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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