What is the percent composition of water in #"Na"_2"SO"_4 * 10"H"_2"O"#?

Your goal here is to figure out how many grams of water you have in #"100 g"# of sodium sulfate decahydrate, #"Na"_2"SO"_4 * 10"H"_2"O"#.

To do that, start with what you know. More specifically, start with the fact that #1# mole of sodium sulfate decahydrate contains

• one mole of sodium sulfate, #1 xx "Na"_2"SO"_4#
• ten moles of water, #10 xx "H"_2"O"#

You also know that sodium sulfate has a molar mass of #"142.04 g mol"^(-1)# and that water has a molar mass of #"18.015 g mol"^(-1)#. This means that #1# mole of sodium sulfate decahydrate contains

• #1 xx "142.04 g " -># sodium sulfate
• #10 xx "18.015 g " -># water

and has a total mass of

#"142.04 g"color(white)(.) + 10 xx "18.105 g" = "322.19 g"#

This means that #"100 g"# of sodium sulfate decahydrate will contain

#100 color(red)(cancel(color(black)("g Na"_ 2"SO"_ 4))) * (10 xx "18.015 g H" _ 2"O")/(322.19 color(red)(cancel(color(black)("g Na"_ 2"SO"_ 4)))) = "55.9 g H"_2"O"#

Therefore, you can say that the percent composition of water in this hydrate is equal to

#color(darkgreen)(ul(color(black)("% H"_2"O" = 55.9%)))#

Keep in mind that the #%# sign means out of #"100 g"# of hydrate.