Question

The compressability factor for the Van der Waal equation of state is Z=(PV/RT)=(V)/(V-b)-(a/RTV). As molar volume becomes large compared to b what happens to V/(V-b)? (What is the limiting value for the fraction V/(V-b) as molar volume gets very large?) What is the limiting value of - a/(RTV) as molar volumes get very large? What is the limiting value for the compressibility factor Z as molar volume increases? Molar volumes increase as pressure _________ .

Answer 1

Given

Z= (PV/RT) = V/(V-b) - (a/RTV)

when molar volume increases when compared b value of term V/(V-b) will be increasing until it reaches limiting value of 1 (because when V is very large to b => (V-b) will tend to V so V / (V-b) will become 1 )

the term (-a/RTV) will keep increasing from -ve some value until it reaches limiting value of 0 ( because as V increases the term (-a/RTV) will decrease as V is in denominator and will eventually tend to 0)

so when V increases Z will tend to 1 as first term will tend to 1 and second term will tend to 0 hence Z will have a limiting value of 1

Molar volume will increase when pressure decreases as pressure and volume are inversely proportional