課程名稱︰物理化學一
課程性質︰必帶
課程教師︰林萬寅
開課學院：理學院
開課系所︰化學系
考試日期（年月日）︰2008/05/13
考試時限（分鐘）：120分鐘
是否需發放獎勵金：YES!!
（如未明確表示，則不予發放）
試題 :
1. Some of the thermodynamic data for benzene are: △fusH = 10.6 kJ/mol;
△vapH = 30.8 kJ/mol; ρ(s) = 0.89 g/mL; ρ(l) = 0.879 g/mL; triple point:
T3 = 5.5℃, P3 = 3.6 torr. Find the melting curve and sublimation curve for
benzene. (10%)
2. For a second-order phase transition, prove the following relations. (10%)
dP △α 1 δV
(A) Use the continuity of volume to show that ─ = ───, where α = ─(──)
dT △κT V δT P
1 δV
κT = -─(──) .
V δP T
dP △Cp
(B) Use the continuity of entropy to show that ─ = ────.
dT T*V*△α
3. Consider an equilibrium phase change of a substance A from α to β at 70℃
and 1 atm. Knowing that q = 640 kJ/mol, △V = 3mL/mol, and △Cp = 8.4
kJ/(moL*K) during the phase change. (15%)
(A) Calculate w, △S, △U, △G, and △H for converting 1 mol of A from α to β
at 70℃ and 1 atm. Assume that Cpα and Cpβ are indep. of temperature.
(B) Calculate △S, △G, and △H for the phase change of 1 mol of A at 25℃ and
1 atm.
4. Some of the thermodynamic properties of ice are: Cp = 36.2 J/(K*mol), Vm =
19.6 mL/mol, α = 1.6*10^(-4) K^(-1), △fusH = 6.0 kJ/mol. The density of
liquid water is 1.0g/mL. Assume these parameters do not change with T and P.
(15%)
δP Cp 1 δV
(A) Prove: (──) = ───, where α = ─(──) .
δT S T*V*α V δT P
(B) Find the P-T relation for the adiabatic, reversible compression of an ice.
(C) Find the melting point of ice.
(D) If the pressure on the ice, originally at -2℃ and 1 atm, is increased
adiabatically and reversibly until the ice melts. Find the temperature
and pressure at this melting point.
5. The excess volume (VE = △mixV - △mixV(ideal)) of mixing propionic acid
with oxane at 40℃ is: VE = x1*x2*[a0 - a1*(x1 - x2)], where x1 is the mole
fraction of propionic acid, x2 that of oxane, a0 = -2.47 mL/mol, a1 = 0.061
mL/mol. The density of propionic acid at 40℃ is 0.972 g/mL, that of oxane
is 0.864. (15%)
(A) Derive an expression of the partial molar volume for each component at 40℃
(B) Find the partial molar volume for each component in an equimolar mixture.
(C) What will be the molar volume for an equimolar mixture when the solution
behaves ideally?
x1
6. The osmotic coefficient, ψ, is defined as ψ = -(─)*㏑a1. The osmotic
x2
coefficient of N-methylacetamide (component 2) in n-nonane (component 1; M1
= 0.128 kg/mol) is given by: ψ = 1 -0.50m + 0.24m^2 - 0.12m^3, where m
is the molality of N-methylacetamide in n-nonane. (15%)
(A) Show that the activity of n-nonane for a dilute solution is given by: ㏑a1
= -M1*(m - 0.50m^2 + 0.24m^3 - 0.12m^4).
(B) Show that the activity coefficient of N-methylacetamide for a dilute
solution is given by: ㏑γ2 = -1.0m + 0.36m^2 - 0.16m^3.
x1 m g-1 ㏑a1
[hint: use d㏑a2 = -─*d㏑a1 or ㏑γ2 = ∫(──)dm + (g-1), where g = ──
x2 0 m ㏑x1
to prove it]
(C) Find γ2 for 0.2m solution of N-methylacetamide in n-nonane.
7. The vapor pressure data for the SiCl4(l)-CCl4(l) system at 25℃ are given
below. Calculate the following properties for the solution with: (20%)
╭──────────────┬──┬──┬──╮
│x(SiCl4) in liquid │ 0│0.48│ 1.0│
├──────────────┼──┼──┼──┤
│x(SiCl4) in vapor │ 0│0.65│ 1.0│
├──────────────┼──┼──┼──┤
│Total vapor pressure (torr) │ 115│ 166│ 238│
╰──────────────┴──┴──┴──╯
(A) Find the activities and activity coefficients of SiCla and CCl4. Assume
that the vapor behaves ideally.
(B) What will be the total vapor pressure above the solution if the solution
obeys Raoult's law?
(C) Find △mixG for 10 moles of the solution at 25℃
(D) Find △mixS for 10 moles of the solution at 25℃
(E) Find the excess free energy GE and excess entropy SE for 10 moles of the
solution at 25℃.
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