In a liter of gas AT STP, there's 22.414 moles. That is something to remember.
You want to make 10.5g of water, but we don't know how much that is until we know how many moles that is of water.
The molecular weight of water is about 18.02g/mol
so for every mole, or 6.022*10^23 molecules of water, that's 18.02 grams.
Ok, but you want 10.5 grams of water, so it's a proportion.
18.02g/1mol = 10.5g/?mol
solve for unknown to get moles and you get
(1/18.02)*10.5 = 0.5826859046... don't round yet to 3 significant figures.
That's how many moles of water you want.
Now for every mole of water, there's 2 moles of hydrogen and one mole of oxygen. But the ratio of oxygen to water is 1:1.
In other words, you need x amount of oxygen to make x amount of water, the same.
So knowing that you need 0.5826859046 moles of oxygen you need and that there's 22.414 moles of a gas in 1 L at STP, you can find how many liters this is.
22.414mol / 1L = 0.5826859046mol / XL
this number is big because it should still be in your calculator, we don't round until the end.
= 0.0259965...
NOW round to 3 significant figures originally from 10.5g in the problem and get
0.0260 L of oxygen needed
