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課程名稱︰物理化學一
課程性質︰化學系系必修
課程教師︰李弘文
開課學院：理學院
開課系所︰化學系
考試日期（年月日）︰2009.05.08
考試時限（分鐘）： 08:10~10:10，120分鐘
是否需發放獎勵金：是
試題 :
Part A: True/False questions (40 point, 2 point for each question)
For something to be true, it must be always true.
a). If one conponent of a solution obey Henry's law, then the other component
obey Raoult's law.
b). If two ideal aqueous solutions containing different solutes but with equal
molecules, the freezing point will be the same for these solutions.
c). In a dilute ideal solution, the plot of chemical potential of a solute
versus the logarithm of its concentration has the slope of +1.
d). The fact that ethanol/water mixture has smaller volume than the ideal
mixture, suggests that ethanol/water do not like to be mixed.
e). When O2 at the surface of earth and O2 at 100m above the surface are in
equilibrium, μ[O2(g), surface] < μ[O2(g), 100 m]
f). For an ideal solution of two substances A and B, μA must be smaller than
μA*.
g). When 10 ml of 3 M sucrose aqueous solution mixed with 50 ml of 2 M sucrose
aqueous solution, the total final volume is 55 ml.
h). For a spontaneous process at constant T and P, ΔG° is always negative.
i). The temperature dependence of an equilibrium constant can be determined
from of ΔH° the reaction.
j). If an exothermic reaction has ΔS>0, the reaction is always spontaneous at
all temperatures.
k). The value of ΔG° at 25℃ is the same as ΔG° at 500℃.
l). An equilibrium mixture of ice and water is held at constant pressure. When
heat is added so that some ice melts, the Gibbs free energy of the system
decreases.
m). The negative change in Helmholtz free energy during an isothermal process
is the maximum work available from the processes.
n). When urea spontaneously dissolves in water, the beaker of solutions feels
cold. It is entropy driven.
o). It is impossible for four phases of a mixture of two conponents to coexist
at equilibrium.
p). The Clautius-Clapeyron equation can be used for a solid liquid phase
transition.
q). At equilibrium, a substance that occurs in two phases will have the same
concentration in both phases.
r). At constant T and P, the molar fraction of naphthalene in a satureated
solution is the same in all solvents with which naphthalene forms ideal
solutions.
s). ΔG is the maximum non-expansion work that a system can do at constant T
and V.
t). For a single conponent system, when the pressure is reduced, the amount of
the boiling temperature change is always smaller than that of the freezing
temperature.
Part B: Descriptive questions (30 points, 6 points each)
Use the limited space below to explain the facts below. If possible,
use figures and other quantitave statements to strengthen your
reasoning.
(1). The phase diagram indicates the stable phase of water at 20℃ and 1 atm
is liquid. Explain why water in a dish placed at open air can evaporate
completely. Does this process contradict the statement from the phase
diagram?
(2). For most single-conponent substances, increasing the pressure above the
solid-liquid coexistance line leads to freezing. This is not true for
water. Sketch the phase diagram of water and explain why?
(3). For ΔA<0 to be the criterion of the spontameous change of the process,
it is required that the system is at constant T and V. Why?
(4). Explain why the fractional distillation can be used to purify compound
from a mixture.
(5). The binding between a drug (small chemical molecule) and its biological
target is mostly mediated by weak, non-covalent interactions. Explain why
creating additional hydrogen bonding (5 KJ/mol) between the drug and the
target can lead to a 10-fold decrease in KD.
Part C: Calculation questions (60 points total. Show your work for partial
credit.)
_
δH
(1). (10 points) Derive the expression of (──) for a van der Waals gas
δP T
_2 _
obeying the following relation: ( P + a / V )( V - b ) = RT
(2). (18 points) Benzene and toluene forms an ideal solution mixture. At 20℃,
the vapor pressures of pure benzene and pure toluene are 74.9 torr and
21.6 torr. When a solution of 1.4 mol of benzene and 1.1 mole of toluene
is mixed, calculate the followings:
(a) (4 points) Gibbs free energy change of mixing and the volume change
of mixing.
(b) (4 points) As the pressure is reduced, at what pressure will the
boiling again?
(c) (4 points) What will be the molar fraction of toluene in the vapor
phase at the pressure specified in (b)?
(d) (6 points) Sketch a pressure (y-axis) - composition (x-axis) plot for
this ideal mixture at liquid/vapor equilibrium, draw a bubble line
(solid) and a dew point line (dotted), and circle the point where the
mixture becomes competely vapor.
│ │
│ │
│ │
│ │
└────┘
(3a). (4 points) Calculate the solubility (in m, molality) of acetylene (C2H2)
in water when the partial pressure of C2H2 is 500 mmHg. The Henry's law
constant for C2H2 in water at 300K is 1×10^6 mmHg.
(3b). (4 points) The vapor pressure of water at 25℃ is 23.756 torr and at
100℃ is 760 torr. Calculate the enthalpy change of vaporizaion of
water.
(3c). (4 points) Estimate the boiling point of the solution when 0.250 mole of
sugar dissolved in 500 ml of water. Assume that the solution is dilute
enough to be ideal. Kb = 0.51 K-kg/mol
(4). (10 points) At 2000℃, water is 2% dissociated into oxygen and hydrogen
at a total pressure of 1 bar.
(a) (6 points) Calculate L for H2O(g) = H2(g) + 1/2 O2(g) at 2000℃.
(b) (2 points) Will the extent of reaction increase or decrease if argon
gas is added, when the total pressure is held equal to 1 bar (Circle
one in the answer box)?
┌───────────────┐
│Increase Unchanged Decrease │
└───────────────┘
(b) (2 points) Will the extent of reaction increase or decrease if oxygen
gas is added while holding the total pressure (Circle one in the
answer box)?
┌───────────────┐
│Increase Unchanged Decrease │
└───────────────┘
(5). (10 points) A protein (membrane receptor) involved in signaling pathway
has found th follow the following obligatory sequential binding scheme to
proceed the signaling cascade.
→ →
P + L ← PL + M ← PLM
o K1 K2
Protein P has to bind to ligand L first in order to bind th ligand M. The
o
dissociation constants of thest two binding precesses are K1 and K2.
(a) (8 points) Y is define as the ratio of protein that is bound only by
PL
ligand L (PL) over total protein concentration. Express Y in the
PL
[L] obs
Langmuir form of Y = Y ────── , and express Y and K
PL max obs max D
K + [L]
D
in terms of K1, K2, L and M.
(b) (2 points) Plot Y v.s. [L].
↑ Y
│↙ max
Y ├-------------------------------------------
PL │ |
│ |
│ |
│ | obs
│ | K
│ |↙ D
└────────────────────→
-----題目結束，以下是答案-----
Part A: T*FFF TFFTT FFTTF FFTFF (*送分)
Part B: 全略
Part C:
(1) 略
(2)(a) ΔGmix = -4179 J, ΔVmix = 0
(b) P = 51.4 torr
(c) 0.185
(d) 略
(3a) 0.028m
(3b) ΔHvap = 42740 J
(3c) 100.255℃
(4)(a) 2.03×10^-3
(b) Increase
(c) Decrease
(5)(a) K2
Y = ─────
max K2 + [M]
obs K1 K2
K = ─────
D K2 + [M]
(b) 圖略
[L] → 0, Y → 0
PL
obs
[L] = K , Y = 1/2 Y
D PL max
[L] → ∞, Y → Y
PL max
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