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

Sep 7, 2017

${10}^{3} \cdot {N}_{A}$

#### Explanation:

The idea here is that $\text{1 kg-mole}$ 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 $\text{12 g}$ of carbon-12.

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

Since you know that

$\text{1 kg" = 10^3color(white)(.)"g}$

you can say that

$\text{1 kg-mole" = 10^3color(white)(.)"g-mole}$

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

As you know, the number of atoms present in $\text{12 g}$ of carbon-12 is given by Avogadro's constant, ${N}_{A}$

${N}_{A} = 6.022 \cdot {10}^{23} \textcolor{w h i t e}{.} {\text{particles mol}}^{- 1}$

Since you have

$\text{1 mole" = 6.022 * 10^(23)color(white)(.)"particles}$

you can say that

$\text{1 kg-mole" = 10^3 * 6.022 * 10^(23)color(white)(.)"particles}$

$\text{1 kg-mole" = 6.022 * 10^(26)color(white)(.)"particles}$

$\text{1 kg-mole} = {10}^{3} \cdot {N}_{A}$

Keep in mind that this represents the number of atoms present in exactly $\text{12 kg}$ of carbon-12.