課程名稱︰普通化學甲下
課程性質︰必修
課程教師︰金必耀
開課學院：理學院
開課系所︰物理學系 材料科學與工程學系
考試日期（年月日）︰104年4月22日
考試時限（分鐘）：10:20 ~ 13:30
試題 :
1.Melting of DNA Double helix
(a) As heat is added to a sample of pure ice (Solid H2O) at constant pressure
,the temperature rises until the melting point of the ice is reached. The ice
then melts at the constant melting temperature,Tm. After the ice is completely
melted the temperature continues to rise. Complete the plots below for heat
added, q v.s. T (Fig. 1) and Cp v.s. T (Fig. 2) for the three stages of this
process of melting ice.
q↑ Cp↑
∣ ╱︴ ∣
∣ ╱ ︴ ∣＿＿＿＿
∣╱ ︴ ∣ ︴
∣ ︴ ∣ ︴
—————→T ——————→T
Tm Tm
Fig.1 Fig.2
(b) As heat is added to a dilute buffer solution, the temperature rises. The
change in temperature is approximately linear with added heat as shown in the
sketches (Fig.3 and 4)
q↑ Cp↑
∣ ╱ ∣
∣ ╱ ∣＿＿＿＿
∣╱ ∣
∣ ∣
—————→T ——————→T
Fig.3 Fig.4
If a solution of DNA in dilute buffer is heated, the DNA double-stranded
helix melts to single strands over a narrow range. Heat is absorbed. Sketch a
q v.s. T and a Cp v.s. T curve for a DNA solution.
(c) Two single stranded self-complementary oligonucleotides can form
double-stranded helices in aqueous solution described by the following
equation：
2S → D
←
where S and D denote single and double-stranded DNA respectively. The
equillibrium constant is：
〔D〕
K = ————
2
〔S〕
Derive an expression for the equillibrium constant K as a function of Co,
the initial concentration of single strands and α, the fraction of single
strands that are in the double-stranded helix at equillibrium, namely
2〔D〕 2〔D〕
α= ——————— = ————
2〔D〕+〔S〕 Co
(d) The melting temperature Tm is defined as the temperature for which α= 0.5
Point out the position of Tm in the heating curves you drawn in problem (b)
(e) From chemical thermodynamics, the relationship between the equillibrium
constant, standard enthalpy of reaction ΔrH, and standare entropy of reaction
ΔrS is given by ΔrH-TΔrS = -RTln K. Shown that the melting temperature of
DNA and the initial concentration of single-stranded DNA satisfy the following
equation:
1 R ΔrS
— = ——ln Co + ————
Tm ΔrH ΔrH
(f) Could you design an experiment, which can give the information about the
reaction enthalpy and entropy for the DNA melting?
2.Estimate of the maximum reserves of fossil energy
We assume that neither free carbon nor free oxygen was present on the earth
before the beginning of organic life because they react quickly with each other
to form CO2 during the early stage of the earth history. The free oxygen found
in the atmosphere today can only be the result of photosynthesis of plants and
photosynthetic bacteria. During photosynthesis, water and carbon dioxide
combine to form carbonhydrates, which build up according to the reaction
H2O + CO2 → CH2O + O2
Therefore, the present-day amount of oxygen in the atmosphere can be used to
estimate the size of carbon reserves on the earth. Assume that there are 20%
of oxygen and 80% of nitrogen in the atmosphere. The pressure of atmosphere on
the surface of the earth is p = 1 atm ≒ 10^5 N/m^2. The acceleration of
gravity is g ≒ 10 m/s^2 and the radius of the earth is approximately
R ≒ 6400 km.
(a) What is the total mass of oxygen in the atmosphere?
(b) Estimate the mount of fossil fuel reserves produced by the photosynthesis.
(Assume fossil fuel reserves consist completely of carbon)
Up to now 10.4 ×10^12 tons coal equivalents have been found.
3. One mole of an ideal gas is changed isothermally from V to 2V with the
following processes. Calculate q, w, ΔU, ΔH, ΔS and ΔG for each of them.
(a) Isothermal reversible expansion
(b) Adiabatic free expansion
(c) Isobatic reversible expansion (P,V) → (P,2V), then isochoric reversible
compression (P,2V) → (P/2,2V)
4. Tungsten melts at 3410 ℃ and has an enthalpy change of fusion of 35.4 kJ/
mol. Calculate the entropy of fusion of tungsten.
5. By examining the following graphs, predict which element — copper or gold
— has the higher absolute entropy at a temperature of 200 K. (Chap.13 — 51)
6. When a gas undergoes a reversible adiabatic expansion, its entropy remains
constant even though the volume increases. Explain how this can be consistent
with the microscopic interpretation of entropy. (Hint: Consider what happens
to the distribution of velocities in the gas.)
7. The total pressure cooker filled with water increases to 4.0 atm when it is
heated, and this pressure is maintained by the periodic operation of a relief
valve. Use the following figure to estimate the temperature of the water in
the pressure cooker. (The figure is Pressure — Temperature of water)
8. Using the Bolztmann formula, calculate the microstates and entropy of the
following systems, in terms of the ideal gas constant, R :
(a) A mole of monoxide crystal at T = 0 K, assuming that each molecule can
have two possible orientations CO or OC and also these two orientations have
exactly the same energy.
(b) A mole of ice crystal at T = 0 K. Assume that there are exactly two OH
bonds and two hydrogen bonds surrounding each oxygen atom as shown in the
following figure, which ill be called the chemical condition. (Hints: For a
mole of ice, there are 2N hydrogen atoms. Along each O-H-O connection, the
hydrogen can have possible choice of positions along its O-O axis. There are
2^(2N) microstates. However, the positions of four hydrogen atoms surrounding
a particular oxygen atom are not independent. So you need to figure out the
fraction of microstates that satisfies the chemical condition.)
9. The primary medium for free energy storage in living cells is adenosine
triphosphate (ATP). Its formation from adenosine diphosphate (ADP) is not
spontaneous:
3- 2- + 4+
ADP (aq) + HPO4 (aq) + H (aq) → ATP (aq) + H2O (l) ΔG = 34.5 kJ
Cells couple ATP production with the metabolism of glucose (a sugar) :
C6H12O6 (aq) + 6 O2 (g) → 6 CO2 (g) + 6 H2O (l) ΔG = -2287.2 kJ
The reaction of 1 molecule of glucose leads to the formation of 38 molecules
of ATP from ADP. Show how the coupling makes this reaction spontaneous. What
fraction of the free energy released in the oxidation of glucose is stored in
the ATP?
10. Solid tin exist in two forms: white and gray. For the transformation:
Sn(s,white) → Sn(s,gray)
the enthalpy change is -2.1 kJ and the entropy change is -7.4 J/K
(a) Calculate the Gibbs free energy change for the conversion of 1.00 mol
white tin to gray tin at -30 ℃.
(b) Calculate the Gibbs free energy change for the conversion of 2.50 mol
white tin to gray tin at -30 ℃.
(c) Will white tin convert spontaneously to gray tin at -30 ℃ ?
(d) At what temperature are white and gray tin in equillibrium at a pressure
of 1 atm ?