Calculating the density, volume of an element and how many atoms there are?
I had a question where i had to find the density of Al and was given the diameter (0.286 nm), avogrados constant and molecular mass (27.8 g/mol).
the teacher said it had cubic centred packing and from that somehow got that there were 4 atoms. How do we know this?
And then how would we find the volume?
the teacher said it had cubic centred packing and from that somehow got that there were 4 atoms. How do we know this?
And then how would we find the volume?
Original post by ErniePicks
I had a question where i had to find the density of Al and was given the diameter (0.286 nm), avogrados constant and molecular mass (27.8 g/mol).
the teacher said it had cubic centred packing and from that somehow got that there were 4 atoms. How do we know this?
And then how would we find the volume?
the teacher said it had cubic centred packing and from that somehow got that there were 4 atoms. How do we know this?
And then how would we find the volume?
Taking "cubic centred packing" to mean the nucleus is one big cube, you have the diameter and thus all the lengths of said cube, so the volume would just be the diameter cubed.
Mass density of a volume is simply the total mass of the object divided by the volume, so you need to use avocados constant and the molecular mass to work out the mass of the nucleus and then divide that by the volume you worked out
Hope that helps
Edit, this may not be correct, not entirely sure on their definition of cubic centred packing..
If it's that each atom is a cube and there are four atoms then the volume would simply be 4 times what I previously said.
(edited 8 years ago)
Original post by Stevo F
Taking "cubic centred packing" to mean the nucleus is one big cube, you have the diameter and thus all the lengths of said cube, so the volume would just be the diameter cubed.
Mass density of a volume is simply the total mass of the object divided by the volume, so you need to use avocados constant and the molecular mass to work out the mass of the nucleus and then divide that by the volume you worked out
Hope that helps
Edit, this may not be correct, not entirely sure on their definition of cubic centred packing..
If it's that each atom is a cube and there are four atoms then the volume would simply be 4 times what I previously said.
Mass density of a volume is simply the total mass of the object divided by the volume, so you need to use avocados constant and the molecular mass to work out the mass of the nucleus and then divide that by the volume you worked out
Hope that helps
Edit, this may not be correct, not entirely sure on their definition of cubic centred packing..
If it's that each atom is a cube and there are four atoms then the volume would simply be 4 times what I previously said.
Couldn't help but laugh at this
Original post by InadequateJusticex
Couldn't help but laugh at this
Damn autocorrect
Not even gunna change it
Original post by ErniePicks
I had a question where i had to find the density of Al and was given the diameter (0.286 nm), avogrados constant and molecular mass (27.8 g/mol).
the teacher said it had cubic centred packing and from that somehow got that there were 4 atoms. How do we know this?
And then how would we find the volume?
the teacher said it had cubic centred packing and from that somehow got that there were 4 atoms. How do we know this?
And then how would we find the volume?
I think that its a little more complicated than the previous answers.
You can work out the volume of the sphere using the diameter and then multiply by Avocados or Avogadro's or AvaGardner's number (as you choose) to get the total volume of the spheres.
Then you take into account that a close packed system has only a certain proportion of the total volume actually occupied by spheres, which is approximately 74%.
Hence, 4/3πr3 = 1.33 * 3.142 * (0.143 x 10-9)3 m3
volume of 1 sphere = 1.22 x 10-29 m3
1 mol spheres = 6.02 x 1023 x 1.22 x 10-29 m3 = 7.36 x 10-6 m3
total volume of aluminium = 100/74 * 7.36 x 10-6 m3 = 9.94 x 10-6 m3 = 9.94 cm3
Mass = 27.8g/mol
Density = 27.8/9.94 g/cm3 = 2.80 g/cm3
This is a shade above the literature value of 2.70 g/cm3, which could be due to the assumption of perfect close packing. Random packing of spheres gives a percentage of about 63% occupation, which would lower the final density value by about 10%.
(edited 8 years ago)
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