Question

Question #eff1e

Answer 1

`2.4 * 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 `color(darkorange)(1)` mole of magnesium has a mass of `color(blue)("24.305 g"`, which means that `"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.

`color(blue)(ul(color(black)("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"))))`

`= color(darkgreen)(ul(color(black)(2.4 * 10^(24)color(white)(.)"atoms Mg")))`

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