Question

Ionic mobility of $A{g^ + }$ (\[{\lambda _{A{g^ + }}} = 5 \times {10^{ - 4}}{\Omega ^{ - 1}}c{m^2}equi{v^{ - 1}}\]) is:

Answer 1

Hint: Ionic mobility for any ion is the average velocity that an atom maintains while drifting through as specified gas under the influence of a unit electric field. It depends on the nature of the gas and also its density.

Complete step by step answer:
Here as per the given question, we are given ionic conductance for Ag (${\lambda _{A{g^ + }}}$) as $5 \times {10^{ - 4}}$ we are not given the electric potential, we will calculate the ionic mobility at unit electric potential also known as absolute ionic mobility and ionic mobility or ionic conductance is given as

Absolute Ionic Mobility (\[{\mu _{A{g^ + }}}\])=$\dfrac{{Ionic\;Conductivity{\text{ }}({\lambda _{A{g^ + }}})}}{{96500}}$

$ \Rightarrow \dfrac{{5 \times {{10}^{ - 4}}}}{{96500}}$

$ \Rightarrow 5.2 \times {10^{ - 9}}cm/s$

Additional Information:
Ionic mobility is affected by viscosity and also by the size of the ions. Large ions have less mobility than the smaller ions due to their mass. We utilize the concept of ionic mobility to remove particles from exhaust gases in industries. Also, there exists a type of analytical technique that involves the use of the concept of ionic mobility to identify and separate the molecules and it is called ion mobility spectrometry

Note: Ionic mobility is directly proportional to the speed of ions. When we have an ion in a vacuum, if we provide a non zero potential gradient to it, the ion accelerates indefinitely as there is an absence of any molecules for collisions. But when the ion accelerates in the gas, it collides with gas molecules and also deflects and its average motion comes out to be uniform as it accelerates for a short time before getting deflected.