[試題] 106-1 陸駿逸 物理化學一-熱力學 期末考
課程名稱︰物理化學一-熱力學
課程性質︰化學系大三必修
課程教師︰陸駿逸
開課學院：理學院
開課系所︰化學系
考試日期（年月日）︰106/1/9
考試時限（分鐘）：120
試題 :
(1) (14 pts) To calculate the rotation partition function of the gas correctly,
one needs the symmetry number of the gas molecule. What are the symmetry
numbers for (a) CO2, (b) CHCl3?
(2) (6 pts) What is the maximum number of phases that can be in mutual
equilibrium in a three-component system?
(3) (15 pts) Given the following standard potential at 25°C
Sn(4+) + 2 e(-) → Sn(2+) E°= +0.15V
Sn(2+) + 2 e(-) → Sn E°= -0.14V
Calculate the equilibrium constant of the reaction
Sn(s) + Sn(4+)(aq) ←→ 2 Sn(2+)(aq) at 25°C.
(4) (15 pts) What is the meaning of the upper critical temperature (UTC) for
the phase diagram of a two-component system? What is the general molecular
explanation to expect the UTC in the phase diagram?
(5) (15 pts) Derive the lever rule n_α·l_α = n_β·l_β where n_α and n_β
are the amounts of the two phases, and l_α and l_β are the distances on
the phases diagram?
(6) (20 pts) The equilibrium constant of a reaction is found to fit the
expression ln K = A + B/T +C/T^2 between 300K and 600K with A = -1.04,
B = -1088 K, C = 1.51 x 10^5 K^2. Calculate the standard reaction enthalpy
and the standard reaction entropy at 500K.
(7) (25 pts) Argon has the molecular potential
σ σ
V(R) = 4 [ ( —— )^12 - ( —— )^6 ]
R R
where σ = 3.4 x 10^(-10) m, ε = 1.7 x 10^(-21) J. (a) Estimate the van
der Waals parameters a and b, where a = -1/2 ∫_(attraction) V(R) d^3 R
and b is one-half of the excluded volume.
(Hint : 4 ∫ [1,∞] 4πx^2 ( x^(-12) - x^(-6))dx = -32π/9)
(b) Estimate the critical temperature, the critical pressure, and the
critical density.
(8) (20 pts) Given that K_sp = 2.4 x 10^(-5) of CaSO4 at 25°C, (a) what is
the solubility in g/L? (M = 136.1 g/mol) (b) What is the Debye length in
the saturated solution? (c) Consider the activity coefficient using the
Debye-Huckel theory, what is the more accurate solubility?
(Hint : log γ_± = -A | z_+·z_- | I^(1/2) where A = 0.509.)
R = 8.314 J K^(-1) mol^(-1),
k_B = 1.38 x 10^(-23) J K^(-1),
ε_0 = 8.854 x 10^(-12) C^2 N^(-1) m^(-2),
ε_r of water = 710 C^2 N^(-1) m^(-2),
F = 96500 C mol^(-1)
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