# A 1.00 carat pure diamond has a mass of 0.2 grams. How many carbon atoms are there within this diamond?

Jul 16, 2016

$1 \cdot {10}^{22}$ atoms

#### Explanation:

In this example you have 0.2 grams of carbon atoms. The first step is to find out how many moles this is.

The molar mass of carbon is 12.01 g/mol, you have 0.2 gram so:

$0.2 \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{g}}}}{12.01 \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{g}}}}{m o l}} = 0.01665 \ldots m o l$

The number of atoms can be calculated using Avogadro's constant that says that 1 mole of any element contains $6.022 \cdot {10}^{23}$ atoms. So the number of atoms in this example is:

$6.022 \cdot {10}^{23} \text{atoms"/color(red)cancel(color(black)(mol)) * 0.01665 color(red)cancel(color(black)(mol)) = 1 *10^22 "atoms}$