Question

11. (15 Points) The Gibbs free energy of the solid phase and the liquid phase of a substance of one mole are shown (dashed lines) below as a function of T under a constant P- 10' N/m2. The molar volume of the solid and of the liquid are 18 x 103 m/mole and 2.0 x 10 m'/mole, respectivel (a) If one mole of the liquid transforms to the solid under a constant P 10 N/m2, calculate the c hanges of A, ΔΗ, and Δυ. (b) The Gibbs free energy also changes with pressure. Briefly sketch the curve of G vs. P for the solid and liquid phases near 300 K. r or second order phase transition? 2.0 1.9 1.8 1.7 A 1.6 solid liquid 280 300 320 T(K)

Answer 1

The Gibbs free energy of the solid phase and the liquid phase of a substance of one mole are shown (dashed lines) above as a function of T under a constant (P).

(a) If one mole of the liquid transforms to the solid under a constant (P), calculate the changes of $\Delta$S, $\Delta$H and $\Delta$U.

The change in an entropy which will be given by -

$\Delta$S = $\Delta$Q / T

$\Delta$S = [(1.8 x 10³ J) / (300 K)]

$\Delta$S = 6 J/K

The change in an enthalpy which will be given by -

$\Delta$G = $\Delta$H - T $\Delta$S

(1.8 x 10³ J) = $\Delta$H - [(300 K) (6 J/K)]

(1.8 x 10³ J) = $\Delta$H - (1.8 x 10³ J)

$\Delta$H = [(1.8 x 10³ J) + (1.8 x 10³ J)]

$\Delta$H = 3.6 x 10³ J

$\Delta$H = 3.6 kJ

The change in an internal energy which will be given by -

$\Delta$U = T $\Delta$S

$\Delta$U = [(300 K) (6 J/K)]

$\Delta$U = 1800 J

$\Delta$U = 1.8 kJ

(c) What is the order of this phase transition?

$\Rightarrow$ First order phase transition

Explanation : We know that, phase transitions from daily experience, water evaporates, water freezes, and materials boil or evaporate. A system under constant pressure and temperature conditions where virtually all phase transitions occur, is best described by the Gibbs free energy. The minima correspond to the liquid and the solid phase, respectively. The system in an equilibrium will always the state of lowest Gibbs free energy. Both phases have different molar volumes.