The compressibility factor
(Z) is a measure of how much a real gas deviates from ideal gas behavior. For an ideal gas, the compressibility factor is 1 . For real gases,
Z can be less than or greater than 1 depending on the conditions, such as pressure and temperature.
The van der Waals equation for real gases is given by:
(P+‌)(Vm−b)=RT Where:
P is the pressure
Vm is the molar volume
R is the universal gas constant
T is the temperature
a and
b are van der Waals constants for the gas
At high pressures, the term
‌ becomes negligible, and the van der Waals equation can
b approximated as:
P(Vm−b)=RTRearranging for
Vm, we get:
Vm=‌+b The compressibility factor
Z is defined as:
Z=‌ Substituting the expression for
Vm into the definition of Z , we get:
Z=‌ Simplifying this expression gives us:
Z=1+‌ Thus, the compressibility factor for a van der Waals gas at high pressure is:
Option B:
1+‌