Solid property of inert gas- LJ potential

[ibysaiyan]

Homework Statement

Hi,
We meet again PF, this time I am little stumped on the following question(link posted down).

Homework Equations

Link to the question

"Question"

The Attempt at a Solution

I think I get the gist of it for part (i) my calculated value for equlibirum separation is about 0.32nm which seems sensible... now carrying on to part two where basically they want me to use the given equation for : The term molar volume is a little vague to me..the value i get on part (i) is about 19.9 cm^3... is that right ? so do I just plug that into the equation or do I convert it into m^3 or simply meter? (this is something i cam confused about).

Thanks
-ibysaiyan

 

[ibysaiyan]

Anyone please ?

Here's the question :
http://pastebin.com/HazHGdZh

 

[ehild]

I think I get the gist of it for part (i) my calculated value for equlibirum separation is about 0.32nm which seems sensible... now carrying on to part two where basically they want me to use the given equation for : The term molar volume is a little vague to me..the value i get on part (i) is about 19.9 cm^3... is that right ? so do I just plug that into the equation or do I convert it into m^3 or simply meter? (this is something i cam confused about).

How did you get 19.9 cm^3 for the molar volume?
If you plug in the molar volume in cm^3 into the equation, you get the interatomic distance in cm.

ehild

 

[ibysaiyan]

How did you get 19.9 cm^3 for the molar volume?
If you plug in the molar volume in cm^3 into the equation, you get the interatomic distance in cm.

ehild

On wiki it said : Molar volume = Molecular mass/ density...
so I simply plugged in the values : 39.95 / 1.8 to give me 22.2 cm^3..
but to get the separation distance at equlibirum using : Vm = Na * r0^3 / √2
I converted Molar volume into m^3... i.e (22.2/100)^3 = 10.92*10^-3 (m^3)

There are basically two answers for the separation distance.. one i get is 0.32nm and other using above equation is 2.9nm

 

[ehild]

So the molar volume is 22.2 cm^3, that is correct. The first question asks you to determine the interatomic distance assuming simple cubic structure. In that case the atoms sit on the vertexes of the unit cells. The unit cells are cubes and there are Na such cubes in the molar volume and the edge of such cub is the cubic root of its volume.
You need to use the other formula when answering the second question.

ehild

 

[ibysaiyan]

So the molar volume is 22.2 cm^3, that is correct. The first question asks you to determine the interatomic distance assuming simple cubic structure. In that case the atoms sit on the vertexes of the unit cells. The unit cells are cubes and there are Na such cubes in the molar volume and the edge of such cub is the cubic root of its volume.
You need to use the other formula when answering the second question.

ehild

Certainly , that is exactly what I have done . For party two using the formula given I get a value of about 8 times larger than part one, is that reasonable ?

 

[ehild]

Certainly , that is exactly what I have done . For party two using the formula given I get a value of about 8 times larger than part one, is that reasonable ?

No, it is wrong. Show your calculation in detail.

ehild

 

[ibysaiyan]

No, it is wrong. Show your calculation in detail.

ehild

Sure.

[itex]V_{m}[/itex] = 22.2 [itex]cm^{3}[/itex] which I have converted into m^3 .. (22.2/100)^3 = 10.92*10^-3 m^3

Formula given is:
[itex]V_{m}[/itex] = Na * r0^3 / √2
which gives me about 2.9nm

 

[ehild]

[itex]V_{m}[/itex] = 22.2 [itex]cm^{3}[/itex] which I have converted into m^3 .. (22.2/100)^3 = 10.92*10^-3 m^3

That is totally wrong... 1 cm =0.01 m, 1 cm^3=10^-6 m³, so 22.2 cm³=22.2x10^-6 m.

The correct procedure for the transformation would be

22.2 cm³= 22.2( cm*m/(100 cm))³

ehild

 

[ibysaiyan]

That is totally wrong... 1 cm =0.01 m, 1 cm^3=10^-6 m³, so 22.2 cm³=22.2x10^-6 m.

The correct procedure for the transformation would be

22.2 cm³= 22.2( cm*m/(100 cm))³

ehild

What was I thinking, the above conversion which I was doing doesn't make any sense.. had I took cube root of that then it would have given me a value in meters.
Thanks for all your help.

Happy new year to you and to the rest of the users.

 

[ehild]

Happy New Year to you, too.

ehild