Respuesta :
Answer:
[tex]d=0.92\frac{kg}{m^{3}}[/tex]
Explanation:
Using the Ideal Gas Law we have [tex]PV=nRT[/tex] and the number of moles n could be expressed as [tex]n=\frac{m}{M}[/tex], where m is the mass and M is the molar mass.
Now, replacing the number of moles in the equation for the ideal gass law:
[tex]PV=\frac{m}{M}RT[/tex]
If we pass the V to divide:
[tex]P=\frac{m}{V}\frac{RT}{M}[/tex]
As the density is expressed as [tex]d=\frac{m}{V}[/tex], we have:
[tex]P=d\frac{RT}{M}[/tex]
Solving for the density:
[tex]d=\frac{PM}{RT}[/tex]
Then we need to convert the units to the S.I.:
[tex]T=100^{o}C+273.15[/tex]
[tex]T=373.15K[/tex]
[tex]P=1bar*\frac{0.98atm}{1bar}[/tex]
[tex]P=0.98atm[/tex]
[tex]M=28.9\frac{kg}{kmol}*\frac{1kmol}{1000mol}[/tex]
[tex]M=0.0289\frac{kg}{mol}[/tex]
Finally we replace the values:
[tex]d=\frac{(0.98atm)(0.0289\frac{kg}{mol})}{(0.082\frac{atm.L}{mol.K})(373.15K)}[/tex]
[tex]d=9.2*10^{-4}\frac{kg}{L}[/tex]
[tex]d=9.2*10^{-4}\frac{kg}{L}*\frac{1L}{0.001m^{3}}[/tex]
[tex]d=0.92\frac{kg}{m^{3}}[/tex]
