The following table gives the values for two different temperatures. Determine the o rder of the reaction, the specifi c rate constant, and the activation energy.
