# How does calculate the density of a compound material?

I have working on a particle detector question. There is a crystal that made of NaI. I need to calculate density of NaI. Here is my calculation way,

$\rho_{NaI} = \omega_{Na}*\rho_{Na}+\omega_{I}*\rho_{I}$

$\omega_i = \frac{A_i}{\Sigma A_i}$

To calculation ratios of the all component of compound, I am using atomical mass ratio. After that, I have obtained $\rho=4.322 g/cm^3$.

But Wikipedia says $\rho=3.67g/cm^3$

What mistake is I made in calculation ?

• There are equal numbers of both ions. And elemental densities are useless here. – Pieter Jan 5 '18 at 23:16
• Actually I did not understand what you mean. I think there is only importing thing is density. So, how can we calculate density of compound if we do not use these densities ? – agenel Jan 5 '18 at 23:25
• This is perhaps easiest to see with allotropes. Both diamond and graphite are made of carbon, yet they have different densities. You cannot calculate the density of compounds starting from elemental densities. – Jon Custer Jan 5 '18 at 23:33
• @JonCuster Good example to catching misunderstanding points. Thank you. – agenel Jan 5 '18 at 23:39

## 2 Answers

You need to consider the crystal structure. Sodium on its own has a body-centered cubic structure, for example, which differs from the structure of iodine on its own, and also from NaI. The effective space taken up by each atom depends on crystal structure, so the effective "density" of those atoms does too.

• Roughly you say that, crystal structure is not building putting elements side-by-side. This structure building with special sequence. Therefore, taking equal atoms for every component to building structure is nonsense ? – agenel Jan 5 '18 at 23:38
• You should in fact be able to calculate the density by considering the weight of each atom. But you need to also consider the volume taken up by a single "cell" of the crystal. This volume depends on the way the atoms fit together, and the spacing between them. – Ben51 Jan 6 '18 at 1:34

Density is the quotient between mass and volume. Density no depends only from the elements: it's depends also from the crystal scructure. The usual method for calculate the density is to weight a piece of material and then put it into water to known his volume. A volumetric flask can be the instrument to know the volume of the piece.

• Sounds like it is useful method to obtain denstiy. But I do not have any NaI or any instrument. Pen and paper only I have. – agenel Jan 5 '18 at 23:41
• NaI will just dissolve in water. Not a good method here. – Pieter Jan 6 '18 at 0:15
• If NaI is very soluble, I agree with you. – Rafael Marazuela Jan 6 '18 at 9:11