Concentration relationships in mass transfer
1) Relationships between mass fraction, molar fraction, density, partial pressure of ideal gases:
(a) Partial density of species i:
(b) Total density of a mixture:
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(c) Mass fraction wi of species i and its relation to density.
(d) Mass concentration and its relationship with density.
(e) Molar concentration Ci and its relationship with density.
Example 1: 23 g ethanol in 1L of ethanol-water solution (density of ethanol = 789 kg/m3)
Example 2: molar concentration of Ar in air (given M(Ar) = 20g/mol; molar fraction in air is 0.9%).
(f) If we know or can calculate the density of a component, then
Repeat the examples in (e)
(g) Average molar mass of a gas mixture.
Example: Mave of air, given MO2 = 32 kg/kmol; MN2 = 28 kg/kmol; Ar = 40 kg/kmol…; their molar fractions in air: 21%; 78.1%; 0.9%, respectively.
(h) Relation between mass fraction wi and molar fraction yi and molecular masses Mi .
Example: mass fraction of O2 in air
(i) Relations between wi, density, molar fraction.
(j) Relation of partial pressure of gas species i and its molar fraction – Dalton’s law Ideal gas and the basic assumptions.
(k) Relation of partial pressure of gas species i and its mass fraction
2) Mass equilibrium between gas and solution phases – Henry’s law
Henry’s law is a gas law that states that the amount of dissolved gas (different ways to describe the amount) in a liquid is proportional to its partial pressure above the liquid. The proportionality factor is called Henry’s law constant (corresponds to ways we describe the “amount” of gas dissolved).
(a) basic form
(b) Locations of Pi and Xi (surface v. bulk)
(c) Variation of unit of H
(d) When Xi is in molar fraction; when it is mass fraction. (give an example)
Example: A tank contains a 50L mixture of ethanol in water and is open to the atmosphere ( 25C, 1 atm) where the relative humidity is 0 %, but in a location where the air above the tank can be considered stagnant. (today’s tutorial question 3)
a) If the mole fraction of ethanol in the tank is 5 %, what is the concentration of
ethanol on the air side of the interface?
b) If the mole fraction of ethanol in the tank is 20 %, what is the concentration
of ethanol on the air side of the interface?
c) How do your answers to (a) and (b) change if the relative humidity is 90 %?
3) Mass equilibrium between gas and solution phases – Raoule’s law. (Partial pressure of each component of an ideal mixture of liquids is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture)
(a) basic form
4) Solubility of gas in solid
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