課程名稱︰物理化學上
課程性質︰物化，課本為 Physical Chemistry - Princieples and applications in
biological science, 4th edition. Tinoco, Sauer, Wang, Puglisi
課程教師︰金必耀
開課系所︰農化系必修，生技系必修
考試時間︰Nov.11,05 18:00~21:00
試題 :
1). Enthalpy as heat Function at constant pressure
Under the assumption that the only work done arises from pV work, show that
the enthalpy change, △H, of a system is equal to the heat change, Qp,
under the common laboratory situation of constant pressure. (10%)
2). Thermodynamics of ideal gas
One mole of an ideal monatomic gas initially at 300K is expanded from an
initial pressure of 10 atm to a final pressure of 1 atm. Calculate △E, q,
w, △H, △S, △G and the final temperature T2 for this expansion carried out
according to each of the following paths. The molar heat capacity at
constant volume for a monatomic gas is Cv = 3/2R. (15%)
a) An isothermal, reversible expansion
b) An expansion against a constant external pressure of 1 atm in a thermally
isolated (adiabatic) system.
c) An expansion against zero external pressure (i.e. against a vacuum) in
an adiabatic system.
3). Carnot Principle
Prove that no real engine operating between two heat reservoirs can have
efficiency greater than a Carnot engine. (10%)
4). Entropy of mixing
The number of left (L) and right (D) rotating molecules of an optically
active compound in a solition and NL and ND, respectively. According to
Boltzmann's statistical inrepretation, the entropy of the mixture is
S = k(NDlnN/ND + NLlnN/NL)
Where N is the total number of molecules of the compound (N = NL + ND) and
k is Boltzmann's constant. In the racemic mixture, the numbers of molecules
of the L and D forms are equal: ND = NL = N/2. Prove that racemic compound
has the highest entropy. (10%)
5). Residual Entropy
Experimental estimates of the absolute entropy of solid carbon monoxide
close to absolute zero suggest that S(0K) = 5.7J/Kmol, not Zero as expected.
Suggest a reason why this might be the case. (8%)
6). Gibbs Energy
Show that the Gibbs energy change for a reversible reaction at constant
temperature and variable pressure in the absence of non-PV work is △G = Vdp
(10%)
7). Helix-Coil transition
Thermodynamic data for transitions from ordered, helical conformations of
typical polypeptides and polynucleotides to disordered states has shown that
the enthalpy changes and entropy changes are positive as expectedl; heat is
absorbed and entropy is gained. However, when synthetic polypeptide
polybenzyl-L-glutamate undergoes a transition from an ordered helix to a
disordered coil in an ethylene dichloride-dichloroacetic acid solvent at
39C and 1 atm, △H = -4.0kJ (permole of amide) and △S = -12J/K (per mole of
amide). (15%)
a). Give a possible explanation for the experimental result that heat is
released and entropy is decreased for this transition. Does increasing
the temperature favor the helix-coil transition?
b). Is this reaction spontaneous at 39C? What thermodynamic criterion did
you use to reach this conclusion?
c). At what temperature will the helix-coil reaction be reversible? This
temperature is often called the "melting" temeprature of the helix.
Assume that △H and △S are independent of temperature.
8). Basic concepts in thermodynamics
You are asked to evaluate critically the following situations. Some of the
proposals or interceptions are reasonable, while others violate very basic
principles of thermodynamics. (16%)
a). It is commonly known that one can supercool water and maintain it as a
liquid at temperatures as low as -10C. If a sample of supercooled
liquid water is isolated in a closed, thermally insulated contained,
after a time it spontaneously with no addition of heat from outside;
futhermore, some low-entropy ice is priduced.
b). On a hot summer's day, your laboratory partner proposes opening the door
of the lab refrigerator to cool off the room.
c). A sample of air is seperated from a large evacuated chamber, and the
entire system is isolated from the surroundings. A small pinhole
between the two chambers is opened, and roughly half the gas is allowed
to effuse into the second chamber before the pinhole is closed. Because
nitrogen effuses faster than oxygen, the gas in the first chamber is
richer in oxygen than the original air. The gases have thus
spontaneously unmixed (at least partially), and this is held to be a
violation of the second law of thermodynamics.
d). The maximum efficiency of a steam engine can be calculated using the
second law of the thermodynamics. If it operates between boiling point
of water and room temperature, the maximum efficiency is about
373-293/373 = 0.215 or 21.5%
e). Photosynthesis by green plants occur almost entirely at ambient
temperatures, yet publications report theoretical limits as high as 85%
of the fraction of the light energy absorbed can be converted into
chemical energy (free energy or net work). Clearly, such estimates must
be wrong, or else the second law cannot apply.
9). Poor Humpty Dumpty!
Humpty Dumpty sat on a wall.
Humpty Dumpty had a great fall.
All the Kings Horses and all the Kings men,
Couldn't put Humpty together again.
Mother Goose
Think about Humpty and consider the following questions: (12%)
a). What form of energy did Humpty have as he sat on the wall?
b). What happened to the energy Humpty had after he fell and hit the ground?
c). Using the second law of thermodynamics, explain why Humpty could not be
put back together again into his exact original from, despite all the
efforts and resources available to the King (i.e., his horses and men).
d). Although Humpty cannot be put back together exactly the way he was,
suppose he could be put back together to a reasonable degree. Discuss
whether it would take more energy, less energy, or the same amount of
energy Humpty initially has sitting on the wall to put him back together
Where might the energy needed to put him back together comes from?
Potentially useful data:
Avogadro's number: 6.022 x 10^23
R = 8.31 J/Kmol
1 atm = 760 torr = 760 mmHg
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