# What is the density of carbon dioxide at STP?

##### 2 Answers

#### Explanation:

Assuming that carbon dioxide behaves ideally, then we can use the ideal gas law:

Since we are looking for the density of

First we replace

Then rearrange the expression to become:

Therefore,

**REFERENCE DENSITY**

Wikipedia gives the density as

Or, one can calculate this from this website.

This also gives a

real mass densityof#color(blue)("0.001951 g/mL")# at#"1 bar"# and#0^@ "C"# .

**DENSITY ASSUMING IDEALITY**

To get an idea of how the density is like when assuming ideality, we can use the **ideal gas law** to compare.

#\mathbf(PV = nRT)# where:

#P# is thepressurein#"bar"# . STP currently involves#"1 bar"# pressure.#V# is thevolumein#"L"# .#n# is the#\mathbf("mol")# s of gas.#R# is theuniversal gas constant,#"0.083145 L"cdot"bar/mol"cdot"K"# .#T# is thetemperaturein#K"# .

#P/(RT) = n/V#

Notice how

#color(blue)(rho) = (PM_m)/(RT)#

#= (("1 bar")("44.009 g/mol"))/(("0.083145 L"cdot"bar/mol"cdot"K")("273.15 K"))#

#=# #"1.94 g/L"#

#=# #color(blue)("0.001937 g/mL")#

That is about

**DENSITY WITHOUT ASSUMING IDEALITY**

Let's calculate the density another way.

We can also use the **compressibility factor** *empirical constant* related to how easily

From this website again, I get

#Z = 0.9934# .

Since

Let's see what its density is this time.

#color(green)(Z) = P/(RT)V/n#

#Z/(M_m) = P/(RT)V/(nM_m)#

#= color(green)(P/(RTrho))#

Thus...

#color(blue)(rho) = (PM_m)/(RTZ)#

#= (("1 bar")("44.009 g/mol"))/(("0.083145 L"cdot"bar/mol"cdot"K")("273.15 K")(0.9934))#

#=# #"1.9507 g/L"#

#~~# #color(blue)("0.001951 g/mL")#

Oh look at that... it's dead-on, and all I did was use *correctional factor* in the ideal gas law. :)