Question

Thermodynamics, or chemistry

Why is Z unitless in the compressibility factor, i.e. Z = (PV)/(nRT)

Answer 1

The deviation from ideal gas behaviour is measured in terms of compressibility factor (Z). Mathematically,

Z = pV/nRT                                       where Z= 1 for ideal gas

In the above equation,

p = Pressure of gas (Pa/ atm/ torr/ bar )

V = Volume of gas (Litre / m³)

n = No. of moles of gas ( mol )

R = Gas constant

T = Temprature of gas ( Kelvin )

The unit of gas constant should be selected on thae basis of the units of pressure and volume,

If Pressure is given in atm and volume in litre, then unit of gas constant to be used is L atm mol^-1 K^-1

If Pressure is given in torr and volume in litre, then unit of gas constant to be used is L Torr mol^-1 K^-1

Now, we calculate unit of Z (Compressibility factor)

Assume that pressure is given in atm.Then,

Z = pV/nRT

On substituting the units of all parametres, we get,

Z = (atm )*( L) / ( mol ) * ( K ) * (L atm mol^-1 K^-1)

Now on solving above equation we can observe that each unit cancels out the other and thus Z (compressibility factor) is always unitless.

NOTE : If we calculate Z for other units of pressure such as pascal, bar or torr the compressibility factor will always be unitless.