111年 - 111 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碩士班：物理化學 (含熱力學與動力學)#147919

(a) Law of corresponding states (b) Joule-Thomson coefficient (c) Chemical potential

(d) The second law of thermodynamic (e) Ideal solutions

2. Three moles of an ideal gas expand isothermally and reversibly from 90 L to 300 L at 300 K. Calculate the w, q, ΔH, ΔS, and ΔG for this system. (15%)

(a) A reaction A + B ↔ Z has an equilibrium constant of 4.5 × 10⁴ dm³ mol⁻¹ at 300 K, and a ΔH° value of -40.2 kJ mol⁻¹. Calculate the entropy change for the reaction at 300 K. (5%)

(b) If the ΔH° and ΔS° values are temperature independent, at what temperature is the equilibrium constant equal to 1? (5%)

4. The vapor pressure for pure water at 22.0 °C is 19.827 mmHg and at 30.0 °C is 31.824 mmHg. Use these data to calculate the change in enthalpy per mol for the vaporization process. (10%)

5. Calculate the mole fraction, activity, and activity coefficients for water when 11.5 g NaCl are dissolved in 100 g water at 298 K. The molecular weight of NaCl is 58.5 g mol⁻¹. The vapor pressure is 95.325 kPa. (15%)

(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? (10%)

7. A sample of milk kept at 25°C is found to sour 40 times as rapidly as when it is kept at 4°C. Estimate the activation energy for the souring process. (10%)

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

(b) A substance decompose at 600 K with a rate constant of 3.72 × 10⁻⁵ s⁻¹. Calculate the half-life of the reaction. (5%)

(c) What fraction will remain undecomposed if the substance is heated for 3 h at 600 K? (5%)