How many molecules are present in 1kg mole of a substance?

1 Answer
Sep 7, 2017

Answer:

#10^3 * N_A#

Explanation:

The idea here is that #"1 kg-mole"# is equal to #10^3# moles.

This is the case because a mole of a substance must contain a number of particles of that substance equal to the number of atoms present in exactly #"12 g"# of carbon-12.

In this regard, you'll sometimes see a mole being referred to as a gram-mole, #"g-mole"#, just because it represents the number of particles equal to the number of atoms present in #"12 g"# of carbon-12.

Since you know that

#"1 kg" = 10^3color(white)(.)"g"#

you can say that

#"1 kg-mole" = 10^3color(white)(.)"g-mole"#

In other words, in order to have #"1 kg-mole"# of a given substance, you need to have the same number of particles of that substance as you would have in #10^3# #"g-moles"#, or #10^3# moles, of that substance.

As you know, the number of atoms present in #"12 g"# of carbon-12 is given by Avogadro's constant, #N_A#

#N_A = 6.022 * 10^(23)color(white)(.)"particles mol"^(-1)#

Since you have

#"1 mole" = 6.022 * 10^(23)color(white)(.)"particles"#

you can say that

#"1 kg-mole" = 10^3 * 6.022 * 10^(23)color(white)(.)"particles"#

#"1 kg-mole" = 6.022 * 10^(26)color(white)(.)"particles"#

#"1 kg-mole" = 10^3 * N_A#

Keep in mind that this represents the number of atoms present in exactly #"12 kg"# of carbon-12.