Question

Calculate V and Z for methyl chloride at 100 ° C and 55bar for the ideal gas equation, by the equation of virial. Data: R = 83.14 cm 3 bar/molK; viral coefficient B equals -242.5 cm3/mol.

Answer 1

From the ideal gas equation

Molar volume V = RT/P

= (83.14 cm3-bar/mol-K) x (100+273)K / 55 bar

= 563.84 cm3/mol

Z = 1 + (B/V) + (C/V^2)

Z = 1 - (242.5/563.84) + ( 25200/563.84^2)

Z = 1 - 0.43 + 0.0793

Z = 0.6493

From virial equation

B' = B/RT = 242.5/(83.14*373) = 0.00782

C' = (C - B^2) / (RT)^2

= (25200 - 242.5^2) / (83.14 x 373)^2

= - 3.49*10^-5

Z = 1 + B'P + C'P^2

= 1 + 0.00782 x 55 - 3.49*10^-5 x 55^2

= 1.325

V = ZRT/P

= 1.325 x 83.14 cm3-bar/mol-K x 373 K / 55 bar

= 746.22 cm3/mol