What is the mass in grams of #9.76 * 10^12# atoms of naturally occurring sodium?

1 Answer
Stefan V.
Nov 11, 2015

#3.73 * 10^(-8)"g"#

Explanation:

The important thing here is to ignore the naturally ocurring part and realize that you're dealing with sodium metal, #"Na"#.

Now, you need to use two concepts to help you solve this problem

  • the molar mass of sulfur
  • the number of atoms you get per mole, also known as Avogadro's number

An element's molar mass tells you what the exact mass of one mole of said element is. Sodium has a molar mass of approximately #"23.0 g/mol"#, which means that one mole of sodium has a mass of #"23.0 g"#.

You also know that one mole of any element contains exactly #6.022 * 10^(23)# atoms of that element. This means that one mole of sodium has a mass of #"23.0 g"# and contains #6.022 * 10^(23)# atoms of sodium.

#"1 mole Na" = "23.0 g" = 6.022 * 10^(23)"atoms of Na"#

Therefore, that many atoms of sodium will have a mass of

#9.76 * 10^(14)color(red)(cancel(color(black)("atoms of Na"))) * "23.0 g"/(6.022 * 10^(23)color(red)(cancel(color(black)("atoms of Na")))) = color(green)(3.73 * 10^(-8)"g")#

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