Question

Estimate the heat of vaporization of diethyl ether at its normal boiling point using Trouton’s rule and Chen’s rule and compare the results with a tabulated value of this quantity. Calculate the percentage error that results from using each estimation. Then estimate ΔH^v at 100°C using Watson’s correlation.

Answer 1

a)

Troutons rule:

dHvap / (R*Tb) = 10

so

dHvap = R*Tb*10

Tb = normal boiling point for diethyl ether = 307.4 K

R = ideal gas constant = 8.31 J/molK

dHvap = 8.314*(307.4)*10 = 25,557.236 J/mol

dHvap = 25.557 kJ/mol

b)

Apply Chen rule:

dHv = R*Tb*(3-974*(Tb/Tc) 3.958 + 1.555*ln(Pc)) / (1.07 - (Tb/Tc)

where, Tc and Pc are critical values

so

Tc = 466.7 K

Pc = 36.4 bar

Substitute data

dHv = (8.314*307.4) (3-974*(307.4/466.7) - 3.958 + 1.555*ln(36.4)) / (1.07 - (307.4/466.7)

dHva = 26400 J/mol

dHv = 26.4 kJ/mol

Actual value for Hvap is approx = 26.52 kJ/mol

for

%error = Real - Calcualted / real * 100

%error Trouton = (26.52- 25.57)/(26.52) * 100 = 3.6%

%error Chen = (26.52.-26.4)/(26.52) * 100 = 0.5 %

c)

Whatson correlation

dH 373 / dH 307 = ((1-Tr2) / (1-Tr1) ) ^0.38

Tr = reduced temperature i.e. Ti/Tc

Tr1 = 307.4/466.7 = 0.685

Tr2 = 373/466.7 = 0.80

So

dH at 373 = dH at 307 * ( 1-Tr2 ) /(1-Tr1)^0.38

dH @ 373 = 26.52* ( 1-0.08) / (1-0.658) ^0.38

dH @ 373 = 21.63 kJ