課程名稱︰物理化學二 課程性質︰必修 課程教師︰戴子安 開課學院：工學院 開課系所︰化工系 考試日期（年月日）︰101/6/8 考試時限（分鐘）：130min 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.(20 points)Explain following terms. Use graph if necessary. (a)Maxwell-Boltzmann distribution of molecular velocity for the one-dimensional motion.(b)Plot the relative position on the graph of the Maxwell distribution of speeds for the most probable, mean, and root-mean speeds for a gas.(c) Collision cross section (d)Lennard-Jones potential and its important parameters (e)Describe methods to determine the rate equation.(f)Interpretation of the Arrhenius equation for the rate constant k (g)Relationship between the equilibrium constants of K and K (h)Relationship between the activation c p energy for the forward and backward reaction (i)Lindermann mechnism for a unimolecular isomerization of A -> 2A (j)Plot the three explosion limits ocurred in the reaction of H and O . 2 2 2.(10 points)The pressure in interplanetary space is estimated to be of the order of 10^-14 Pa. Calculate(a)the average number of molecules per cubic centimeter, (b)the collision frequency, and(c)the mean free path in kilometer. Assume that only hydrogen atoms are present and that the temparature is 1000K. (d =0.2nm) 11 3.(10 points)You are an engineer faced with the task of ensuring that the material on the body of a spacecraft can withstand puncturing by space debris. The initial cabin air pressure in the craft of 1atm can drop to 0.7atm before the safety of the crew is endangered. The volume of the cabin is 100m^3, and the temparature in the cabin is 285K. Assuming it takes the space shuttle about 8 hours from entry into orbit until landing, what is the largest circular aperture created by a hull puncture that can be safely tolerated with the flow of gas out of the spaceship is effusive? Can the escaping gas from the spaceship be considered as an effusive process?(You can assume that the air is adequately represented by N .) 2 4.(10 points)Based on the Fick's first law of diffusion and the idea of free mean path of gas particles, derive the approximate expression for the diffusion coefficient, D , in terms of the collision diameter of a gas. a 5.(15 points)The overall reaction for the halogenations of a hydrocarbon(RH) using Br as the halogen is RH + Br -> RBr + HBr. The following mechnism has 2 been proposed for this process: k1 k2 k3 k4 Br ---> 2Br．, Br．---> R． + HBr, R．+ Br ---> RBr + Br．, Br．+ R．---> RBr 2 2 Determine the rate law predicted by this mechnism. 6.(15 points)Consider the thermal decomposition of 1atm of (CH COC(CH ) ) to 3 3 3 acetone and ethane, which occurs with a rate constant of 0.0019s^-1. After initiation of the reaction, at what time would you expect the pressure to be 1.8atm? 7.(10 points)For the gas reaction: k ---> O + O + M O + M 2 <--- 3 k' When M = O , the rate constant is given by k = 6×10^7(L^2/mol^2*s)e^(2.5/RT), 2 where the activation energy is in kJ/mol. Calculate the values of the parameters 。 。 in Arrhenius equation for the reverse reaction assuming Δ H and Δ S are r r independent of temparatue. Δ H Δ G Δ S f f f O (g) 249.17 231.731 161.055 O 2(g) 0 0 205.138 O 3(g) 142.7 163.2 238.93 (kJ/mol) (kJ/mol) (J/Kmol) 8.(10 points)The third explosion limit for the reaction 2H +O ---> 2H O 2(g) 2(g) 2 (g) can be explained by the following mechnism. Demonstrate the existence of this limit. H ---> 2H (v = v = constant) 2 uni k2 H + OH ---> H + H O 2 2 k3 O + H ---> O + OH 2 k4 O + H ---> OH + H 2 k5 1 k6 k7 H + wall ---> ---H , H + O + M ---> HO + M, HO + H ---> H O + OH 2 2 2 2 2 2 2 --

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