課程名稱︰普通化學甲下 課程性質︰必帶 課程教師︰金必耀 開課學院：理學院 開課系所︰物理系 考試日期（年月日）︰100/4/20 考試時限（分鐘）：130 mins 是否需發放獎勵金：是 （如未明確表示，則不予發放） ======================================================= Dear all, You can bring an A4 to the test. Write anything you want. Besides, this is not an open-book exam. The related thermodynamic data would attached in the exam. TA ======================================================== 試題 : General Chemistry A 2011/04/20 Wed Midterm Exam 109 pts , 3 pages 1.(5pts) The vibrational frequency of the ICl molecule is 1.15*10^13s^(-1). For every million molecules in the ground vibrational state,jow many will be in the first excitef vibrational state at a temperature of 300K ? 2.(5pts) A 200-cm^3 vessel contains hydrogen gas at a temperature of 25°C and a pressure of 0.990 atm.The vessel has a tiny hole in its wall,and over a period of 3 hours,the pressure drops to 0.984 atm.What os the radius of the hole(assu,ed to be circular)? (H=1.008 amu) 3.(10pts) At what pressure does the mean free path of krypton(Kr=83.798) atoms (d=3.16*10^-10m) become comparable with the diameter of the 1-L spherical vessel that contains them at 300K? Calculate the diffusion constant,D,at this pressure. D = (3/8)*(RT/πM)^0.5 *(d^2 * N/V)^-1 4.(5pts) The later halogens from pentafluorides: ClF5 , BrF5,and IF5. At 0°C,one of these is a solid,one a liquid,and one a gas.Specify which is which,and explain your resoning. 5.Suppose 2.00 mol of an ideal,monatomic gas is initial at a pressure of 3.00 atm and a temperature T=350 K.It is expanded irreversibly and adiabatically against a constant wxternal pressure of 1.00 atm until the volume has doubled. (a)(2pts)Calculate the final volume. (b)(2pts)Calculate w,q,and ΔU for this process,in Joules. (c)(2pts)Calculate the final temperature of the gas. (d)(3pts)Calculate ΔS for the system,the surrounding,and the universe. (e)(3pts)If the absolute entropy per mole of thw gas before the wxpansion is 158.2 JK^-1mol^-1,calculate ΔGsys for the process. 6.(10pts) Ethanol's enthaipy of vaporization is 38.7 kJmol^-1 at its normal boiling point,78°C.Calculate q,w,ΔU,and ΔG when 1.00 mol ethanol is vaporized reversibly at 78°C and 1 atm.Assume that the vapor is an ideal gas and neglect the vilume of liquid ethanol relative to that of its vapor. 7.(5pts) The primarymedium for free energy storage in living cells is adenosine triphosphate(ATP).Its formation from adenosine diphosphate(ADP) is not spontaneous: 3- 2- + 4- ADP(aq) + HPO4(aq) + H(aq) → ATP(aq) + H2O(l) ΔG=+34.5 kJ Cell couple ATP production with the metabolism of glucose(a sugar): C6H12O6(aq) + 6O2(g) → 6CO2(g) + 6H2O(l) ΔG= -2872 kJ The reaction of 1 molecule of glucose leads to the formation of 38 molecules of ATP from ADP.Show how the coupling makes this reaction spontaneous.What fraction of the free energy released in the oxidation of glucose is stored in the ATP? 8.The N2O molecule has the stucture N-N-O.In an ordered crystal of N2O,the molecules are lined up in a regular fashion,with the orientation of each determined by its position in the crystal.In a random crystal,each molecules has two equally likely orientations. (a)(2pts) Calculate the number od microstates available to a random crystal of NA(Avogagro's number) of molecules. (b)(3pts) Calculate the entropy change when 1.00 mole of a random crystal is converted to an ordered crystal. 9.(10pts) Estimate the temperature at which I2(g) and I2(s) are in equilibrium at a pressure of 1atm.Can this equilibrium actually be achieved?The melting point and the boiling point of I2 are 113.5°C and 184.35°C at 1atm ,respectively. ------------------------------------------------------------------------- ΔHf(kJmol^-1) S(kJmol^-1) ΔGf(kJmol^-1) ΔCp(kJmol^-1) I2(s) 0 116.14 0 54.44 I2(g) 62.44 260.58 19.36 36.90 ------------------------------------------------------------------------- 10.For the synthesis of amminia form its elements, N2(g) + 3H2(g) ←→ 2NH3(g) the equilibrim constant K=6.78*10^5 at 298K and ΔH=-92.2 kJmol^-1. (a)(5pts) Calculate the equilibrium partial pressure of N2(g),H2(g),and NH3(g) at 298 K of the total pressure is 1.00 atm and the H:N aton ratio in the system is 3:1. (b)(5pts) Calculate the equilibrim constant for the reaction at 600K,assuming no change in ΔH and ΔS between 298K and 600K. 11. There are two isomeric hydrocarbons with formula C4J10,butane and isobutane,which we donate here B and I.The standard enthalpies of formation for the gaseous species are -124.7 kJmol^-1 for B,-131.3 kJmol^-1 for I ;the standard free energies of formation are 15.9 kJol^-1 for B,-18.0 for I. (a)(5pts) Which is the more stavle under standard conditions,and which has the higher entropy? (b)(5pts) The reaction B←→I can occur in the presence of a catalyst. Calculate the equilibrium constant at 298K for the conversion fo B to I.and calculate the percentage of B in the equilibrium mixure. 12.Poor Humpty Dumpty Humpty Dumpty sat on a wall Humpty Dumpty had a great fall All the Kings Horses and all the Kings men, Couldn't put Humpty together again. Mother Goose "When I used a word," Humpty Dumpty said in a rather scornful tone,"it means just what I choose it to mean-neither more nor less." "The question is," said Alice,"whether you can make words mean so many different things," "The question is," said Humpty Dumpty,"which is to be master-that's all." Think about Humpty and consider the following questions: (a)(2pts) What form of energy did Humpty have as he sat on the wall? (b)(2pts) What happened to the energy Humpty had after he fell and hit the ground? (c)(3pts) Using the second law of thermodynamics,explain why Humpty could not be put back together again into his exact original form,despite all the efforts and resources available to the King(i.e.,his horses and men). (d)(5pts) Althouh Humpty cannot be put back togerher exactly the same way he was,suppose he could be put back to a reasonable fegree.Discuss whether it would take more energy,less energy,or the same amount of energy Humpty initially had sitting on the wall to put him back. Where might the energy needed to put him back together come from? 13.Foe a reaction, aA+bB→cC+dD, Δ G = cΔ G + dΔ G - aΔ G -bΔ G and Δ G = -RTlnK r f C f D f A f B r Using these two expressions (a)(5pts) Show that d Δ G 　 Δ H ---(--f-i) = － ---f-i,m-　　　　　(註：小寫＝下標) dT T T^2 where Δ H is the standard molar enthalpy of formation of species i. f i,m (b)(5pts) From the result obtained in part (a) and the relation between lnK and the standard reaction Gibbs energy,show that d ln K Δ H ---------- = －　---r--- d (1/T) R even if Δ H is temperature dependent. r --

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