[skeme]

Calculate the molar volume of methane at 0°C and 1x10^7Pa assuming that the gas behaves perfectly.

I know that at stp the molar volume of a gas is 22.413 L/mol

Methane is not a perfect gas. Given the second virial coefficient (B) of methane under these conditions is -0.2393, calculate the molar volume

Any help with the above would be much appreciated

[Yggdrasil]

Molar volume is n/V.  The ideal gas equation of PV=nRT.  Solve for n/V.

For the second equation, look up the virial equation of state in your chem book, then solve for n/V.

[skeme]

by using V/n = RT/p i got 22.710 L/mol is this right?

[Yggdrasil]

At STP (0^oC, 1.013x10⁵ Pa), a gas has a molar volume of 22.413 L/mol.  When you increase the pressure to 1x10⁷ Pa, do you expect one mole of gas to occupy a greater volume or a smaller volume?

[skeme]

I would expect it to have a smaller volume 


by using V/n = RT/p i got 0.0002271 L/mol

[AWK]

22.7 or 22.4 L/mol is a correct value depending on a standard pressure taken (10⁵ Pa or 1.013x10⁵ Pa)

[Yggdrasil]

For the molar volume of an ideal gas at 273K and 10⁷Pa, I get 0.227 L/mol.

V/n = RT/P
R = 8.314 L kPa mol^-1 K^-1
T = 273 K
P = 1x10⁴ kPa

[skeme]

Thanks for the help 

Before you mentioned virial equation of state did you mean this

PV/nRT = z = 1 + B(T)n/V?

[Yggdrasil]

Yes.

[skeme]

I'm having problem rearranging the equation to make n/v the subject

[Yggdrasil]

It ends up giving you a quadratic equation for n/V.

[skeme]

would it be pVm =  RT (1 + B/Vm) ?

[Yggdrasil]

If you multiply through by V_m, you can get a quadratic equation of the form:

aV_m² + bV_m + c = 0