2005年第37屆IChO預備試題答案（英文）理論19-27實驗30

101 Answer 19 Works in Thermodynamics 19 1 Isothermal reversible expansion We have 100 22 41 4 461 moles and the final volume is l100 1 1010 V 2 11 2 P VP 1 The work done by gas is joules V V nRTqw 23290 10ln2 273341 8461 4 ln 1 2 2 19 2 Adiabatic reversible expansion Notice that 3 5 2 3 C R RR CV P 3 Thus l8 39 10 10 5 3 1 2 1 2 1 2 V P P V 4 and the final temperature is obtained from K nR VP T o 8 108 08205 0461 4 81 391 22 2 5 For adiabatic processes 0 q and wwqE ie joulesTvCnEw9141 6 19 3 Irreversible adiabatic expansion Since q 0 we have 12 TTCnwE v 7 102 122 VVPw 8 and 10 2 273 1 2 273 2 3 2 2 nRnRT TnR 9 It follows that KT o 8 174 2 10 and joules nRwE 5474 2 2738 174 2 3 11 Answer 20 Kinetics Atmosphere Chemistry 20 1 kt PP kP dt dP NONO NO NO 0 2 22 2 2 11 where 0 2 NO P devotes the initial pressure of NO2 20 2 At 2 1 tt 0 22 2 1 NONO PP or tP k NO2 1 0 2 1 422 0 760 600 3 1 k l atm min Answer 21 Kinetics and Thermodynamics 21 1 In the beginning 4 min of the reaction 103 1 2 1 divided by 2 gives 21 2 When the reaction is complete the system reaches thermal equilibrium 21 3 A C thermodynamic controlled reaction process is favored when temperature increases The system will reach thermal equilibrium more rapidly Answer 22 Phase Diagram 22 1 A solid B solid liquid and gas states coexist C liquid and gas states coexist 22 2 The negative slope of the solid liquid line indicates the liquid state of water is denser than its solid state Therefore ice may not sink in its own liquid 22 3 Clapeyron equation is expressed as VT H dT dP where H is molar enthalpy of water and V is volume change The phase diagram shows that the slope of dP dT for the liquid solid coexistence region is negative indicating the volume expands when water freezes 22 4 As pressure is lowered liquid phase transforms directly to gas phase at the same temperature Thus water may vaporize At the same time the process of water evaporation is endothermic as to make the surrounding cooled The left water becomes frozen The solid state will sublime until none is left if the pump is left on 22 5 The ice surface exerted by a pressure more than one atm turns to liquid state at 0 oC 1 Ak dt Bd 2 Ak dt Cd 2 1 k k Cd Bd 10 1 0 1 2 1 k k C B 1 1 k k A B 2 2 k k A C 2 1 200 100 0005 01 0 01 01 22 11 kk kk C B 104 Answer 23 Standard Deviation in One Dimensional Quantum Mechanics 23 1 average speed 0 dvvvF dvv RT Mv RT M 3 2 0 2 3 2 exp 2 4 M RT 8 032 014 3 30031 88 x xx 4 45 x 10 2 ms 1 standard deviation v 0 dvvvF dvv RT Mv RT M 4 2 0 2 3 2 exp 2 4 032 0 30031 833xx M RT 2 33 x 10 5 m2s 2 v 22 vv 225 1045 4 1033 2xx 1 87 x 10 2 ms 1 23 2 average position dxx dx x x 2 exp 2 1 2 0 standard deviation x dxx 2 dx x x 2 exp 2 1 2 2 1 x 22 xx 1 23 3 dx x h i 2 dx ihxe x 24 2 2 0 dx x h 4 22 22 2 2 16 h p 4 22 h pp 23 4 x p 4 h 105 Answer 24 A Particle in 2 D Box Quantum Mechanics 24 1 E1 1 2E0 E1 2 E2 1 5E0 E2 2 8E0 E1 3 E3 1 10E0 E2 3 E3 2 13E0 E1 4 E4 1 17E0 E3 3 18E0 E2 4 E4 2 20E0 E3 4 E4 3 25E0 E1 5 E5 1 26E0 where E0 h 2 8 mL2 24 2 The total number of electrons in the highest occupied energy level is 4 24 3 Ground state is diamagnetic 24 4 The longest wavelength excitation energy is E 25 20 E0 where E0 6 63 10 34 Js 2 8 9 11 10 31 kg 1 10 9 m 2 6 02 10 20 J 1 E 25 20 E0 3 01 10 19 J 2 The wavelength is hc E 6 63 10 34 Js 3 108 3 01 10 19 660 nm 3 Answer 25 Spectrum Analysis 25 1 355 00 2 sin60 00 204 96 DFDL 2 1 40 204 96 573 89 nm Answer 26 Time of Flight Mass Spectrometer 26 1 a 2 1 1 6022 10 19 C 20000 V 12362 1 6605 10 27 kg 17669 5 m s 26 2 c t 1 00 m 17669 5 m s 56 59 s 106 Answer 27 Enzyme Catalysis 27 1 A bC C A b mol C x V volume 0 1 27 7 9 2 x 10 3 x 5 x 10 3 2 7 x 10 8 mol sec 27 2 Four electrons are needed to reduce one molecule of oxygen therefore the oxygen consuming rate is 2 7 x 10 8 4 6 75 x 10 9 mol sec 27 3 By definition the turnover number equals 6 75 x 10 9 mol sec 2 7 x 10 9 M x 5 x 10 3 L Therefore oxidase has a turnover number of 500 Practical Problems Answer 30 Identification of Unknown Solutions II 1 Use the indicator to find out NaOH HCl and H2SO4 confirmed by Pb2 2 Find out the Na2S by the odor and use it to find Cd2 and Zn2 by precipitation and color 3 By electrolysis of the f