Concept: Polarizing Power

The polarizing power of a cation is its ability to distort the electron cloud of an anion. It is directly proportional to the charge of the cation and inversely proportional to its size. This relationship is often expressed as the charge-to-size ratio (charge density).

Why (C) is correct:

We need to determine the increasing order of polarizing power for the given cations: ${\mathrm{K}}^{+},{\mathrm{Ca}}^{2+},{\mathrm{Mg}}^{2+}$, and ${\mathrm{Be}}^{2+}$. We will compare their charge-to-size ratios.

1. Charge: ${\mathrm{K}}^{+}$ has a charge of +1. ${\mathrm{Ca}}^{2+},{\mathrm{Mg}}^{2+},{\mathrm{Be}}^{2+}$ all have a charge of +2.

2. Size: For isoelectronic species or elements in the same period/group, size trends are important. In general, cationic size decreases across a period and increases down a group. Also, for ions with the same charge, size decreases with increasing atomic number within a period and increases with increasing atomic number within a group.

• ${\mathrm{K}}^{+}$ is larger than ${\mathrm{Ca}}^{2+}$ because $\mathrm{K}$ is to the left of $\mathrm{Ca}$ in the same period (though ${\mathrm{K}}^{+}$ and ${\mathrm{Ca}}^{2+}$ are isoelectronic with Argon, ${\mathrm{Ca}}^{2+}$ has a higher nuclear charge, pulling electrons more tightly).
• Within Group 2, the size decreases as we go up: ${\mathrm{Ca}}^{2+}>{\mathrm{Mg}}^{2+}>{\mathrm{Be}}^{2+}$.

Combining these, the approximate order of ionic radii is: ${\mathrm{K}}^{+}>{\mathrm{Ca}}^{2+}>{\mathrm{Mg}}^{2+}>{\mathrm{Be}}^{2+}$.

Now let's consider the charge-to-size ratio (polarizing power):

• ${\mathrm{K}}^{+}$: Charge = +1, Largest size. Therefore, lowest polarizing power.
• ${\mathrm{Ca}}^{2+}$: Charge = +2, Larger size than ${\mathrm{Mg}}^{2+}$ and ${\mathrm{Be}}^{2+}$.
• ${\mathrm{Mg}}^{2+}$: Charge = +2, Smaller size than ${\mathrm{Ca}}^{2+}$.
• ${\mathrm{Be}}^{2+}$: Charge = +2, Smallest size among the +2 ions. Therefore, highest polarizing power.

Comparing ${\mathrm{K}}^{+}$ and ${\mathrm{Ca}}^{2+}$: Although ${\mathrm{K}}^{+}$ is larger than ${\mathrm{Ca}}^{2+}$, its charge is only +1, while ${\mathrm{Ca}}^{2+}$ has a charge of +2. The higher charge of ${\mathrm{Ca}}^{2+}$ dominates, giving it a higher polarizing power than ${\mathrm{K}}^{+}$.

Thus, the increasing order of polarizing power is: ${\mathrm{K}}^{+}<{\mathrm{Ca}}^{2+}<{\mathrm{Mg}}^{2+}<{\mathrm{Be}}^{2+}$.

Option Analysis:

• A) ${\mathrm{Ca}}^{2+}<{\mathrm{Mg}}^{2+}<{\mathrm{Be}}^{2+}<{\mathrm{K}}^{+}$: Incorrect. ${\mathrm{K}}^{+}$ has the lowest polarizing power, not the highest.
• B) ${\mathrm{Mg}}^{2+}<{\mathrm{Be}}^{2+}<{\mathrm{K}}^{+}<{\mathrm{Ca}}^{2+}$: Incorrect. The order is completely scrambled.
• C) ${\mathrm{K}}^{+}<{\mathrm{Ca}}^{2+}<{\mathrm{Mg}}^{2+}<{\mathrm{Be}}^{2+}$: Correct. This sequence correctly reflects the increasing charge-to-size ratio.
• D) ${\mathrm{Be}}^{2+}<{\mathrm{K}}^{+}<{\mathrm{Ca}}^{2+}<{\mathrm{Mg}}^{2+}$: Incorrect. ${\mathrm{Be}}^{2+}$ has the highest polarizing power, not the lowest.

Correct Answer: (C)