課程名稱︰物理化學
課程性質︰系上選修
課程教師︰趙基揚
開課學院：工學院
開課系所︰材料系
考試日期（年月日）︰96/11/30
考試時限（分鐘）：190
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(28pts)Agree or disagree the following statements,explain your answers as
quantitatively as possible and give the correct answers with reasonable
explanation if you thinkthe statements given are wrong
(a)Super critical CO2 can be obtained by compressing CO2 gas at arbitrary
temperature and the density of supercritical CO2 is much smaller than
that in the gas phase
(b)If the variation of concentration is sharp,the change of concentration
will be fast
(c)The rate law of a chemical reaction is determined by the reaction formula.
(d)The viscosity of a gas decrease as the temperature increase
(e)Thermal conduction of a gas in a close box originates from the density
variation in the container.
(f)The molar conductivity of a weak electrolyte decrease linearly with the
increase of the concentration of the electrolyte.
(g)For the reaction A + B←→I →P,the rate determine step is I→ A + B.
2.(15pts)An equation of state,known as Berthelot equation,is illustrated
below. The formula is similar to that of the van der Waals eqution.
(a)Explan how the Berthelot equation describes the real gas behavior deviated
from the perfect gas behavior.
(b)What is the compression factor derived from the Berthelot eqution?(Hint:
Virial coefficients can be expressed using a and b)
(c)What's the Boyle temperture according to the Bertholet equation?
P=RT/(Vm-b)-a/(TVm^2)
3.(18pts)For an ion carried ze charge in an aqueous solution,it will move
under the influence of an external electric field E.
(a)Express the drift speed of the ion. Given that the friction coefficient
of the ion moving in an aqueous solution is f=6πηa.
(b)Express "mobility,μ" from your result in (a)
(c)Show that λ=zμF ,where λ is the limiting molar conductivity of a
certain ion.
(d)Based on your expression of the mobility,qualitatively compare the
mobility of Li and K ions.
(e)It was observed that the relative mobility of Li and K ions opposes the
prediction of the mobility expression. Explain the mechanism behind
this contradiction.
4.(10pts)The equilibrium A←→B+C at 25℃ is subjected to a temperture jump
that slightly increases the concentrations of B and C. The measured
relaxation time is 3.0μs. The equilibrium constant for the system is
2.0*10^-16 at 25℃,and the equilibrium concentrations of B and C at 25℃
are both 2.0*10^-4mol dm^-3 . Calculate the rate constants for forward and
reverse reaction.
5.(12pts)The nuclide 244Bk(berkdlium) decay by producing α particles,which
capture electrons and form He atoms. Its half-life is t1/2 . If a sample
of mass W grams was placed in a container with volume V that was impermeable
to α radiation, but there was also a hole of area A in the wall. The
pressure of helium at temperture T inside the container after certain time
t can be obtained by solving the following differential equation.
Where kr=ln2/t ,m is the mass of a He atom and k is the Boltzman constant
1/2
dp k kr T W NA -krt p A k T / V
－ = ——－－(－－－)e^ - －－－－－－－－
dt V 244 ( 2πmkT )^0.5
Please derive the equation starting from the derivation of collision flux
Zw with the help of the follwing information.
f(vx)=(M/2πRT)^0.5 *e^(-Mvx/2RT)
∞
∫ vx f(vx) dvx=(kT/2πm)^0.5
0
6.(18pts)
(a)Show that t1/2 正比於 1/[A]0^n-1 for a reaction that is nth-order in A.
(b)Show that the ratio t1/2/t3/4,where t1/2is the half-life and t3/4 is the
time for the concentration of A to decrease to 3/4 of its initial value
(implying that t3/4<t1/2)can be written as a function of n alone, and can
be written as a function of n alone,and can therefore be used as rapid
assessment of the order of a reaction.
(c)Sucrose is readily hydrolysed to glucose and fructose in acidic solution.
An experiment on the hydrolysis of sucrose in 0.50M HCl(aq) produced the
following data:
t/min 0 14 39 60 80 110 140 170 210
[sucrose]/(mol dm^-3) 0.316 0.300 0.274 0.256 0.238 0.211 0.190 0.170 0.146
Determine the rate constant of the reaction and the half-life of a sucrose
molecule.
7.(8pts)The rate constant for the decomposition of a certain snbstance is
2.80*10^-3 dm^3 mol^-1 s^-1 at 30℃ and 1.38*10^-2 dm^3 mol^-1 s^-1 at 50℃.
Evaluate the Arrhenius parameters of the reaction.
8.(16pts)Viscosity,η,is a measure of the property of a fluid to resist the
force causing the fluid to flow,which is associated with the momentum
transfer.Fick's 1st law can be used to describe the relationship between the
momentum transfer and the viscosity.
(a)Write the Fick's first law.Show that for a perfect gas,the sane equation
can also be obtained from the molecular kinetics and the viscosity is
equal to Nmλc/3 ,where N is the average number density,m is the mass
of gas molecule,λis the mean free path,c is the average velocity of the
gas molecules.
(b)Deduce the effective molecular diameter of NH3 based on the following
vapour-phase viscosity coefficients:η=9.08*10^-6 kg m^-1 s^-1 at 270K
and 1.00 bar.(Note:MFP is a function of the size of molecules)
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