Question #65ef0

1 Answer
Mar 18, 2017

#"1.30 g"#


In order to find the mass of the sample, you must

  • use Avogadro's constant to convert the number of atoms of aluminium to moles of aluminium
  • use the molar mass of the element to convert the number of moles of aluminium to grams

So, Avogadro's constant tells you the number of atoms of aluminium that are needed in order to have #1# mole of this element. More specifically, you know that

#color(blue)(ul(color(black)("1 mole Al" = 6.022 * 10^(23)color(white)(.)"atoms Al")))#

In your case, the sample will contain

#2.91 * 10^(22)color(red)(cancel(color(black)("atoms Al"))) * "1 mole Al"/(6.022 * 10^(23)color(red)(cancel(color(black)("atoms Al")))) = "0.04832 moles Al"#

You also know that aluminium has a molar mass equal to #"26.98 g mol"^(-1)#. This tells you that #1# mole of this element has a mass of #"26.98 g"#.

You can thus say that your sample will have a mass of

#0.04832color(red)(cancel(color(black)("moles Al"))) * "26.98 g"/(1color(red)(cancel(color(black)("mole Al")))) = color(darkgreen)(ul(color(black)("1.30 g")))#

The answer is rounded to three sig figs, the number of sig figs you have for the number of atoms present in the sample.