Posted by **sandy** on Friday, February 6, 2009 at 7:34pm.

Magnesium crstallizes in the hcp arrangment. The dimensions of the unit cell are height 520om, length on an edge, 320. Calculate the density of Mg (s) and compare it with the measured value of 1.738 g/cm^3

this is what i did :

m= 2* 24.30g/6.022*10^23 = 8.07*10^-23

v= l^2*h

v= (320)^2*520= .0053248

d=m/v

d= 8.07*10^-23/. 0053248

d= 1.51* 10^-20 cm

BUT the answer is suppose to be 1.75

I think I made a mistake on the volume :S

- density of Magnesium! -
**DrBob222**, Friday, February 6, 2009 at 7:52pm
You don't list units for all of the measurements but I assume the 320 and 520 are picometers. You must convert the volume you have, which I assume is in cubic picometers, OR convert to cm before you begin. I highly recommend that you convert 320 to cm and convert 520 to cm.

320 pm x (1 m/10^12 pm) x (100 cm/1 m) = 3.2 x 10^-8 cm BEFORE doing the calculations. See if that helps.

- density of Magnesium! -
**sandy**, Friday, February 6, 2009 at 8:10pm
sorry yes they were in pm I corrected my units:

m= 2* 24.30g/6.022*10^23 = 8.07*10^-23

v= l^2*h

v=(3.2*10^-8cm)^2* 5.2*10^-8cm v=5.32*10^-23cm

d=m/v

d= 8.07*10^-23/5.32*10^-23

d= 1.52cm

> it's still 1.52 where as the correct answer is suppose to be 1.75g/cm^3. Is my method of calculation correct?

- density of Magnesium! -
**drwls**, Friday, February 6, 2009 at 9:00pm
Is your volume formula consistent with the hexagonal close packed crystal structure? That might be the cause of your disagreement.

See http://www.chm.davidson.edu/ChemistryApplets/Crystals/UnitCells/hcp.html

- density of Magnesium! -
**Anonymous**, Friday, February 6, 2009 at 10:27pm
that just pretty much explains how to calculate height. and the length = 2r

- density of Magnesium! -
**drwls**, Saturday, February 7, 2009 at 10:30am
It says a lot more than that. The base area of a unit cell is not the square of 2r. It is a hexagon

- density of Magnesium! -
**Chem**, Wednesday, June 10, 2015 at 12:43pm
To find the volume of a HCP structure given the height and the lenght, you should use this formula:

l^2*h*((3)^1/3)/2)

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