Clausius-Clapeyron equation
The Clausius-Clapeyron equation was developed by Émile Clapeyron in 1834 and later derived from the theories of thermodynamics by Rudolf Clausius . It is a special form of the Clapeyron equation (derivation there). The course of the boiling point curve can be calculated using the Clausius-Clapeyron equation , i.e. H. the phase boundary line of a phase diagram between the liquid and the gaseous phase of a substance .
Thermodynamically correct equation
The thermodynamically correct version of the equation is
With
- - vapor pressure
- - temperature in K
- - Molar enthalpy of evaporation (index for evaporation or English vapor = vapor ) and
- - Change in molar volume between gaseous and liquid phase.
Approximation in the case of an ideal gas
As a rule, the Clausius-Clapeyron equation is the approximately valid equation
With
Derivation:
Since for most purposes the molar volume of the gas is significantly larger than that of the liquid:
the volume difference was expressed by the molar volume of the gas compared to the thermodynamically correct equation :
In addition, an ideal gas was assumed for the gaseous phase , for which the following equation of state applies:
Integrated form
If the enthalpy of vaporization of a substance is considered to be constant over a small temperature range ( up to ), the Clausius-Clapeyron equation can be integrated over this temperature range. Then:
With
- the known saturation vapor pressure and the temperature of the initial state,
- the pressure and temperature of the state to be calculated.
Web links
- Video: Vapor pressure of pure substances according to Clausius-Clapeyron - How comfortable does a component feel in a phase? . Jakob Günter Lauth (SciFox) 2013, made available by the Technical Information Library (TIB), doi : 10.5446 / 15670 .
literature
- MK Yau, RR Rogers: Short Course in Cloud Physics, Third Edition , Butterworth-Heinemann, January 1989, 304 pages. ISBN 0-7506-3215-1 .
- Gerd Wedler : Textbook of Physical Chemistry: Fifth, completely revised and updated edition , Wiley-VCH Verlag GmbH & Co. KGaA, August 2004, 1102 pages. ISBN 3527310665