van der Waals Equation of State

The Dutch physicist, Johannes Diderik van der Waals(1837-1923) received a 1910 Nobel Prize for his work on the equation of state for gases and liquids.  Johannes father was a carpenter so he could only afford to send Johannes to primary school.  Back then in the Netherlands, learning the classical languages was one of the prerequisites for entering university and Johannes had not learnt the languages.  Although Johannes was not allowed to take university classes, he studied at the Leiden University from 1862-1865 and he obtained teaching certificates in physics and math.  At the age of 36 van der Waals completed his Ph.D. when a new legislation passed that stated that science students could be enrolled in university without having the classical language requirement.  In van der Waals paper, “On the continuity of the gas and liquid state” he introduced the equation of state that has been used in physics and chemistry today.


Johannes van der Waals modified the ideal gas law, which assumes that molecules are very very very small and that they have no forces acting between them, which is the following equation:

PV = nRT

Where P is the pressure
V is the volume of the container
n is the number of moles of gases present in the container
R is the universal gas constant
T is the temperature

van der Waals came to the conclusion that the actual pressure felt by the container would be less if the molecules hitting the walls are pulled back due to the attraction by other molecules.  As well, that the actual volume available for the gas molecules would be less as the molecules have a finite size and occupy some volume. Therefore, the ideal gas law would have to work when P is increased and V is decreased.  He then introduced two constants a and b (van der Waals parameters) to make the following "van der Waals Equation of State":

The volume occupied by the gas molecules is directly proportional to the number of moles and the pressure depends on the square of n/V, the number of moles per unit volume.

Change of mind... and Raoult's Law

Hello everyone!

So, just recently I decided to change the topic of my blog.  I thought just talking about the basics of organic chemistry was kind of dull and boring.  I got the idea from a classmate (Lindsay Jmaiff) about talking about chemical equations, formulas, laws and theorems and the famous scientists who came up with them.  I believe that this topic will be much more interesting by giving everyone a little insight about some major formulas and equations that are used in everyday chemistry.

To begin, I would like to discuss a fairly simple law which is “Raoult’s Law”.  The “Raoult Law” was developed by the french chemist, Francois-Marie Raoult(1830-1901) in 1882.  Francois-Marie Raoult started the developement of the Raoult Law by carrying out a set of experiments and he studied the vapor pressure of a number of binary solutions that contained volatile and non-volatile electrolye solutes.


This law states that the vapor pressure of a solution is dependent on the vapor pressure of each of the chemical components and the mole fraction of the components present in the solution.  There are a number of different ways of expressing this law, it all depends on the situtaion given. The following is the most common expression for "Raoult's Law":

P_solvent = X_solventP^o_solvent

Psolvent represents the vapor pressure of a solvent of a non-volatite solute
Xsolvent represents the mole fraction of the solvent
P^osolvent represents the vapor pressure of a pure solvent at a certain temperature


Just one last quick note, "Raoult's Law" only works for ideal solutions.  An ideal soluiton is a mixture of substances that has physical properties that are related to the properties of the pure components.  In this case, it is important to remember that it works for highly diluted solutions and solutions that have the molecules of a solute and solvent being the same as the interaction between the molecules and the mixture itself.