# 24.08 times 10^23 atoms of boron is equal to how many moles of Boron?

Jul 6, 2017

Here's what I got.

#### Explanation:

For starters, notice that your sample contains

$24.08 \cdot {10}^{23} = 4 \cdot \left(\textcolor{b l u e}{6.02 \cdot {10}^{23}}\right)$

atoms of boron. At this point, you should be able to recognize the fact that $6.02 \cdot {10}^{23}$ represents the number of atoms of boron needed in order to have $1$ mole of boron.

In other words, a mole of boron is defined as $6.02 \cdot {10}^{23}$ atoms of boron $\to$ this is known as Avogadro's constant.

This means that your sample contains

4 * color(blue)("1 mole B") = color(darkgreen)(ul(color(black)("4.000 moles B")))

You must report the answer rounded to four sig figs, the number of sig figs you have for the number of atoms present in your sample.

SIDE NOTE As an interesting fact, Avogadro's constant is often times approximated to $6.022 \cdot {10}^{23}$. In this case, your sample would contain

24.08 * 10^(23) color(red)(cancel(color(black)("atoms B"))) * "1 mole B"/(6.022 * 10^(23)color(red)(cancel(color(black)("atoms B")))) = "3.99867 moles B"

Rounded to four sig figs, the answer would be

$\text{no. of moles = 3.999 moles B}$

So make sure that you use the value for Avogadro's constant provided to you by your textbook.