Question #380d4

1 Answer
Jun 28, 2017

Answer:

#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.