The **key difference between mobility and diffusion coefficient** is that mobility is the ability of a charged particle to move due to the effect of an electrical field whereas diffusion coefficient is a constant that describes the relationship between molar flux and the concentration gradient.

Mobility is the ability of charged particles to move through a medium as a response to an electric field. The diffusion coefficient is a constant of proportionality between the molar flux (due to molecular diffusion) and the concentration gradient of chemical species.

### CONTENT

1. Overview and Key Difference

2. What is Mobility

3. What is Diffusion Coefficient

4. Relationship Between Mobility and Diffusion Coefficient

5. Mobility and Diffusion Coefficient in Tabular Form

6. Summary – Mobility vs Diffusion Coefficient

## What is Mobility

Mobility is the ability of charged particles to move through a medium as a response to an electric field. This electric field pulls the charged particles. In this context, charged particles are mainly electrons or protons. We can separate different ions according to their mobility; when this separation is done in the gas phase, it is called ion mobility spectrometry, and if it is in the liquid state, we can call it electrophoresis.

When there is a charged particle in a gas or liquid state that occurs at a uniform electric field, the charged particle can be accelerated to a velocity that is called a constant drift velocity. The mathematical expression for mobility is as follows:

**v _{d }= µE**

In this equation, v_{d} refers to the drift velocity, µ refers to the mobility and E is the magnitude of the electric field. The unit of measurement for v_{d} is m/s, the unit of measurement for µ is m^{2}/V.s, and the unit of measurement for E is V/m. Therefore, the mobility of charged particles is the ratio of the drift velocity to the magnitude of the electric field.

Moreover, electrical mobility is directly proportional to the net electrical charge of the charged particle.

## What is Diffusion Coefficient?

Diffusion coefficient is a constant of proportionality between the molar flux (due to molecular diffusion) and the concentration gradient of chemical species. It describes the driving force of diffusion. Therefore, the higher the diffusion coefficient, the faster the diffusion of substances. The unit of measurement of this parameter is m^{2}/s.

Typically, the diffusion coefficient depends on temperature. In solids, the diffusion coefficient at different temperatures can be calculated using the Arrhenius equation. Similarly, we can use the Stokes-Einstein equation to calculate the temperature dependence of diffusion coefficient in liquids. In gases, the relationship between diffusion coefficient and temperature can be determined using the Chapman-Enskog theory.

## Relationship Between Mobility and Diffusion Coefficient

Mobility and diffusion coefficient are closely related terms. Here, electrical mobility is related to the diffusion coefficient of the sample species through the following equation. It is called the Einstein relation.

**µ = (q/kT)D**

In this equation, µ is the mobility, q is the electrical charge, k is the Boltzmann constant, T is the temperature of the gas, and D is the diffusion coefficient. Therefore, depending on the gas temperature and the electrical charge of the charged particle, the mobility is directly proportional to the diffusion coefficient.

## Difference Between Mobility and Diffusion Coefficient

The key difference between mobility and diffusion coefficient is that mobility is the ability of a charged particle to move due to the effect of an electrical field whereas diffusion coefficient is a constant which describe the relationship between molar flux and the concentration gradient.

The following table summarizes the difference between mobility and diffusion coefficient for side by side comparison.

## Summary – Mobility vs Diffusion Coefficient

Mobility and diffusion coefficient are two related chemical terms. The key difference between mobility and diffusion coefficient is that mobility is the ability of a charged particle to move due to the effect of an electrical field whereas diffusion coefficient is a constant which describe the relationship between molar flux and the concentration gradient.

##### Reference:

1. “Diffusion Coefficient.” *An Overview | ScienceDirect Topics*.

##### Image Courtesy:

1. “Motion by electrophoresis of a charged particle” By Daniele Pugliesi – File:Moto di uno ione in un elettrolita.svg (my work) (CC BY-SA 3.0) via Commons Wikimedia

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