Question

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

Answer 1

Sodium sulfate decahydrate is `55.9 %"H"_2"O"`.

Explanation:

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.