Assuming that carbon dioxide behaves ideally, climate we deserve to use the ideal gas law:

#PV=nRT#.

You are watching: What is the density of carbon dioxide at stp

Since us are looking for the thickness of #CO_2#, we have the right to modify the law as follows:

First we change #n# by #n=m/(MM)# where, #m# is the mass and #MM=40g/(mol)# is the molar mass of #CO_2#.

#=>PV=nRT=>PV=(m)/(MM)RT#

Then rearrange the expression to become:

#P=m/V(RT)/(MM)# whereby #m/V=d# (#d# is the density).

#=>P=(dRT)/(MM)=>d=(PxxMM)/(RT)#

Therefore, #d=(1cancel(atm)xx40g/(cancel(mol)))/(0.08201(L*cancel(atm))/(cancel(K)*cancel(mol))xx273cancel(K))=1.79g*L^(-1)#


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Truong-Son N.
might 18, 2016

REFERENCE DENSITY

Wikipedia offers the density as #"0.001977 g/mL"# in ~ #"1 atm"#, or if we convert it because that #"1 bar"#, #color(blue)("0.001951 g/mL")#.

Or, one have the right to calculate this native this website.

This additionally gives a real fixed density of #color(blue)("0.001951 g/mL")# in ~ #"1 bar"# and also #0^
"C"#.

DENSITY presume IDEALITY

To gain an idea of how the thickness is like when assuming ideality, we can use the ideal gas law come compare.

#mathbf(PV = nRT)#

where:

#P# is the pressure in #"bar"#. STP at this time involves #"1 bar"# pressure.#V# is the volume in #"L"#.#n# is the #mathbf("mol")#s of gas .#R# is the universal gas constant, #"0.083145 L"cdot"bar/mol"cdot"K"#.#T# is the temperature in #K"#.

#P/(RT) = n/V#

Notice how #(nM_m)/V = rho#, whereby #M_m# is the molar massive of #"CO"_2# (#"44.009 g/mol"#, not #"40 g/mol"#...), and #rho# is the mass thickness in #"g/L"#. Thus:

#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 #0.72%# error indigenous the true density, which is fairly good. Thus, #"CO"_2# is fairly ideal.

DENSITY there is no ASSUMING IDEALITY

Let"s calculation the density one more way.

We can likewise use the compressibility factor #Z = (PV)/(nRT)#, which is one empirical constant regarded how easily #"CO"_2# responds come compression. If #Z = 1#, then #"CO"_2# is perfectly ideal.

From this website again, I acquire #Z = 0.9934#.

Since #Z , #"CO"_2# is much easier to compress 보다 a similar ideal gas (thus the molar volume is much less than #22.711# at #"1 bar"# and also #"273.15 K"#).

Let"s check out what its density is this time.

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#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 in ~ that... It"s dead-on, and also all ns did was usage #Z# as a correctional factor in the best gas law. :)