5. The heat of vaporization of a liquid may be obtained from the following equat
ID: 557551 • Letter: 5
Question
5. The heat of vaporization of a liquid may be obtained from the following equation: In p, 1 1 T-T, P (This is an approximated integrated form of the Clausius-Clapeyron equation.) The vapor pressure of water at different temperature is given in the following table: 9.2 Torr 110.0c 55.3 Torr 40.0 (a) Calculate H (b) Considering the error (rmsd) to be 0.1 K and 0.1 Torr in the measurement of the temperature and pressure, calculate the error (rmsd) AH and report the value in ± z format with proper unit.Explanation / Answer
Clausius-Clapeyron equation,
ln(P2/P1) = dH/R[1/T1 - 1/T2]
a) with,
P1 = 9.2 torr ; P2 = 55.3 torr
T1 = 10oC + 273 = 283 K ; T2 = 40oC + 273 = 313 K
we get,
ln(55.3/9.2) = dH/8.314[1/283 - 1/313]
dH = 44.03 kJ/mol
(b) error calculation
with maximum
P1 = 9.2 + 0.1 torr ; P2 = 55.3 + 0.1 torr
T1 = 10.1oC + 273 = 283.1 K ; T2 = 40.1oC + 273 = 313.1 K
we get,
ln(55.4/9.3) = dH/8.314[1/283.1 - 1/313.1]
dH = 43.84 kJ/mol
with minimum
P1 = 9.2 - 0.1 torr ; P2 = 55.3 - 0.1 torr
T1 = 9.9oC + 273 = 282.9 K ; T2 = 39.9oC + 273 = 312.9 K
we get,
ln(55.4/9.3) = dH/8.314[1/283.1 - 1/313.1]
dH = 44.22 kJ/mol
dH = 44.03 +/- 0.19 kJ/mol
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