Knowing the mole fractions in a mixture leads to calculation of several important properties of the mixture:
• the molecular weight, Mm
• molal specific heat, MCp(m)
• the critical pressure, Pc(m), and
• critical temperature Tc(m).
A sample problem is included in Appendix B. Also see Figure 100-6 for a sample calculation.
The mole fraction X is
Nm = Total moles in a mixture
N1, etc. = Number of moles of each individual component
A “mole” is actually a number of molecules (about 6 x 1023 ). A “mole fraction” is the ratio of molecules of one component in a mixture. For example, if the mole fraction of methane in natural gas is 0.90, this means that 90% of the molecules are methane. Since volume fractions are equivalent to mole fractions, the mixture is also 90% (by volume) methane.
The mixture fractions could also be calculated on a mass or weight basis. The mole (volume) basis is used in compressor calculations because it is a simpler, less confusing method.
The molal specific heat is used to determine the k value (ratio of specific heats) as follows. The k value is often called the adiabatic exponent, and is a value used in the calculation of horsepower, adiabatic head, and adiabatic discharge temperature. (Refer to Isentropic [Adiabatic] Compression.) The k value is:
MCp(m) = Molal specific heat (heat capacity) of mixture at constant pressure
778 = Conversion factor, ft-lb/BTU
Cp = Specific heat at constant pressure
Cv = Specific heat at constant volume
Ro = See Equation 100-1 for Ro definition
MCp(m) should be taken at the desired temperature (usually the average of suction and discharge temperature). This aspect will be covered in Isentropic (Adiabatic) Compression. Note that the k value of the mixture must be determined by first determining the molal heat capacity of the mixture (see Figure 100-6). It is a common mistake to multiply the k values of the individual gas components by their respective mole fractions to determine the k value of the mixture.