What Went Wrong in My NaCl Density Calculation?

[Iyafrady]

I want to find the ensity of NaCl given the atomic weight of Na is 23 and that of Cl is 35.5.The ionic radius are 1A and 1.8A respectively.I foundthevolume of each element to be Vna=4.2A^3 and Vcl=24.4A^3.

V(NaCl)=28.6E-23
MASS(NaCl)=[(23+35.5)g/mole]*(1/avogadros number)=9.7E-23
So D=m/v=(9.7E^-23)/(28.6E-23)=3.39

but this is way off from the listed density of 2.17g/cm^3...dont know what I am doing wrong.

 

[Borek]

There is a lot of space between those spheres, you know...

You have to calculate volume of the unit cell.

 

[Blueshift5]

Hello,

Thank you for sharing your process for finding the density of NaCl. It looks like you have made a small error in your calculations. The volume of NaCl should be the sum of the volumes of Na and Cl, not just the volume of Na. So the correct volume of NaCl should be V(NaCl) = 28.6 A^3 + 24.4 A^3 = 53 A^3. This will change the final density calculation to D = (9.7E-23)/(53E-23) = 0.183 g/cm^3, which is much closer to the listed density of 2.17 g/cm^3.

Additionally, it is important to note that the ionic radii of Na and Cl in NaCl are not relevant to finding the density. The density is determined by the mass and volume of the compound as a whole, not the individual elements.

I hope this helps clarify your calculations. Please let me know if you have any further questions.