Book: Welty, James R.; Wicks, Charles E.; Wilson, Robert E. Fundamentals of Momentum, Heat, and Mass Transfer, third edition. New York: John Wiley and Sons. 1984.
Chapter 24: Fundamentals of Mass Transfer, Page 471
Note: LaTex causes certain parts of the text to be raised, italicized, and larger. It is not to the power. I believe the “power” will be recognizable once I point the latter out.
The composition of air is often given in terms of only the two principle species in the gas mixture
Determine the mass fraction of both oxygen and nitrogen and the mean molecular weight of the air when it is maintained at 25C (298 K) and 1 ATM . The molecular weight of oxygen is 0.032 kg/mol and of nitrogen is 0.028 kg/mol.
As a basis for our calculations, consider 1 mole of the gas mixture;
moles of oxygen present = (1 mol) = (1 mol)(0.21) = 0.21 mol oxygen
mass of oxygen present = (0.21 mol) = (0.21 mol) = 0.00672 kg oxygen
moles of nitrogen present = (1 mol) = (1 mol)(0.79) = 0.79 mol nitrogen
mass of nitrogen present = (0.79 mol) = (0.79) = 0.0221 kg nitrogen
total mass present = kg oxygen + kg nitrogen = 0.00672 kg oxygen + 0.0221 kg nitrogen = 0.0288 kg
Since 1 mole of the gas mixture has a mass of 0.0288 kg, the mean molecular weight of the air must be 0.0288: = 0.0288 kg/mol. When one takes into account the other constituents that are present in air, the mean molecular weight of air is often rounded off to .
This problem could also be solved using the ideal gas law, PV = nRT. At ideal conditions, 0C or 273 K and 1 atm or pressure, the gas constant is evaluated to be
Remember, we want to calculate the mass fraction of oxygen and nitrogen, and the mean molecular weight of air. Which to calculate first is the key
PV = nRT
n = 1 mole; T = 273 K; P = ; V =
R = =
R = =
The of volume the gas mixture, at 298 K, is
The concentrations are (1 mole basis)
The total density, is
mass of =
mass of =
total mass = 0.00672 kg + 0.0221 kg = 0.0288 kg
total density =
and the mean molecular weight of the mixture is
As a side note, density, , can be used to calculate mass percent of and