[theguywhoisnottheguy]

I am trying to calculate the molar volume of a gas based on their Van Der Waals radii and calculated radii, and am coming up with issues. First of all, what is the difference between these two radii, and which is more accurate? For example, the Van Der Waals radii of helium is 140pm, but its calculated radii is 31pm. From what I have read, the calculated radii is based on a computer simulation, but I am still not sure which is accurate. Despite this, I have tried to calculate the molar volume of both, and consistently get numbers vastly larger than the actual volumes. The way I am doing this is by plugging a radius into the volume of a sphere formula (4/3*pi*r^3) and then multiplying by Avogadro's constant(6.022*10^23). Using my helium example, I got the value of 3.893micrometers^3/mol for calculated and 751.5nm^3/mol for the Van Der Waals radii. The actual volume, according to wolfram, is .02242m^3/mol. I think my issue is that I am assuming the molecules are as close together as physically possible without bonding. I am not allowed to use the ideal gas law or the Van Der Waals equation in these calculations. Can anyone explain what I am doing wrong in these calculations, and given my limitations, if there is a way to determine them to a reasonable level of accuracy? Assume that the gasses are in STP.

[AWK]

VDW radii give you a good approximation of volume in the solid state (eg solid helium).

[theguywhoisnottheguy]

That is about what I figured, is there any way to account for this without using the VDW equation or ideal gas law?

[fledarmus]

You're looking at at least two, and possibly three, very different things. I'm not sure what you mean by "calculated radii" or what assumptions were made for the calculation, so I will stick to the other two.

The number you have given as the "actual volume, according to wolfram (who is wolfram?)" is 22.4 L/mol, which is the space occupied by one mole of an ideal gas at standard temperature and pressure. Note - this is the space occupied, not the actual volume of the molecules - everything between the molecules is empty space that the molecules are flying around in.

What you are trying to calculate using the Van der Waals radii is how close molecules can be packed together. Calculating the total volume using this radius would give you the volume occupied by a condensed solid form of helium, where all of the molecules are as close together as possible and there is no space between them. This should be very different from the volume occupied by the gas phase. Solids occupy much less volume than the gaseous form of the same material.