Question

How many water molecules are in 4.0 moles of water?

Answer 1

`2.4 * 10^(24)`

Explanation:

All that you need to know here is that in order for a given sample of water to contain exactly `1` mole of water, it must contain `6.022 * 10^(23)` molecules of water.

This is known as Avogadro's constant and essentially acts as the definition of a mole. If you have `6.022 * 10^(23)` molecules of water, then you can say for a fact that you have `1` mole of water.

`color(white)(overbrace(color(blue)(ul(color(black)("1 mole H"_2"O" = 6.022 * 10^(23) quad "molecules H"_2"O"))))^(color(red)(ul("Avogadro's constant")))`

Now, you know that your sample contains `4.0` moles of water. In order to find the number of molecules of water it contains, you can use Avogadro's constant as a conversion factor.

You start with moles and you want to find the number of molecules, so set up the conversion factor like this.

`(6.022 * 10^(23) quad "molecules H"_2"O")/("1 mole H"_2"O")" "color(white)( (color(blue)(larr " what you need"))/(color(blue)(larr " what you have"))`

Finally, multiply the number of moles of water by the conversion factor to get

`4.0 color(red)(cancel(color(black)("moles H"_2"O"))) * (6.022 * 10^(23) quad "molecules H"_2"O")/(1color(red)(cancel(color(black)("mole H"_2"O")))) = color(darkgreen)(ul(color(black)(2.4 * 10^(24) quad "molecules H"_2"O")))`

The answer is rounded to two sig figs, the number of sig figs you have for the number of moles present in your sample.