Question

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

Answer 1

`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.