How many water molecules are in 4.0 moles of water?

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.