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# how to calculate average spacing between atoms/molecules?(physics) help please Watch

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1. Is it possible to calculate the spacing between atoms using the formula:

(1/x)^3 = total number of molecules, where "x" is the spacing between atoms?

In the textbook (the physics OCR A2 Heinemann) on page 60/61, that given the density of water (in its three states of matter, solid liquid and gas). We know the density of water in each state. e.g. for gas it is 0.59kgm^3. This tells us that 0.59kg of gas molecules occupies 1m^3 of volume. ofcourse, since we know the mass of an individual molecule we can calculate the total number of molecules.
0.59/(mass of an individual molecule) = total number of molecules.

Hence we would have the total number of molecules in 1m^3.

However it then goes on to say that the average spacing between molecules can be worked out using (1/x)^3 = total number of molecules, where "x" is the spacing between atoms

Just cube root both sides and you get the total number of molecules on one edge, which would have length 1 metre.

But how is it possible that "x" can be the average spacing between the molecules?

I donot understand this point, especially when I try and illustrate it.

Thank you
2. first stop looking at textbooks to find formulas and try prove it yourself. it'll lead to a much better understanding in the long term.

to make it easier assume the atoms are spaced out in a cubic sort of fashion.

draw a diagram and go on from there. diagrams should always be the first thing you do when you approach a problem, not the last.
3. Can't you just use a ruler?
4. Visualise the molecules as identical perfect spheres

It is then helpful to realise that the average spacing between molecules is the same as the diameter of one sphere.
5. (Original post by didgeridoo12uk)
first stop looking at textbooks to find formulas and try prove it yourself. it'll lead to a much better understanding in the long term.

to make it easier assume the atoms are spaced out in a cubic sort of fashion.

draw a diagram and go on from there. diagrams should always be the first thing you do when you approach a problem, not the last.
I have drawn it out many times, but still I cannot understand how this is possible. Especially when I consider for instance if I had a 1 metre edge, and 6 molecules and said to myself: 1/x = 6 therefore the average spacing between the molecules is 1/6, I find this disturbing since when I draw 6 molecules, along the edge, It seems as though the total spacing gives me 5/6. Should it not total 1?

I understood after that well perhaps I have not been taking the diameters of the spheres into account, although when I did for calculating the average spacing between gas molecules(in a question) I was wrong.
6. (Original post by bl0b)
Visualise the molecules as identical perfect spheres

It is then helpful to realise that the average spacing between molecules is the same as the diameter of one sphere.
In the question it stated: " imagine that each atom was in the centre of an identical box."

Now from the question, I know that 22.43dm3 is the amount of space 1mol of gas molecules occupies. Since the total number of molecules in 1 mol of a gas is equal to ===> 6.022x10^(23) atoms.

It makes sense that the length of each box containing the molecule can be calculated. I assume that the length of each box = the diameter of the circle contained within each box?

Now if we do:

22.43 dm3 (this is equal to 22.43 x 10^-3 m3) divided by 6.022x10^23

Then I get 3.73 x 10^-26 m^3 (this is the volume of each box) hence the length of one side of this box is equal to the cube root of the volume of this box which is equal to 3.34 x 10^-9 m

So I assume that the diameter of one molecule (sphere) is equal to
3.34 x 10^-9 m

now then in terms of the 22.43dm3 volume which is occupied by 1 mol of this gas, if we cube root this (22.43 x 10^-3)m3 we get the following:

0.282 m , which would be the length of one edge of this big cube of volume
22.43dm3

Note: the diameter of one molecule is 3.34 x 10^-9 m(From above- worked out at the top)

well if we cube root 6.02x10^23, which is the number of gas molecules that occupies 22.43dm3 of volume, then the cube root of this will give us the number of gas molecules that lies along one edge of the cube, and that is equal to 84436877.34 molecules we could say 8.44 x 10^7 molecules

SO we know the diameter of one molecule to be 3.34 x 10^-9 m
we know the length of one edge to be 0.282
and we know that there are 8.44 x 10^7 molecules

Well then if I did 0.282/x = number of molecules along the edge, I get x = diameter of one molecule. That is interesting since in the book it gives an answer which is the same as the length of one small box(I thought diameter) which is 3.34 x 10^-9m, and it gives this same answer for the average length between the centres of the atoms, it then mentions that this is 10x the atomic diameter.
But how is 3.34 x 10^-9, 10 times greater than, 3.34x10^-9?

Is this an error?
7. (Original post by sulexk)
In the question it stated: " imagine that each atom was in the centre of an identical box."

Now from the question, I know that 22.43dm3 is the amount of space 1mol of gas molecules occupies. Since the total number of molecules in 1 mol of a gas is equal to ===> 6.022x10^(23) atoms.

It makes sense that the length of each box containing the molecule can be calculated. I assume that the length of each box = the diameter of the circle contained within each box?

Now if we do:

22.43 dm3 (this is equal to 22.43 x 10^-3 m3) divided by 6.022x10^23

Then I get 3.73 x 10^-26 m^3 (this is the volume of each box) hence the length of one side of this box is equal to the cube root of the volume of this box which is equal to 3.34 x 10^-9 m

So I assume that the diameter of one molecule (sphere) is equal to
3.34 x 10^-9 m

now then in terms of the 22.43dm3 volume which is occupied by 1 mol of this gas, if we cube root this (22.43 x 10^-3)m3 we get the following:

0.282 m , which would be the length of one edge of this big cube of volume
22.43dm3

Note: the diameter of one molecule is 3.34 x 10^-9 m(From above- worked out at the top)

well if we cube root 6.02x10^23, which is the number of gas molecules that occupies 22.43dm3 of volume, then the cube root of this will give us the number of gas molecules that lies along one edge of the cube, and that is equal to 84436877.34 molecules we could say 8.44 x 10^7 molecules

SO we know the diameter of one molecule to be 3.34 x 10^-9 m
we know the length of one edge to be 0.282
and we know that there are 8.44 x 10^7 molecules

Well then if I did 0.282/x = number of molecules along the edge, I get x = diameter of one molecule. That is interesting since in the book it gives an answer which is the same as the length of one small box(I thought diameter) which is 3.34 x 10^-9m, and it gives this same answer for the average length between the centres of the atoms, it then mentions that this is 10x the atomic diameter.
But how is 3.34 x 10^-9, 10 times greater than, 3.34x10^-9?

Is this an error?
In the context of the question problem solved!(hopefully...)

Well since the atom is in the centre of the cube, and all of these small cubes when connected together, occupy this volume of 22.43dm3

So if this is in the centre then the distance between this and the next sphere is 3.34 x 10^-9 m.

However how do we that the distance between these molecules is 10x the atomic diameter?

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