# The Density of gas + solved problems

From ideal gas equation:

If we rearrange the ideal gas equation, we can calculate the density of a gas:

where m is the mass of the gas in grams and µ is its molar mass. Therefore

Because density, d, is mass per unit volume, we can write:

Unlike molecules in condensed matter (that is, in liquids and solids), gaseous molecules are separated by distances that are large compared with their size. Consequently, the density of gases is very low under atmospheric conditions. For this reason, gas densities are usually expressed in grams per liter (g/L) rather than grams per milliliter (g/mL).

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**Solved problems**

**Example (1):**

**Calculate the density of carbon dioxide (CO**

_{2}) in grams per liter (g/L) at 0.990 atm and 55^{o}C.**Strategy:**

We need the combined gas Equation to calculate gas density. Is sufficient information provided in the problem? What temperature unit should be used?

**Solution:**

To use the combined gas Equation, we convert temperature to kelvins ( T = 273 + 55 = 328 K) and use 44.01 g for the molar mass of CO

_{2}:
Alternatively, we can solve for the density by writing:

Assuming that we have 1 mole of CO

_{2}, the mass is 44.01 g. The volume of the gas can be obtained from the ideal gas equation
Therefore, the density of CO

_{2}is given by:**Comment:**

ln units of grams per milliliter, the gas density is 1.62 × 10

^{-3}g/mL, which is a very small number. In comparison, the density of water is 1.0 g/mL and that of gold is 19.3 g/cm^{3}.

**Problem (2): Determine the density of nitrogen at STP.**

**Solution**

It is easy to calculate the number of moles of nitrogen gas per
liter using the ideal gas law:

The density, the number of grams per liter, is obtained using the
molar mass as a conversion factor:

**Problem (3): Calculate the pressure at at 22**

^{o}C which oxygen has a density of 1.44 g/L.**Solution**

We first change the density in grams per liter to moles per liter, then use that value in the ideal gas law:

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