# Question 70b01

Apr 10, 2017

"density" = (Zxx "mol.wt")/(a^3xxN_a)

Where Z is the molecules per unit cell(dont confuse Z with atom per unit). Z is different for all different types of crystals. A BBC can contain 2 atoms(not molecules) per unit. A FCC can contain 4 atoms(again not molecules )per unit.

mol.wt is the molar mass
${a}^{3}$ where a is the length of each side in a cubic crystal

You can see what is a and loook carefully and observe that it can be seed that $a$ is the side of a cube

So like we find out the volume ina cube

${a}^{3} = \text{volume of one atom}$

and ${N}_{a}$ is the Avogadro's constant which is equal to $6.023 \times {10}^{23}$

$\text{Why are we doing this equation?}$

Z means the no. of atoms per unit. SO if we multiply itwith the molar mass we are actually getting the weight of the unit by measuring the weight of the total atoms in a mole of a unit cell

${a}^{3}$ we have already discussed so you know that ${a}^{3}$ is actually the volume of unit cell.

But why are are we multiplying it with Avogadro's constant?
This is because we want to to know the volume of 1mol.

So actually we can simplify the equation and can obtain

$\text{density" =" weight of one mole of unit cell"/" volume of one mole of unit cell}$

I know that there are no units in the equation but still cut out the same words

"density" =(" weight of" cancel("6.022*10^23atoms in unit cells"))/("volume of" cancel("6.022*10^23atoms of unit cells"))#

Finally we obtain

$\text{density" = "weight"/"volume}$

So we can be sure that this is a correct equation