Standard Entropy of a liquid at melting point with no S(298.15) given

[DiffusConfuse]

Homework Statement

Vapour pressures of a liquid have been measured and fit to the following equation:
Log₁₀ P (mmHg) = -3571/T + 8.999
The melting point has been determined to be 392.7 K.
A Cp value given for the liquid is 250 J/mol K
and the ΔS_vap is 117.20 J/mol K

Homework Equations

Clausius Clapeyron:

ln(P₁/P₂)= ΔH/R*(1/T₂ - 1/T₁)

The Attempt at a Solution

T₁= 392.7 K P₁ = 0.8045 mmHg (from the equation, giving the vapour pressure of the LIQUID at the melting point).
T₂= 298.15 K P₂= 1.052E-3 mmHg

From the Clausius Clapeyron:

ln(0.8045 mmHg/1.052E-3 mmHg)= ΔH/R*(1/298.15 K - 1/392.7 K)

ΔH/R = 8221.89 K^-1
ΔH = 68361 J/mol

ΔH/T = ΔS = 68361/298.15 = 229.29 J/mol K

However the answer is 350.60 J/mol K.

I tried adding the ΔS_vap to the derived value (229.29+117.2) , however that only gives me 346.5 J/mol K

 

[unscientific]

Maybe this relation might be helpful: $L = T\Delta S = T(S_2 - S_1)$.

 

[DiffusConfuse]

I would use L= TΔS = 68361 J/mol = 229.29 J/mol K x 392.7 K
= 392.7(S₂-S₁),
At this point I am unsure what to use for S₂ to solve for S₁ or vice versa.