Question

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

Answer 1

`"39.1 g"`

Explanation:

The first thing to note here is that the atomic mass, `m_a`, of potassium, `"K"`, is not `39.1`, it is `"39.1 u"`.

The relative atomic mass of potassium, `A_r`, which is equal to its atomic mass, `"39.1 u"`, divided by `1/12"th"` of the mass of single, unbound carbon-12 atom, i.e. `"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, `"u"`.

Relative atomic masses are unitless because they express the mass of an element relative to `1/12"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 * 10^(23)` atoms of that element `->` this is known as Avogadro's number.

In your case, `6.02 * 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 = "39.1 u"`

By definition, the unified atomic mass unit is equal to

`color(purple)(|bar(ul(color(white)(a/a)color(black)("1 u " = " 1 g mol"^(-1))color(white)(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 `"39.1 g"`.