Question

Ethyl alcohol has a vapor pressure of 20.0mm Hg at 8.0 ° C and a normal boiling point of 78.4 ° C.Estimate the vapor pressure at 45 ° C using (a) the Antoine equation; (b) the Clausius – Clapeyronequation and the two given data points; and (c) linear interpolation between the two given points.Taking the fi rst estimate to be correct, calculate the percentage error associated with the secondand third estimates.

Answer 1

According to antoine equation vapor pressure and temperature is related by Antoine eqn as follows.

log P = A - B/(C+T) where A = 8.20417 B= 1642.89 C=230.300

At T= 45oc

Log P = 8.20417-1642.89/(230.300+45) = 2.24

P = 173.78 mm Hg

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By using Causius Clapeyron equation.

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

ln (760/20) = -Hvap/8.314 J/K/mol (1/351.4-1/281)

3.64 = -Hvap/ 8.314 J/K/mol *-7.13 *10^-4

Hvap = 3.64 * 8.314 J/K/mol/ 7.13 *10^-4 = 4.24 *10^4 J/mol

Using the value of Hvap , calculate the vapor pressure at 45oC

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

ln (760/P2) = - (-4.24 *10^4 J/mol)/ 8.314 J/K/mol [1/351.4-1/318]

or, ln (760/P2) = 1.50

or, P2 = 169.64 mm Hg

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Linear extrapolation of the two points is shown below.

According to the above graph the vapor pressure at 45oc is 400mm Hg.

Percet error in second estimate = 173.78-169.64 /173.78 *100 = 2.38 %

Percent error in third estimate = 400-173.78/173.78 *100 = 130%