# Van der Waals diameter

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1. May 24, 2015

### mikeclinton

1. The problem statement, all variables and given/known data
Calculate the molecular diameter of hydrogen, assuming the spherical shape on the basis of van der Waals coefficients.

Van der Waals Coefficients for hydrogen
a = 0.244 atm L2.mol-2
b*103 = 26.6 L.mol-1

2. Relevant equations
Not indicated in the problem but I would think the Van der Waals equation of state.

3. The attempt at a solution
For hydrogen:
Since the constant b is an indication of molecular volume, it could be used to estimate the radius of an atom or molecule, modeled as a sphere. This leads to the following estimate of radius:

V = b/N = (26.6 x 10-6)/6.02*1023 (I have first converted b unit to m3/mol)
V = 4πr3/3
which gives r = 0.219nm
corresponding to a molecular diameter D = 0.438nm

I would like to know if my reasoning is correct; especially the equation V = b/N
I'm also confused about the inclusion of the a constant in the problem when it isn't needed as far as I know.

2. May 24, 2015

### BvU

Hello Mike,

I think what you did looks good. You can check it here with the simplest of all googles.
There it also explains the other coefficient has to do with attractive force among molecules -- and indeed isn't relevant.

3. May 28, 2015

### mikeclinton

Hi there, sorry for the late reply. Thank you for confirming my solution; I was starting to wonder if there was another shortcut that involves a...