Answer to Question #297006 in Physical Chemistry for key

Question

At 273 K measurements on argon gave B = -21.7 cm3 mol-1 and C = 1200 cm6 mol-2, where B and C are the second and third virial coefficients in the expansion of Z in powers of 1/Vm. Assuming that the perfect gas law holds sufficiently well for the estimation of the second and third terms of the expansion, calculate the compression factor of argon at 100 atm and 273 K. From your result, estimate the molar volume of argon under these conditions

Answer 1

$Z= 1+B(\frac{1}{v_m})+C(\frac{1}{v_m})^2+....…$

$PV= nRT$

But$\frac{V}{n}=V_m$

For an ideal gas

$V_m= \frac{0.08205×273}{100}=0.224L\\=224cm^3/mol$

Compression factor

$Z=1+-21.7(\frac{1}{224})+1200(\frac{1}{224}) \\=0.9270$

Real $V_m= Z(V_m)$

$= 0.9270×224\\=207.7cm^3$