This question is providing the mass, volume and temperature of carbon dioxide gas for us to calculate the pressure according to the van der Waals equation of state given the parameters a and b as well. The obtained result was 7.1 atm according to the following work:
First, we calculate the molar volume of carbon dioxide gas by dividing the volume over the moles of this gas:
[tex]n=\frac{165g}{44g/mol} =3.75mol\\\\V_m=\frac{12.5L}{3.75mol} =3.33L/mol[/tex]
After that, we can write the van der Waals equation of state:
[tex]P=\frac{RT}{V_m-b} -\frac{a}{V_m^2}[/tex]
Then, we plug in the numbers we were given and we calculated before:
[tex]P=\frac{0.08206\frac{atm*L}{mol*K}*(25+273)K}{3.33\frac{L}{mol} -0.0427\frac{L}{mol}} -\frac{3.59\frac{atm*L^2}{mol^2} }{(3.33\frac{L}{mol})^2}[/tex]
Finally, we obtain the numerical result by taking into account that all the Kelvin, liters and moles are cancelled out due to the dimensional analysis one can have done.
[tex]P=7.1atm[/tex]
Learn more:
