Question

Find the molar volume of propane at 375 K and 21 atm using the following methods. For each method, calculate the emor in the ideal gas estimation

a) Ideal gas equation

b) Viral equation

c) Van der Waal equation

d) SRK equation

Answer 1

Molar volume

a) Ideal gas equation

Using,

molar volume = RT/P

with,

R = gas constant, T = 375 K , P = 21 atm

we get,

molar volume = 0.0805 x 375/21 = 1.465 L/mol

b) Virial equation

second virial coefficient for propane (B) = 0.0905 - 9.39/0.08205 x 375 = -0.215 L/mol

Using,

Pressure(P) = (RT/Vm)(1+B/Vm)

feeding values,

21 = (0.08205 x 375/Vm)(1+ (-0.215/Vm))

0.68Vm = 0.215Vm + 1

Vm = 0.316 L/mol

c) Van der waal equation,

For propane a = 9.39 L^2.atm/mol^2, b = 0.0905 L/mol

Rearranging Van der Waal equation,

let Vm represents molar volume, then,

Vm^3 - (RT/P + b)Vm^2 + (a/P)Vm - ab/P = 0

feeding the values,

Vm^3 - ((0.08205 x 375/21) + 0.0905)Vm^2 + 9.39Vm/21 - 9.39 x 0.0905/21 = 0

Vm^3 - 1.55Vm^2 + 0.45Vm - 0.04 = 0

Solving,

molar volume Vm = 0.120 L/mol

Missing standard values for the last one.