Handbook of Solvents - George Wypych - ChemTech - Ventech!

244 Valery Yu. Senichev, Vasiliy V. Tereshatov
thermal losses, thus single-error corrections for the heat exchange can be used to increase
precision of measurement.
The calorimeters used for the measurement of the heat of reaction can also be used for
a measurement of the latent heat of vaporization. These are calorimeters for liquids, micro-calorimeters,
mass calorimeters, and double calorimeters. 7
The calorimeters with carrier gas are also used. 8-9 Evaporation of substance is accelerated
by a stream of gas (for example, nitrogen) at reduced pressure. The heat loss by a calorimeter,
due to evaporation, is compensated by an electrical current to keep temperature of
calorimeter constant and equal to the temperature of the thermostating bath.
5.1.1.2 Indirect methods of evaluation of evaporation enthalpy
Because the calorimetric methods of measurement of enthalpy of vapor formation are very
difficult, the indirect methods are used, especially for less volatile substances. The application
of generalized expression of the first and second laws of thermodynamics to the heterogeneous
equilibrium between a condensed phase in isobaric- thermal conditions is given in
the Clausius-Clapeyron equation that relates enthalpy of a vapor formation at the vapor
pressure, P, and temperature, T. For one component system, the Clausius-Clapeyron equation
has the form: 7
dP / dT =ΔH / TΔ V
[5.1.2]
p
where:
ΔV difference between molar volumes of vapor and liquid
The ratio that neglects volume of a condensed phase with assumption that vapor at low
pressure is ideal can be derived from the above equation:
( )
dln P / d 1 / T =−Δ H / R
[5.1.3]
After integration:
p
ln P =− Δ H / RT + const
[5.1.4]
p
Introducing compressibility factors of gas and liquids, ΔZ, the Clausius-Clapeyron
equation can be written as:
( )
dln P / d 1 / T =−ΔH / RΔ Z
[5.1.5]
p
where:
ΔZ difference between compressibility factors of gas and liquids
The value ΔZ includes corrections for volume of liquid and non-ideality of a vapor
phase. The simplifying assumptions give the equation:
ln P = A+ B / T
[5.1.6]
Approximate dependence of a vapor pressure on inverse temperature is frequently linear
but the dependence may also be non-linear because of changing ratio of ΔH p/ΔZ on heating.
The mathematical expressions of the dependence lnP on 1/T of real substances in a
wide range of temperatures should be taken into account. If ΔH p/ΔZ=a+bT,itresults in an
equation with three constants: