Question

t-butyl alcohol: T_m = 25.3 ⁰C, mw = 74.12

Temperature (0C)	P (mm Hg)
-20.4 5.5 24.5 39.8 68.0 82.9 102.0 130.0 154.2 184.5 222.5	1 10 40 100 400 760 1520 3800 7600 15200 30400

How can you determine the boiling point of this compound from these data?

Using these data, calculate DH_vap (in kJ/mol), DS_vap (in J/mol.K), DH_melt, and DS_melt. Also, determine the vapor pressure (in atm.) of the solid at 20 0C, as well as the vapor pressure of the hypothetical subcooled liquid at this temperature.

c) How do your calculated values in section (B) above compare with what you might predict? (Show all details of your calculations in making these predictions). Feel free to use more than one technique, if appropriate, in making these estimates; if you can compute more than one estimate, indicate which estimate (assuming that you didn’t already know the true value) you might have been most inclined to trust and why. Rationalize any discrepancies between estimated and actual values.

Answer 1

a) Boiling point determination using Calusius-Clapeyron equation,

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

let, T1 = normal boiling point

T2 = 102 oC = 102 + 273 = 375 K

P1 = 760 mmHg

P2 = 1520 mmHg

R = 8.314 J/K.mol

Feed values,

ln(1520/760) = 46.69 x 1000/8.314 [1/T1 - 1/375]

0.693 = 5615.83[1/T1-0.0027]

T2 = 358.411 K

boiling point of compound = 81.20 oC

deltaHvap from graph

plot lnP on y-axis and 1/T (K-1) on x-axis

slope = -deltaHvap/R = -4165

deltaHvap = 4165 x 8.314 = 34.63 kJ/mol

deltaSvap = deltaHvap/T = 34.63 x 1000 / 25.3+273 = 116.10 J/K.mol

deltaHmelt = -34.63 kJ/mol

deltaSmelt = -116.10 J/K.mol

using Calusius-Clapeyron equation,

ln(760/P1) = 34630/8.314[1/20+273 - 1/82.2+273]

P1 = 63.04 mmHg is the vapor pressure at 20 oC

c) The actual value for boiling point of t-BuOH = 82.20 oC

experimental found value = 81.20 oC

So we have an error = 82.20-81.20 = 1.0 oC

% error = 1/82.2 x 100 = 1.21 % in boiling point determination.