Question

Unit of ionic mobility is:
A. \[{{m}^{2}}{{\sec }^{-1}}vol{{t}^{-1}}\]
B. \[m{{\sec }^{-1}}\]
C. \[m{{\sec }^{-1}}volt\]
D. \[m{{\sec }^{-1}}vol{{t}^{-1}}\]

Answer 1

Hint: As the name suggests, ionic mobility refers to the mobility, i.e., the ability of ions to move, as a result of an electrical field. So, solve this question by relating units of velocity and electric field.

Complete step by step answer:
Ionic mobility is also known as electrical mobility. It is defined as the speed achieved by a charged particle or an ion moving through a gas as a response to an electric field that is pulling them. It is denoted by the symbol \[(\mu )\].
Ionic mobility can be expressed as a ratio of drift velocity of a particle to the magnitude of electric field.

Therefore, \[\mu =\dfrac{{{v}_{d}}}{E}\]

Where,
\[\mu \] = Ionic mobility
\[{{v}_{d}}\] = Drift velocity \[\left( \dfrac{m}{\sec } \right)\]
\[E\] = Magnitude of electric field \[\left( \dfrac{Volt}{m} \right)\]

Taking the ratio of drift velocity and electric field, we get the unit –
\[{\dfrac{m}{\sec }}/{}_{\dfrac{Volt}{m}}\] = \[\left( \dfrac{{{m}^{2}}}{Volt.\sec } \right)\].

Therefore, the answer is – option (a) – Unit of ionic mobility is \[{{m}^{2}}{{\sec }^{-1}}vol{{t}^{-1}}\].

Additional information: Drift velocity is defined as the average velocity which is attained by charged particles, such as electrons and ions in a material due to an electric field. Drift velocity is proportional to the flow of current.

Note: Ionic mobility is directly proportional to the net charge of the particle. Ionic mobility is also inversely proportional to the Stokes radius of the ion, which is equal to the effective radius of the moving ion including any molecules of water or other solvent that move with it.