# Question #fd577

Jul 6, 2017

$1.7 \cdot {10}^{- 24}$ $\text{g}$

#### Explanation:

All you have to do here is to use Avogadro's constant and the mass of $1$ mole of carbon as a conversion factor to go from the mass of $1$ mole of atoms of carbon to the mass of $1$ atom of carbon.

So, you should know that, by definition, a mole of carbon must contain $6.022 \cdot {10}^{23}$ atoms of carbon. In other words, if you don't have $6.022 \cdot {10}^{23}$ atoms of carbon in your sample, then you don't have $1$ mole of carbon.

$\text{1 mole C} = 6.022 \cdot {10}^{23}$ $\text{atoms of C } \to$ Avogadro's constant

Now, you know that the mass of $1$ mole of carbon, i.e. the molar mass of carbon, is equal to $\text{12 g}$.

This is equivalent to saying that the mass of $6.022 \cdot {10}^{23}$ atoms of carbon is equal to $\text{12 g}$.

Therefore, you can say that the mass of a single atom of carbon will be equal to

$1 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{atom C"))) * "12 g"/(6.022 * 10^(23)color(red)(cancel(color(black)("atom C")))) = color(darkgreen)(ul(color(black)(1.7 * 10^(-24)color(white)(.)"g}}}}$

The answer is rounded to two sig figs.