Physical equilibria: pure substances 자연과학대학 화학과 박영동 교수

Physical equilibria: pure substances 5.1 The thermodynamics of transition The condition of stability The variation of Gibbs energy with pressure The variation of Gibbs energy with temperature 5.2 Phase diagrams Phase boundaries The location of phase boundaries Characteristic points The phase rule Phase diagrams of typical materials The molecular structure of liquids

The condition of stability When an amount dn of the substance changes from phase 1 with G m (1) to phase 2 with G m (2), G i = n 1 G m (1) +n 2 G m (2) G f = (n 1 - dn)G m (1) +(n 2 +dn) G m (2) ΔG < 0 to be spontaneous if G m (2) > G m (1), dn < 0; 2 →1 if G m (2) 0; 1 →2 if G m (2) = G m (1), at equilibrium n1n1 n2n2 phase 1 phase 2 n 1 - dn n 2 + dn phase 1 phase 2 ΔG = {G m (2) − G m (1)}dn

Pressure dependence of G G = H – TS dG = dH – TdS – SdT = Vdp - SdT For liquid or solid, ΔG = VΔp For vapor, ΔG = ∫Vdp = nRT ∫(1/p)dp =nRT ln(p f /p i ) ΔG m = RT ln(p f /p i )

Standard Gibbs Energy, ΔG ⦵ (p)

Calculate the Vapor pressure increase of water, when the pressure is increased by 10 bar (Δp = 1.0 × 10 6 Pa) at 25°C. water: density g cm -3 at 25°C, molar volume 18.1 cm 3 mol -1. G m,i (l) G m,i (g) water, p 1 = 1 bar vapor, p i G m,f (l) G m,f (g) water, p 2 = 11 bar vapor, p f

Temperature dependence of G G = H – TS dG = dH – TdS – SdT = Vdp - SdT ΔG m = -S m ΔT For liquid or solid, 1. S m > 0, so G will decrease as T increases. 2. S m (s) < S m (l) <<S m (g)

Phase Diagram G FH GHF DBECA

Vapor pressure

Vapor pressure and Temperature

Cooling and Thermal Analysis

The location of phase boundaries and Clapeyron equation dG m (1) = V m (1)dp − S m (1)dT dG m (2) = V m (2)dp − S m (2)dT dG m (1) = dG m (2),

p vap (T ) and Clausius–Clapeyron equation

The significant points of a phase diagram

(a) Use the Clapeyron equation to estimate the slope of the solid–liquid phase boundary of water given the enthalpy of fusion is kJ mol −1 and the densities of ice and water at 0°C are and g cm −3, respectively. Hint: Express the entropy of fusion in terms of the enthalpy of fusion and the melting point of ice. (b) Estimate the pressure required to lower the melting point of ice by 1°C.

Usual and Unusual Substances

The phase rule, F=C-P+2

Water - phase diagram

Water

carbon dioxide

helium-4 superfluid flows without viscosity

열역학 제 1 법칙은 많은 사실에 적용된다. 전압이 1.2V 인 어떤 건전지가 있 다. 이 전지가 1A 의 전류로 1 시간 동안 소형 모터를 작동하는데 사용되었다. a. 이 건전지의 일을 계산해 보시오. b. 이 건전지의 내부에너지 변화를 계산해 보시오.

다음과 같은 관계가 C p 와 C v 사이에 성립한다. 이는 또한 다음과 같이 표현할 수도 있다. 이 사실을 이용하여 van der Waals 기체에 대하여 다음 사실을 밝히 고, 이 값을 CO 2 기체에 대하여 25 ℃, 1 기압에서 계산해 보시오.