EoS: Intermolecular Potentials and Equations of State

Intermolecular Potentials and Equations of State

We are now ready to build EoS based on our understanding on intermolecular interactions.

Note

Intermolecular interactions are at least pairwise, therefore, as $v$ decreases binary interactions are the first ones to become important

pairwise interactions

The number of pairwise interactions scales with the number of molecules as follows:

# of pairwise interactions per molecule = $\left ( N-1 \right )$

total # of pairwise interactions = # of pairwise interactions per molecule X # of molecules

total # of pairwise interactions = $\left ( N-1 \right )xN \approx N^2$

Note

Since the number of pairwise interactions increases with decreasing $v$ -- total # of pairwise interactions $\propto \frac{1}{v^2}$

Revisiting our friend the van der Waals equation, we can then write:

$P = \frac{RT}{v-b} - \frac{a}{v^2}$

Question?

Why do we "correct" P? Why is that "correction" negative?

We could also write this as:

$v^3 - \left (\frac{RT+Pb}{P}\right )v^2 + \left (\frac{a}{P}\right )v - \frac{ab}{P} = 0$

Outcome

Explain how the terms in the van der Waals equation relax these assumptions

Outcome

Describe how cubic equations of state account for attractive and repulsive interactions