# The atomic mass of potassium is 39.1. What is the mass of 6.02 * 10^23 atoms of potassium?

Aug 2, 2016

$\text{39.1 g}$

#### Explanation:

The first thing to note here is that the atomic mass, ${m}_{a}$, of potassium, $\text{K}$, is not $39.1$, it is $\text{39.1 u}$.

The relative atomic mass of potassium, ${A}_{r}$, which is equal to its atomic mass, $\text{39.1 u}$, divided by $\frac{1}{12} \text{th}$ of the mass of single, unbound carbon-12 atom, i.e. $\text{1 u}$, is equal to

A_(rcolor(white)(a)"K") = (39.1 color(red)(cancel(color(black)("u"))))/(1color(red)(cancel(color(black)("u")))) = 39.1

So remember, the atomic mass of an element is not a unitless quantity. Atomic masses are expressed in unified atomic mass units, $\text{u}$.

Relative atomic masses are unitless because they express the mass of an element relative to $\frac{1}{12} \text{th}$ of the mass of single, unbound carbon-12 atom.

Now, all you have to do here is remember that one mole of a given element is defined as $6.02 \cdot {10}^{23}$ atoms of that element $\to$ this is known as Avogadro's number.

In your case, $6.02 \cdot {10}^{23}$ atoms of potassium will be equivalent to one mole of potassium. Here is where the cool part comes in.

The atomic mass of potassium is equal to

${m}_{a} = \text{39.1 u}$

By definition, the unified atomic mass unit is equal to

$\textcolor{p u r p \le}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\text{1 u " = " 1 g mol}}^{- 1}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

This means that the molar mass of potassium, which tells you the mass of one mole of the element, will be equal to

39.1 color(red)(cancel(color(black)("u"))) * "1 g mol"^(-1)/(1color(red)(cancel(color(black)("u")))) = "39.1 g mol"^(-1)

Therefore, you can say that one mole of potassium has a mass of $\text{39.1 g}$.