Question

Find density with given edge length?

There is a compound X composed of zinc and sulfur atoms. The edge length of the cell is 5.411Å. I need to calculate the density of compound X.

I try to use edge length to calculate the volume=(edge length)^(3)
However, i am stuck on the calculation of the mass.
How should I do this?

Answer 1

We ASSUME that we have a cubic unit cell....

Explanation:

AND such a cubic cell contains FOUR formula units of `ZnS`, which each have a formula mass of `97.47*g*mol^-1`.

Eight zinc atoms at the corners, four zinc atoms at the faces, and one at the center gives `4` whole `Zn`, and four whole sulfur atoms at the center gives `4` whole `S`.

And thus FOUR formula units of zinc sulfide has a mass of ...

`(4*97.47*g*mol^-1)/(6.022xx10^23*mol^-1)=6.474xx10^-22*g`

And all I have done is divide the molar mass by the Avocado number to get the mass of a SINGLE formula unit.

And so to take the density, we simply take the quotient...`rho_"density"="mass"/"volume"=(6.474xx10^-22*g)/((5.411xx10^-10*m)^3)`

`=4086557.4*g*m^3`

`(4086557.4*g*m^-3)/(10^6*cm^3*m^-3)=4.087*g*cm^-3`...

The calculation is in the right order of magnitude. I would suspect `rho=4-5*g*cm^-3`.