Question

Which of the following pairs of ions have nearly the same polarising power?
A. $N{a^ + }, M{g^{2 + }}$
B. $M{g^{2 + }}, A{l^{3 + }}$
C. $L{i^ + }, M{g^{2 + }}$
D. $N{a^ + }, R{b^ + }$

Answer 1

Hint: The polarising power of a cation is described as its ability to pull the electron cloud towards itself. The polarising power of a cation is its ability to distort the electron cloud of an anion. The polarising power of a cation is expressed by the symbol known as phi or $\Phi $ and it is referred to as the ionic potential. The ratio of charge on the cation to that of radius of the cation is equal to the value of $\Phi $ for that cation.

Complete step by step answer:
Here, different pairs of cations are given containing cations of alkali earth metals and alkaline earth metals. Sodium, lithium and rubidium are alkali metals whereas magnesium and aluminium are alkaline earth metals. As these all elements are metals, they lose electrons to form cations.
When these cations form an ionic compound with anions, they try to pull an ion's electron cloud towards itself but repel the positive nucleus of that anion. This results in the deformation of electron clouds of anion by the cation which is described as the polarising power of the cation.
Let us compare the polarising power of a pair of cations given in each option to identify the correct answer.
In option (A), the pair of cations given consists of $N{a^ + }$and $M{g^{2 + }}$ ions. Now, it is experimentally proved that, the cations with smaller size or higher charge will have higher polarising power than that of cations with larger size or smaller charge. The sodium ion ($N{a^ + }$) is a monovalent ion and has only $ + 1$ positive charge whereas, the $M{g^{2 + }}$ ion is divalent and possess $ + 2$ positive charge. The size of $N{a^ + }$ will be larger than that of $M{g^{2 + }}$. Hence, the polarising power of $N{a^ + }$ ion will be smaller than that of $M{g^{2 + }}$ ion due to high charge and smaller size of $M{g^{2 + }}$ ion.
Hence, option (A) is incorrect.
In option (A), the pair of cations given consists of $M{g^{2 + }}$ and $A{l^{3 + }}$ ions. Hence, the polarising power of $M{g^{2 + }}$ ion will be smaller than that of $A{l^{3 + }}$ ion due to high charge and smaller size of $A{l^{3 + }}$ ion. Therefore, option (B) is incorrect.
In option (C), the pair of cations given consists of $L{i^ + }$ and $M{g^{2 + }}$ ions. Though lithium is categorised as the alkali metals in the periodic table, it shows many similarities with the alkaline earth metal, magnesium. This is because the diagonal relationship between lithium and magnesium. It is assumed that there is an existence of a diagonal relationship between the pair of elements belonging to the second and third period of the Periodic table. These pairs of elements exhibit resemblance in their properties. On moving diagonally in the Periodic table, the ratio of charge on the cations of the elements and the cationic radius is almost same (The value of ionic radius for $L{i^ + }$ and $M{g^{2 + }}$ are 60 and 65pm respectively.). Therefore, the value of polarising power of $L{i^ + }$ and $M{g^{2 + }}$ ions will be almost the same. Hence, option (C) is correct.
The polarising power of a cation is inversely proportional to that of the size of that cation. Sodium and rubidium both are alkali metals placed in the same group in the periodic table. In the case of alkali metals, lithium has the highest polarizing power followed by sodium, potassium, rubidium and caesium. Amongst the alkali metals, caesium has the lowest polarizing power. Hence, sodium will definitely have higher polarizing power than that of rubidium. Hence, option (D) is incorrect.
The pair of ions which have nearly the same polarising power is $L{i^ + },M{g^{2 + }}$.

Hence, the correct option is option C.

Additional information:
Remember that, the increase in the value of ionic potential or $\Phi $causes an increase in the polarising power of a cation. This means an increase in the value of $\Phi $ for a cation will also result in increasing the covalent character of the ionic compound.
In the periodic table, the value of $\Phi $ increases as we move from left to right, as the charge on the cation increases but the cationic radius decreases. In the periodic table, as we move down the group, the extent of charge on the cation remains the same but there is an increase in cationic radius. This leads to a decrease in the value of $\Phi $.

Note: A polarising power is a characteristic of a cation whereas polarizability is a term used in the context of an anion. Both polarising power and polarizability are different terms. Polarizability of an anion is the ability of anion to become polarized by the cation. The polarizability of anions with large size will be large and hence, the electron cloud of that anion will distort easily by cation. Also, as the charge on the anion increases, the polarizability will also increase.