112年 - 112 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)#148000

(a) Dalton’s Law of Partial Pressure

(b) Law of Corresponding States

(c) Efficiency of aReversible Carnot Engine

(d) Arrhenius Equation

(e) Phase Rule

(a) q,

(b) w,

(c) ΔG,

(d) ΔH,

(e) ΔU and

(f) ΔS of this process, assuminghelium is an ideal gas.

3. (a) Derive the Gibbs-Helmholtz equation. (5%)

(b) The value of ΔGfo for Fe(g) is 370.7 kJ mol^-1 at 298.15 K, and ΔH_f^o for Fe(g) is 416.3 kJmol^-1 at the same temperature. Assuming that ΔH_f^o is constant in the interval 250 – 400 K,calculate ΔGfo for Fe(g) at 400 K. (5%)

4. Calculate the ΔmixG and Δ_mixS for the formation of a quantity of air containing 1 mol of gas bymixing nitrogen and oxygen at 298.15 K. Air may be taken to be 80% nitrogen and 20% oxygenby volume. (10%)

5. (a) Derive the Clausius-Clapeyron equation \( \ln \frac{P_2}{P_1} = \frac{\Delta_{vap}H}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right). \). (5%)

(b) Derive the van’t Hoff equation \( \frac{d\ln K_P^O}{d(\frac{1}{T})} = -\frac{\Delta H^O}{R} \). (5%)

(a) theequilibrium constants, and

(b) the enthalpy of dissociation per mole of HgO.

(a) For a 40 wt.% Sn-60 wt.% Pb alloy at150 °C (point B in the figure), what phase(s)is (are) present? What is (are) thecomposition(s) of the phase(s)? (10%)

(b) Calculate the mass fraction of each phasepresent. (10%)

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

(b) If a first-order reaction has an activation energy of 104,600 J mol-1 and a pre-exponentioalfactor A of 5 × 10¹³ s^-1, at what temperature will the reaction have a half-life of (a) 1 min and (b)30 days? (10%)