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van der Waals contants and Heat of Evaporation

Posted 10 months ago
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In the notebook attached a procedure is given to calculate the heat of evaporation of a substance from its van der Waals constants.

The notebook basically has three parts. In part 1 the single steps are outlined and explained, in part 2 all these steps are integrated into a single function and in part 3 some caluclations are performed.

It seems that the results are "always" wrong by a factor of about two, and I would like to ask the community to do many more calculations ( perhaps someone has access to databases with vdW-constants and heats of evaporation) to verify this finding.

Johannes Diderik van der Waals devised his equation in 1873 ( and got the Nobel Prize in 1910 ) to describe the behaviour of real gases. Somewhere I read that he already knew that his equation wasn't more than a crude approximation, but unfortunately I forgot the site where this statement is given. Anyhow, his equation can be interpreted to describe the two-phase-equilibria of gases and the existence of a critical point.

The main point is that for certain temperatures the p,V-curves have a maximun and a minimum, and the equlibrium pressure for one of these temperatures is given by the condition that the blue and red area are equal.

![pV-curve for gas-liquid equlibrium][1]

I tried to find the equlibrium - pressure with FindRoot and / or Reduce, but often these failed by giving complex results, so I decided to use an "old-fashioned" bisection, with which I never encountered any problems.

Having the ( equilibrium pressure, temperature ) data the heat of evaporation is found by using the Clausius-Clapeyron equation.


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