113年 - 113 國立宜蘭大學_碩士班考試入學招生試題_化學工程與材料工程學系：物理化學 ( 含熱力學與動力學)#147927

1. Explain the following items: (20%)

(a) Ideal gas (b) The first law of thermodynamics (c) The second law of thermodynamics
(d) The critical point (e) Phase Rule

2. One mole of an ideal gas at 300 K is reversibly and isothermally compressed from a volume of 25.0 L to a volume of 10.0 L. Calculate the (a) q, (b) w, (c) ΔU, (d) ΔG, and (e) ΔS of this process. (20%)

3. A sample containing 2.25 moles of He (1 bar, 298 K) is mixed with 3.00 moles of Ne (1 bar, 298 K) and 1.75 moles of Ar (1 bar, 298 K). Calculate the ΔSmixing value. (10%)

(a) Derive the Clausius-Clapeyron equation $$\ln \frac{P2}{P1} = \frac{\Delta{vap}H}{R} \left( \frac{1}{T1} - \frac{1}{T_2} \right).$$ (5%)

(b) The vapor pressure of liquid SO₂ is 2,232 Pa at 201 K, and ΔHvaporization is 24,940 J mol⁻¹. Calculate the temperature of SO₂ at 101,325 Pa. (10%)

5. For the reaction N₂(g) + 3H₂(g) ↔ 2NH₃(g), K = 1.60 × 10⁻⁴ at 400 °C. Calculate the ΔG° of the reaction. (10%)

(a) Calculate the ratio of the mass of the water-rich layer (L₁) to that of the aniline-rich layer (L₂), for a 20-wt% water-aniline mixture at 363K. The compositions along the tie line be are maintained at 363K. The composition at c is 20%; for L₁ at b, it is 8%; and for L₂ at e, it is 90%. (5%)

(b) What are the compositions of L₁ and L₂ at this temperature? (5%)

(a) Derive the half-life of a first-order reaction is $$t_{1/2} = \frac{\ln 2}{k}.$$ (5%)

(b) The half-life for the first-order decomposition of N₂O₅ is 2.05 × 10⁴ s. What is the rate constant for the decay reaction? (5%)

(c) How long will it take for a sample of N₂O₅ to decay to 60% of its initial value? (5%)