# Question 3ba68

Oct 17, 2016

#### Answer:

$2.093 \cdot {10}^{24}$

#### Explanation:

Your strategy here will be to convert the mass of magnesium to moles by using the element's molar mass, and the moles of magnesium to atoms by using Avogadro's constant.

So, magnesium has a molar mass of ${\text{24.305 g mol}}^{- 1}$, which means that every mole of magnesium has a mass of $\text{24.305 g}$.

Your sample will thus contain

84.48 color(red)(cancel(color(black)("g"))) * "1 mol Mg"/(24.305color(red)(cancel(color(black)("g")))) = "3.4758 moles Mg"

Now, in order to have one mole of a given element, you need to have $6.022 \cdot {10}^{23}$ atoms of said element -- this is known as Avogadro's constant.

In your case, the sample will contain

3.4758 color(red)(cancel(color(black)("moles Mg"))) * (6.022 * 10^(23)"atoms Mg")/(1color(red)(cancel(color(black)("mole Mg"))))#

$= \textcolor{g r e e n}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{2.093 \cdot {10}^{24} \text{atoms Mg}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

The answer is rounded to four sig figs, the number of sig figs you have for the mass of magnesium.