Question

Question #380d4

Answer 1

`7 * 10^11`

Explanation:

An interesting approach to use here would be to convert the molar mass of magnesium from grams per mole, `"g mol"^(-1)`, to picograms per mole, `"pg mol"^(-1)`.

Now, magnesium has a molar mass of `"24.305 g mol"^(-1)`. As you know

`"1 g" = 10^12` `"pg"`

This means that the molar mass of magnesium is equal to

`24.305 color(red)(cancel(color(black)("g"))) "mol"^(-1) * (10^12color(white)(.)"pg")/(1color(red)(cancel(color(black)("g")))) = 2.4305 * 10^(13)` `"pg mol"^(-1)`

This means that `1` mole of magnesium has a mass of `2.4305 * 10^(12)` `"pg"`. You can thus say that your sample will contain

`3 color(red)(cancel(color(black)("pg"))) * "1 mole Mg"/(2.4305 * 10^12color(red)(cancel(color(black)("pg")))) = 1.234 * 10^(-12)` `"moles Mg"`

Finally, to find the number of atoms of magnesium present in the sample, use the fact that `1` mole of magnesium must contain `6.022 * 10^(23)` atoms of magnesium `->` this is given by Avogadro's constant.

You can thus say that your sample will contain

`1.234 * 10^(-12) 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)(7 * 10^11color(white)(.)"atoms Mg")))`

The answer must be rounded to one significant figure, the number of sig figs you have for the mass of magnesium.