How many atoms of hydrogen are in a 10 gram sample of water?
1 Answer
Explanation:
In order to be able to determine how many atoms of hydrogen you get in
#"grams" stackrel(color(red)(1)color(white)(aa))(->) "moles" stackrel(color(blue)(2)color(white)(aa))(->) "no. of molecules" stackrel(color(green)(3)color(white)(aa))(->) "no. of atoms"#
So, let's take these steps in order
#color(red)(1) -># Grams of water to moles of water
In order to determine how many moles you have in a given mass of a compound, you must use said compound's molar mass. In water's case, you will have
#10 color(red)(cancel(color(black)("g"))) * ("1 moleH"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "0.5551 moles H"_2"O"#
#color(blue)(2) -># Moles of water to number of molecules of water
Your conversion factor here will be Avogadro's number, which tells you how many molecules are needed in order to have exactly one mole of a substance.
More specifically, you have
#color(blue)(|bar(ul(color(white)(a/a)color(black)("1 mole" = 6.022 * 10^(23)"molecules")color(white)(a/a)|))) -># Avogadro's number
In your case, you will have
#0.5551color(blue)(cancel(color(black)("moles H"_2"O"))) * (6.022 * 10^(23)"molec H"_2"O")/(1color(blue)(cancel(color(black)("mole H"_2"O")))) = 3.343 * 10^(23)"molec. H"_2"O"#
#color(green)(3) -># Molecules of water to atoms of hydrogen
Now, in order to find the number of atoms of hydrogen you have in your sample, you must use the fact that one water molecule is made up of
This means that your sample will contain
#3.343 * 10^(23)color(green)(cancel(color(black)("molec. H"_2"O"))) * "2 atoms of H"/(1color(green)(cancel(color(black)("molec. H"_2"O")))) = 6.7 * 10^(23)"atoms of H"#
I'll leave the answer rounded to two sig figs.