Question

Use the 2^nd Law to determine whether the freezing of supercooled water (i.e. in the liquid phase) at -4 ºC is spontaneous.

Hints: The entropy change of the surroundings is equal to –q_{sys, actual}/T, while the entropy change of the system must be determined by finding a reversible path. When are phase transitions reversible?

Answer 1

dSuniverse > 0 for spontaneous process

then

dSsystem + dSsurroundings > 0

dSsystem = dSsolid - dSliquid = -22.0 J/K-mol

dSsurroundings = Q/T

T = -4°C = -4+273 = 269 K

Q = Qlost =- Qsystem =-Hsystem = - Hfusion = -(291.83) kJ/mol = 291830 J/molK

dS = 291830 /269

dS = 1084.86

then

Get dSuniverse

dS univ = dSsystem + dSsurroundings

dS univ = 1084.86 -22.0 = 1062.86

since this is positive, this is possible (forward process)

Phase transitino is reverseible whenever

T > 0°C or T > 273