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課程名稱︰普通化學甲下
課程性質︰系定必修
課程教師︰蘇志明
開課學院：理學院
開課系所︰物理學系
考試日期（年月日）︰2008.06.20
考試時限（分鐘）：180
是否需發放獎勵金：是的！
（如未明確表示，則不予發放）
試題 :
Third General Chemistry Examination June 20,2008
1.The decomposition of ozone to oxygen follows the following balanced reaction
:
2 O3(g) → 3 O2(g)
The observed rate law is
2
d[O3] [O3]
-─── = k ───
2dt obs [O2]
The mechanism proposed for this process is
k1
O3 ←─→ O2 + O (1)
k-1
k2
O + O3 ──→ 2 O3 (2)
Assuming that step (2) is rate-determining, derive the differential rate law
for the above mechanism under two different approximations: (a) equilibrium
approximation, (b) steady state approximation. Express k(obs) in terms of
the k's in Steps (1) and (2) for each approximation method. Which
approximation method is better or less-restricted in describing the reaction
? Give your arguments.
2.It is known that the collision rate of the gas particles with a secton of
container wall is dependent on the following factors:
_ ╭ 8k(B)t ╮
(i)The average speed of the gas particles, u = √│────│
╰ πm ╯
(ii)The size of the area being considered
(iii)The number density of the gas particles
After some considerations, one could find that the proportionality constant
between the collision rate and the above three factors is 1/4.
(a)Write down the formula for the collision rate of gas particles with the
container wall.
(b)We now set up an effusion experiment in a vacuum system. The diameter of
the circular pin hole on the gas container wall is 0.10 cm. The gas
container is a close system (i.e. there is no gas supply to keep a
constant pressure) except the opening of the pin hole. If the container
volume is V, the initial gas pressure is P0, the molecular weight of the
gas is M, and the temperature is kept at T, derive the differential rate
law for the container's pressure (or the number of moles of the gas).
(c)If the container volume is 1 L, the initial pressure is 1 atm, the gas is
oxygen, and the temperature is 300 K, what would be the life time of the
oxygen gas to remain in the container? How about the half life of the
oxygen gas in the container?
3.Consider the following elementary reaction in the gas phase:
k
A(g) + B(g) ──→ C(g) + D(g)
(a) Write down the differential rate law of this reaction. What is the unit
of the rate constant k?
(b) In the following, we shall use the hard-sphere collision theory to
derive the theoretical rate constant. Assume that the A and B molecules
are hard spheres with radii of rA and rB, respectively. We also know
that their number densities in the system are NA and NB, and their
molecular weights are MA and MB, respectively. The threshold energy for
the reaction is Et. The system temperature is T. It has been known that
the number of collisions for one single A molecule to collide with the B
molecules per second is
╭ 8πRT ╮
Z = N d^2 √│────│
B ╰ μ ╯
What do d and μ stand for in the above formula?
(c) What would be the total collision number per second (or per unit time)
between the A and B molecules in a volume of 1 L?
(d) What would be the total collision number per second (or per unit time)
between the A and B molecules which could react to form the product in a
volume of 1 L?
(e) How do you relate the result obtained in (d) with the rate constant
defined in (a)? Watch out that the units in (a) and (d) are different.
4.The following figure indicates three types of electrostatic interactions.
Assuming that R is much larger than d, derive the functional forms of the
interaction potential for each of these three electric charge configurations
. (Note: the final forms should be expressed in terms of the dipole moment
and R for the charge-dipole and dipole-dipole interactions, and each + or -
sign indicates a positive or negative elementary charge e)
├───────────┤
○ R ○ charge-charge
＋ －
├────────────┤
○ R ○──○ charge-dipole
＋ － ＋
├──┤
d
├──────────────┤
○──○ R ○──○ dipole-dipole
－ ＋ － ＋
├──┤ ├──┤
d d
5.(a)Give the Arrhenius equation for the rate constant of an elementary
reaction? Explain the physical meaning for each of the experimental
parameters and variables in this equation.
(b)The Arrhenius equation usually works fine if the experimental
temperatures were in a limited range. However, in dealing with the
situation with huge temperature variation, one would find that the
activation energy is no more temperature independent. How do you redefine
the activation energy to deal with this situaton?
(c)Calculate the activation energy of the rate constant derived by the hard-
sphere collision theory in Problem (3)
6.Dry nitrogen gas is bubbled through liquid benzene at 20.0℃. From 100.0 L
of the gaseous mixture of nitrogen and benzene, 24.7 g of benzene is
condensed by passing the mixture through a trap at a temperature where
nitrogen is gaseous and the vapor pressure of benzene is negligible. What is
the vapor pressure of benzene at 20.0℃?
7.In the vapor over a pentane-hexane solution at 25℃, the mole fraction of
pentane is equal to 0.15. What is the mole fraction of pentane in the
solution? (At 25℃ the vapor pressures of pentane and hexane are 511 and
150 torr, respectively.)
8.(a)prove the thermodynamics relation
╭╮
╭╭┤(G/T) ╮
│╰╯ │ H
│─────│ = - ──
│╭╮ │ T^2
╰╭┤ T ╯p
╰╯
(b)From (a) derive the van Hoff's equation for equilibrium constant, i.e.
express the equilibrium constant as a function of temperature.
9.Consider an osmotic pressure apparatus as shown in the following figure.
Assume that the internal aqueous sugar solution with water mole fraction of
x(water) is at equilibrium with the external pure water phase. The osmotic
pressure is measured to be π. The temperature is kept at T. The volume of
the sugar solution is V.
(a) What is the molar Gibbs' free energy of water in the sugar solution near
the membrane surface? (Note the reference state of water is just the
pure water at 1 atm)
(b) From (a) and the equilibrium condition, derive the relation between the
osmotic pressure and the number of moles of the sugar in the sugar
solution.
(c) An aqueous solution is 1.00% NaCl by mass and has a density of 1.07
g/cm^3 at 25℃. The observed osmotic pressure of this solution is 7.8
atm at 25℃. What fraction of the moles of NaCl in this solution exists
as ion pairs in general sense?
----------------------------------------------
Some constants and equations:
R = 1.987 cal/mol-deg = 8.314 J/mol-deg = 0.082 L atm K-1 mol-1
dG = VdP - SdT
ΔG°= -RT ln(K)
G = H - TS
ln(1-x) ≒ -x for abs(x) << 1
1
─── ≒ x for |x| << 1
1-x
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