# Is there a formula for density of any gaseous substance just based on its molar mass?

$\pu{112 ml}$ of hydrogen combines with $\pu{56 mL}$ of oxygen to form water. When $\pu{224 mL}$ of hydrogen is passed over heated cupric oxide, the cupric oxide loses $\pu{0.160 g}$ of its weight. All volumes are measured at STP. Show that the result agrees with the law of constant composition.

Although I solved the question, I came across a very interesting step in the procedure of doing so:

Weight of $\pu{112 mL}$ of $\ce{H2}$ at STP is calculated as $\frac{112 \times 2}{22400}$

Does this mean density of a gaseous substance at STP can be given as

$$\text{density} = \dfrac{\text{Mass}}{\text{Volume}} = \dfrac{\dfrac{\text{Volume(mL)}\times\text{Molar Mass}}{22400}}{\text{Volume(mL)}} = \dfrac{\text{Molar Mass}}{22400}$$

Can we say that this holds true?

• There have been different values for STP in the past. Currently at STP the molar volume is 22.7 liters. – MaxW Jun 27 '18 at 17:45
• Yes...Just knowing T, P and its identity, you can derive a density formula. [for an ideal gas] – user43021 Jun 27 '18 at 18:34

## 1 Answer

This is true for ideal gases at standard temperature and pressure. The Volume of an ideal gas is 22.4 L/mol at 298.15 K and 1 bar. You can check this yourself by rearranging the ideal gas equation and solving for the molar volume at STP.

Edit: Make sure you always use correct units, preferably SI in your equations. And use them in all equations.