Question

The vapor pressures of SO₂(s) and SO₂(l) in the vicinity of the triple point are given by the equations, Ln (P/torr) = 23.9812 - 4244.7/T and Ln (P/torr) = 19.2453 - 3298.4/T, respectively, where T is absolute temperature. (i)Determine from these equations the three phase change enthalpies, ∆_subH°, ∆_vapH° and ∆_fusH°.

Answer 1

Recall that in equilibrium; especially in vapor-liquid equilibriums, we can use Clasius Clapyeron combination equation in order to relate two points in the same equilibrium line.

The equation is given as:

ln(P2/P1) = -dHvap/R*(1/T2-1/T1)

Where

P2,P1 = vapor pressure at point 1 and 2

dH = Enthalpy of vaporization, typically reported in kJ/mol, but we need to use J/mol

R = 8.314 J/mol K

T1,T2 = Saturation temperature at point 1 and 2

Therefore, we need at least 4 variables in order to solve this.

Substitute all known data:

ln(P2/P1) = -dHvap/R*(1/T2-1/T1)

Therefore, we can get Hphase/R from the slopes:

Ln (P/torr) = 23.9812 - 4244.7/T

Ln (P/torr) = 19.2453 - 3298.4/T

Slope 1 = 4244.7

Slope 2 = 3298.4

Hs1 = 4244.7*8.314 = 35290.4 J/mol

Hs2 = 3298.4*8.314 = 27422.89 J/mol

note that

Hs1 = solid/vapor; Hs2 = lqidui/vapor

Hliqud-solid = 35290.4 - 27422.89 = 7867.51

then

Hvap = 27422.89 J/mol = 27.42 kJ/mol

Hfus = 7867.51 J/mol = 78.67 kJ/mol

Hsub = 35290.4 J/mol = 35.29  kJ/mol