Question

The ionic mobility of alkali metal ions in aqueous solution is maximum for:
A.${{\rm{K}}^ + }$
B.${\rm{R}}{{\rm{b}}^ + }$
C.${\rm{L}}{{\rm{i}}^ + }$
D.\[{\rm{N}}{{\rm{a}}^ + }\]

Answer 1

Hint: The dependence of ionic mobility on the size of hydrated ion can be used to deduce the order of increasing ionic mobility for the given ions

Step by step answer:
We have $7$ horizontal periods and $18$ vertical groups as per periodic classification of elements in the modern periodic table. This classification has helped us in establishing some general trends for properties of elements such as atomic radius, ionization enthalpy, ionic radius, hydration enthalpy and many more.

Here, we will have a look at the hydration enthalpy for elements in a group. We know that size increases down a group as additional shells are being added up. This leads to decrease in the hydration enthalpy because the two are inversely proportional to each other. So, we can say that the topmost element would have the smallest size and the highest hydration enthalpy.
Now, we know that ionic mobility is related to the ease or speed with which an ion can move in a solution. We can add to this that highly solvated ions have a large number of solvent molecules around them and thus have less mobility. So, hydration enthalpy is inversely proportional to the ionic mobility as well.

Now, as we consider the given ions, all of them belong to the first group. They can be arranged in the increasing order of ionic radius as follows:
\[{\rm{L}}{{\rm{i}}^ + } < {\rm{N}}{{\rm{a}}^ + } < {{\rm{K}}^ + } < {\rm{R}}{{\rm{b}}^ + }\]
Depending on the ionic size, we can arrange them in the increasing order of hydration enthalpy as follows:

\[{\rm{R}}{{\rm{b}}^ + } < {{\rm{K}}^ + } < {\rm{N}}{{\rm{a}}^ + } < {\rm{L}}{{\rm{i}}^ + }\]
Finally, they can be arranged in the increasing order of ionic mobility which is inversely proportional to the hydration enthalpy as follows:

\[{\rm{L}}{{\rm{i}}^ + } < {\rm{N}}{{\rm{a}}^ + } < {{\rm{K}}^ + } < {\rm{R}}{{\rm{b}}^ + }\]
Hence, \[{\rm{R}}{{\rm{b}}^ + }\] has the maximum ionic mobility which makes option B to be the correct one.


Note: Most of the trends in the properties are inter-related so we can use as per our convenience. For example, effective nuclear charge down a group can be related to its tendency to attract more solvent particles that would make it too big/heavy to move quickly.