# Question eff1e

Apr 2, 2017

$2.4 \cdot {10}^{24}$

#### Explanation:

The first thing you need to do here is to convert the mass of magnesium to moles by using the element's molar mass.

M_"M Mg" = color(blue)("24.305 g")color(white)(.)color(darkorange)("mol"^(-1))

In this case, you know that $\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{1}$ mole of magnesium has a mass of color(blue)("24.305 g", which means that $\text{96 g}$ of magnesium will be equivalent to

96 color(red)(cancel(color(black)("g"))) * "1 mole Mg"/(24.305 color(red)(cancel(color(black)("g")))) = "3.95 moles Mg"

Now, to convert the number of moles of magnesium to number of atoms, you must use Avogadro's constant, which represents the definition of a mole.

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{1 mole Mg" = 6.022 * 10^(23)color(white)(.)"atoms Mg}}}}$

You can thus say that your sample of magnesium will contain

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

$= \textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{2.4 \cdot {10}^{24} \textcolor{w h i t e}{.} \text{atoms Mg}}}}$

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