Definition of Concentration Terms in Mass Transfer

For a particular species, its concentration can be expressed in several ways.

In mass transfer applications, the only driving force is the concentration gradient while other driving forces like temperature and pressure gradients are kept constant. There needs to be a gradient of chemical potential between two points to create a driving force that allows mass transfer to occur.

A concentration gradient is a spatial difference in the abundance of the chemical species.

A concentration profile is a sketch indicating the magnitude of the concentration as a function of position and is often superimposed on a process to indicate where these changes occur. It is analogous to the velocity profile in fluid flow examples and illustrated below:

Mass concentration or molar concentration of components and mass or mole fraction of species are used to express concentration gradients.

Mass Concentration

For any species i, the mass concentration is expressed as ρ_i. It is defined as the mass of i per unit volume of a multi-component mixture. This is expressed as follows and has the same units as density:

Total mass concentration within a mixture is equal to overall density which can be expressed as follows, where n is the number of species in a mixture:

Mass Fraction

The mass fraction of species i (w_i) is the ratio of mass concentration of species i to the total mass density and can be expressed as:

From the definitions used for mass concentration into the above equation, we obtain the following expression:

Molar Concentration

The molar concentration (C_i) of component is the number of moles of the i^th component per unit volume of mixture. The total concentration in the system can be obtained by adding up all the molar concentrations of all the species in the mixture and is represented as:

To convert from mass to molar concentration, divide the mass concentration of species i by its molar weight. For an ideal gas mixture, the molar concentration of species i can be obtained from the ideal gas law (PV = nRT) as follows:

Where:

• ρ_i is the partial pressure of species i in the mixture,
• T is the absolute temperature,
• R is the universal gas constant. 

Thus, the total concentration in the gaseous system can be represented by:

Mole Fraction

The mole fraction of species i in a mixture is found by dividing the molar concentration of species i by total concentration in the system and is expressed as;

and

The summation of mole fractions of species in a mixture always adds up to 1 as shown: