# How much oxygen is in a cup of water?

I know that water is 2 parts hydrogen and 1 part oxygen. Hydrogen and oxygen are quite light gasses, they don't weigh very much compared to water. Water is very heavy and it made me wonder exactly how much oxygen I'd need to make a cup of water.

Please answer in terms of cubic meters of air, assuming the air is 21 % oxygen, and that my small cup contains only 100 ml. I suppose the exact question is: How many cubic meters of air contains the same amount of oxygen as found in 100 ml of water?

• 2/3 hydrogen, 1/3 oxygen. – Freddy Sep 3 '14 at 17:10
• @Freddy - The first sentence of my question explains that I already know that. I actually wanted to know how much that is. – Gerve Sep 3 '14 at 17:25

Since the molecular weight of water is $18\ \mathrm{g/mol}$, $100\ \mathrm{ml}$ (density = $1\ \mathrm{g/ml}$, so $100\ \mathrm{ml} \overset{\wedge}{=} 100\ \mathrm{g}$ of water) of water contains $$\frac{100}{18} = 5.56$$ moles of water, or 5.56 moles of atomic oxygen ($\ce{O}$), or 5.56/2 = 2.78 moles of molecular oxygen ($\ce{O2}$).
• Please note that the value $V_\mathrm m=22.4\ \mathrm{l/mol}$ for the molar volume of an ideal gas corresponds to the old definition of standard temperature and pressure (STP), which is a temperature of $T=273.15\ \mathrm K$ and a pressure of $1\ \mathrm{atm}$. Since 1982, $p=1\ \mathrm{bar}=100\,000\ \mathrm{Pa}$ is used as the standard pressure for tabulating thermodynamic data. At this pressure, the molar volume of an ideal gas actually is $V_\mathrm m=22.710\,947(13)\ \mathrm{l/mol}$. – Faded Giant Nov 9 '15 at 12:07