Equimolal Diffusion

Definition

Equimolal diffusion is a mass transfer phenomenon occurring in a binary gas mixture where the molar flux of one component diffusing in one direction is exactly equal in magnitude but opposite in direction to the molar flux of the second component. In this process, there is no net molar flow of the total gas mixture.

Main Content

1. The Condition of Steady State

In equimolal diffusion, the total pressure of the system remains constant throughout the process.
Because the moles of gas moving in one direction are replaced by an equal number of moles moving in the opposite direction, the total concentration of the gas mixture remains unchanged.

2. Binary System Dynamics

The process involves two components, let’s call them A and B.
As molecule A moves from a region of high concentration to low concentration, molecule B moves from its high concentration region to its low concentration region, effectively "swapping" places.

3. Fick’s Law of Diffusion

The governing equation for this process is derived from Fick's Law of Diffusion.
The molar flux ($N_A$) is directly proportional to the concentration gradient: $N_A = -D_{AB} \frac{dc_A}{dz}$.

Working / Process

1. Establishing the Concentration Gradient

A concentration gradient is established between two points, $z_1$ and $z_2$.
For example, if a gas bulb contains pure A at $z_1$ and pure B at $z_2$, A will naturally diffuse toward $z_2$ and B toward $z_1$.

2. Counter-Diffusion Mechanism

As A molecules move into the space occupied by B, they displace an equal volume of B molecules.
This creates a continuous counter-current motion where the net velocity of the center of gravity of the mixture is zero.

3. Mathematical Integration

Since $N_A = -N_B$, we integrate the flux equation across the distance of travel.
The resulting design equation is: $N_A = \frac{D_{AB} \cdot P}{RT \cdot \Delta z} \cdot (p_{A1} - p_{A2})$.

       Concentration Gradient

    High (A) --------> Diffusing (A) --------> Low (A)
    [z1]                                        [z2]

    Low (B) <-------- Diffusing (B) <-------- High (B)
    [z1]                                        [z2]

(Diagram: Illustrating the equal and opposite molar exchange between two components across a distance.)

Advantages / Applications

Used extensively in the design of distillation columns where vapor and liquid phases exchange components in a counter-current manner.
Simplifies the mathematical modeling of gas separation processes in chemical engineering.
Found in the study of gas-phase reactions occurring on catalyst surfaces where the product and reactant diffuse in opposite directions.

Summary

Equimolal diffusion is a balanced mass transfer process where two substances diffuse at the same molar rate in opposite directions, resulting in no net change in the total number of moles in the system. It is a fundamental concept in chemical engineering used to simplify mass transfer calculations in steady-state binary gas systems.

Important terms to remember: - Molar Flux: The amount of substance passing through a unit area per unit time. - Binary Mixture: A system consisting of only two chemical components. - Concentration Gradient: The change in concentration of a substance over a specific distance. - Steady State: A condition where the properties at any point in the system do not change over time.