Question #eb525

1 Answer
Jun 30, 2016

Answer:

#2.6 * 10^(24)"atoms"#

Explanation:

I assume that you're interested in finding out how may atoms of sodium, #"Na"#, you have in your #"0.1 kg"# sample.

The first thing to do here is convert the mass of sodium from kilograms to grams

#0.1 color(red)(cancel(color(black)("kg"))) * (10^3"g")/(1color(red)(cancel(color(black)("kg")))) = "100 g"#

From this point on, you will have to use two conversion factors

  • grams to moles #-># use the molar mass of sodium #" "color(blue)((1))#
  • moles to number of atoms #-># use Avogadro's number #" "color(darkgreen)((2))#

#color(blue)((1))" "#Grams to moles

The molar mass of an element essentially tells you the mass of one mole of said element. In this case, sodium has a molar mass of #"23.0 g mol"^(-1)#, which means that one mole of sodium has a mass of #"23.0 g"#.

In your case, #"100 g"# of sodium will be equivalent to

#100color(blue)(cancel(color(black)("g"))) * "1 mole Na"/(23.0color(blue)(cancel(color(black)("g")))) = "4.35 moles Na"#

#color(darkgreen)((2))" "# Moles to number of atoms

A mole is simply a very, very large collection of atoms. In order to have one mole of a given element, you need to have #6.022 * 10^(23)# atoms of said element.

#color(blue)(|bar(ul(color(white)(a/a)"1 mole" = 6.022 * 10^(23)"atoms"color(white)(a/a)|))) -># Avogadro's number

In your case, #4.35# moles of sodium will contain

#4.35 color(darkgreen)(cancel(color(black)("moles Na"))) * (6.022 * 10^(23)"atoms of Na")/(1color(darkgreen)(cancel(color(black)("moles Na")))) = color(green)(|bar(ul(color(white)(a/a)color(black)(2.6 * 10^(24)"atoms Na")color(white)(a/a)|)))#

I'll leave the answer rounded to two sig figs, but keep in mind that you only have one sig fig for the mass of sodium.