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PV=nRT
Since V=mρ, where m is the mass of the gas and ρ its and n=mM, where M is the molar mass of the gas, we can write:
Pmρ=mRTM
We now have to solve for ρ. Dividing both sides by Pm gives:
1ρ=mRTMPm
Which reduces to:
1ρ=RTMP
Reciprocate both sides:
ρ=MPRT.
Here,
M=16.04g/mol
P=1atm
T=273.15K
R=0.0821L atm K−1mol−1.
Inputting:
ρ=16.04⋅10.0821⋅273.15
ρ=0.72
Now we have our number. What about the unit?
We know that density's units are a mass unit divided by a volume unit.
The mass unit here is grams, as the molar mass was expressed in g/mol. The volume unit is liters, as the value of R contained that value. As 1L=1dm3, we can write the density as:
0.72g/dm3
Here, T=27
∘
C=27+273=300K
P=2.5 atm
The molar mass of(M) CO
2
=44g/mol
From ideal gas equation,
d=
RT
PM
=
0.0821×300
2.5×44
=4.46 g L
−1
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