課程名稱︰物理化學
課程性質︰材料系選修
課程教師︰趙基揚
開課學院：工學院
開課系所︰材料系
考試時間︰10, Nov, 2006(2hr)
是否需發放獎勵金：是的，謝謝
試題 :
Physical Chemistry, Fall 2006
Prelim 1
1. Explain the following terms, especially their physical meanings and
the associated mathematical equations.
(a) Critical temperature. How does one can obtain the critical volume
and critical pressure of a gas?(8pts)
(b) The Fick's 2nd law and its application.(4pts)
(c) Arrhenius equation fo a chemical reaction.(4pts)
(d) Viscosity. Also explain why the viscosity of a gas increases with
temperature, whereas the viscosity of a liquid decreases with
increasing temperature?(8pts)
(e) Thermal conductance of a gas.(4pts)
(f) The dependences of molar conductivity upon concentration of a weak
electrolyte and a strong electrolyte and why is that.(8pts)
(g) The drift speed of an ion. How does it related to the electric
field applied?(4pts)
2. Two types of equations of state, the virial equation and the van der
Waals equation, are commonly used to describe the behavior of real
gases.
(a) Write these two equations of state and explain how they interpret
the deviation of a real gas from the ideal gas.(8pts)
(b) Use the van der Waals parameters for chlorine(a=6.260 dm^6 atm mol ^-2,
b=5.42*10^-2 dm^-3 mol^-1)to calculate approximate values of (i)
the Boyle temperature of chlorine and (ii) the molar volume of
chlorine at 350K and 2.3 atm.(12pts)(Note: you don't need to solve
the van der Waals equation but instead, use the ideal gas
approximation as a start.)
Hint: Virial coefficients can be expressed using van der Waals parameters.
3. A Knudsen cell was used to determine the vapour pressure of metals
based on the rate of effusion. The rate of effusion is a functional
of the collision flux which can be obtained through the equation
shown below.N is the average number density, c is the mean speed of
the gas while f(v) represent the Maxwell distribuion of velocity of
gas molecules at a cetain temperature.(a) Show that c=(8RT/πM)^0.5
and Zw=p/(2πMRT)^0.5.(7pts)
For 1.0mg of germanium(MW=72.6) in a cell of 1.0 cm^3 at 1000℃,
duringan interval of 7200s the mass loss through a hole of radius
0.50mm amounted to 43μg.(b) What is the vapour pressure of germanium
at 1000℃?(6pts) (c)What is t1/2, the time required for the pressure
to decrease to half its initial value if the cell is not replenished
as the gas escape?(6pts)
Zw=Nc/4
f(v)=4π(M/2πRT)^(3/2)V^2e^(-Mv^2/2RT)
4. Diffusion is a phenomenon regarding the flow of matters. Fick's 1st
law is an empirical equation describing the phenomenon. (a) Write
the fick's 1st law. Show that for a perfect gs, the same equation
can also be obtained from the molecular kinetics and the diffusion
coefficient of is equal to λc/3 where λ is the mean free path and
c is the average velocity of the gas molecules.(12pts) (b) For an
ion in aqueous solution, it's diffusion coefficient is a function of
mobility, temperature and charges it carries. Its limiting molar
conductivity depends on the mobility too. The experiment value of
the mobility of a sulfate ion in water is 8.29*10^-8 m2V-1s-1.
Evaluate its diffusion coefficient, limiting moalr conducivity and
hydrodynamic radius at 298K. The viscosity of water at 298K is
8.91*10^-4 kg m-1 s-1(9pts)
5. The data below apply to the formation of urea from ammonium cyanate,
NH4CNO → NH2CONH2. Initially 22.9g of ammonium cyanate was dissolved
in enough water to prepare 1.00 dm3 of solution. Determine the order
of the reaction, the rate constant, and the mass of ammonium cyanate
left after 300 min.(15pts)
t/min 0 20.0 50.0 65.0 150
m(urea)g 0 7.0 12.1 13.8 17.7
Mathematics you might use:
f(x)=f(a)+(df/dx)(x-a)+(1/2!)(d2f/dx2)a(x-a)^2+....+(1/n!)(dnf/dxn)(x-a)^n
=Σ(n=0→∞)(1/n!)(dnf/dxn)(x-a)^n
lim(x→0)(1/1-x)=1+x+x^2+.......
c0+c1(x-a)+c2(x-a)^2+........+cn(x-a)^n+.....=Σcn(x-a)^n
∫x^3e^(-ax^2)dx=1/(2a^2)
∫x^4e^(-ax^2)dx=(3/8)(π/a^5)^0.5
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