課程名稱︰物理化學上
課程性質︰農業化學系大二必修
課程教師︰蘇志明
開課學院：生物資源暨農學院
開課系所︰農業化學系 (化學系開課)
考試日期（年月日）︰2009年 1月15日
考試時限（分鐘）：125 min
是否需發放獎勵金：YES!!
（如未明確表示，則不予發放）
試題 :
1.(a) Assuming that glucose and water form an ideal solution, what is the
equilibrium vapor presure at 20℃ of a solution of 1.00 g of glucose
(mol wt. 180) in 100 g of water? The vapor pressure of pure water is
17.54 torr at 20℃.
(b) What is the osmotic pressure, in torr, of the solution in part (a)
versus pure water?
(c) What is the activity of water as a solvent in such a solution?
(d) What would be the osmotic pressure versus pure water of a solution
containing both 1.00 g of glucose and 1.00 g of sucrose (mol wt. 342)
in 100 g of water at 20℃.
2. Which of the following has the largest (most positive) value for the:
(a) Molar entropy increase?
(Ⅰ) H2O(l,0℃) ─→ H2O(l,100℃)
(Ⅱ) H2O(s,0℃) ─→ H2O(l,0℃)
(Ⅲ) H2O(l,100℃) ─→ H2O(g,1atm,100℃)
(Ⅳ) H2O(g,1atm,100℃) ─→ H2O(g,0.1atm,100℃)
(b) Free energy of transfer of 1 mol of the substance from inside to out-
side a cell, all at 37℃?
(Ⅰ) NaCl(a＝0.010 inside) ─→ NaCl(a＝0.140 outside)
(Ⅱ) KCl (a＝0.100 inside) ─→ KCl (a＝0.005 outside)
(Ⅲ) NaCl(a＝0.100 inside) ─→ NaCl(a＝0.200 outside)
3. Consider the nitrogen gas at 25℃ and 1 atm. In hard-sphere model, the
diameter of an N2 molecule can be taken as 3.74 A (3.74x10^-10 m).
(a) Calculate the mean speed and the mean square speed of the nitrogen
molecule.
(b) Calculate the number of collisions each nitrogen molecule encounter
in 1 sec.
(c) Calculate the total number of collisions in a volume of 1 m^3 in 1 s.
(d) Calculate the mean free path of a nitrogen molecule.
(e) What is the total distance traveled by one N2 molecule along the
zigzag path in 1 s?
(f) As described in (e), estimate how far it will move in 1 s away from
where it started.
4. The problem of the separation and purification of protein molecules through
density-gradient centrifugation is equivalent to the problem of the flight
heights of hydrogen(or helium)-filled balloons in the atmosphere. Assuming
that our atmosphere is consisted of pure nitrogen gas and the temperature
is uniformly at 25℃, the pressure is exactly at 1 atm on the earth surface,
and the gravitational acceleration g is 9.80 m/s^2 and may be taken as a
constant, answer the following questions:
(a) Taking the gravitational potential be 0 at the earth surface, what is
the gravitational potential at an elevation of h? What are the density
and pressure of nitrogen gas at the elevation of h?
(b) What are the atmospheric pressure (in atm) and the nitrogen gas density
(in the unit of g/L) at the top of Jade Mountain which has an altitude
of 4000 m?
(c) What would be the buoyancy forces for a 1 L balloon at the earth surface
and also at the top of the Jade Mountain, respectively? Here we assume
that the balloon size is constant.
(d) If the 1 L balloon has a mass of 0.3 g, and assuming the balloon size
is constant, theoretically, how high could the balloon reach? Note that
this situation is equivalent to the equilibrium position of a protein
molecule in a centrifuge tube under the density-gradient centrifugation
condition.
5. The diffusion coefficient D of ribonuclease from bovine pancreas, an enzyme
that digests RNA, has been measured in a dilute buffer at 20℃. The value
is D＝13.1x10^-7 cm^2/s. (Hint: be careful with the units)
(a) Calculate the frictional coefficient f.
(b) Assuming that the protein molecule is sphere, calculate its hydrodynamic
radius from the Stokes equation. The viscosity of dilute aqueous buffer
is approximately equal to 1.00x10^-2 g/s*cm.
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Some constants and equations:
1 L*atm＝24.2 cal; 1 cal＝4.18 J; Ｒ＝0.082 L*atm/℃*mol＝8.31 J/K*mol;
k＝1.38x10^-23 J/K＝1.38x10^-16 erg/K; 1 erg＝1 g*cm^2/s^2;
o
μ＝μ ＋ＲＴ㏑ａ; ΠＶ＝ｎＲＴ; <ｕ>＝(8kT/πm)^0.5; <ｕ^2>＝(3kT/m);
z＝(√2)π(Ｎ/Ｖ)σ^2<ｕ>; l＝<ｕ>/z; d^2＝zl^2 (random walk model);
D＝kT/f; f＝6πηr
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