How many molecules are in 48.90 grams of water?

1 Answer
Jan 27, 2016

#1.635 * 10^(24)" molecules"#


In order to figure out how many molecules of water are present in that #"48.90-g"# sample, you first need to determine how many moles of water you have there.

As you know, a mole is simply a very large collection of molecules. In order to have one mole of something, you need to have exactly #6.022 * 10^(23)# molecules of that something - this is known as Avogadro's number.

In order to get to moles, you must use water's molar mass. A substance's molar mass tells you the mass of one mole of molecules of said substance.

Water has a molar mass of #"18.015 g/mol"#. This means that one mole of water molecules has a mass of #"18.015 g"#.

So, to sum this up, #6.022 * 10^(23)# molecules of water will amount to #"1 mole"# of water, which in turn will have a mass of #"18.015 g"#.

So, use water's molar mass to find the number of moles present in that sample

#48.90 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "2.7144 moles H"_2"O"#

Now use Avogadro's number to find the number of molecules of water

#2.7144 color(red)(cancel(color(black)("moles H"_2"O"))) * (6.022 * 10^(23)"molec.")/(1color(red)(cancel(color(black)("mole H"_2"O")))) = color(green)(1.635 * 10^(24)"molec.")#

The answer is rounded to four sig figs, the number of sig figs you have for the mass of water.