Question

Which one of the ions in the table below would have the highest value of enthalpy of hydration?

Ionic radius (in mm)	Charge of ion
0.0065	+2
0.095	+1
0.135	+2
0.169	+1
0.181	+1

Answer 1

Hint: (1) The term ‘enthalpy of hydration’ or ‘hydration enthalpy’ is used to refer to the amount of energy which is released when one mole of gaseous ions is dissolved in water to form an infinitely dilute solution.
(2) The extent of hydration of an ion depends upon the charge density of the ion, i.e., the extent of hydration depends upon the size and the charge of the ion.

Complete step by step answer: The enthalpy of hydration is directly proportional to the charge density of the ion. Now, the charge density is directly proportional to the charge of the ion and inversely proportional to the radius of the ion. In other words, charge density of an ion is the ratio of the charge of the ion to its radius. So, we can write:
Charge density ${\text{ = }}\dfrac{{{\text{Charge}}}}{{{\text{Radius}}}}$
This means the ion with highest charge and smallest radius will have the highest charge density and hence the highest enthalpy of hydration.
This is because when the charge density of an ion is high, the force of attraction between the ion and the polar end of the water molecule is also high. This makes the hydration energy smaller for smaller ions.
Now, in the given question, three ions have +1 charge and two ions have +2 charge. So, the ions with charge +2 will have higher hydration enthalpy. Now, among the +2 charged ions, one has radius ${\text{0}}{\text{.0065mm}}$ and the other has ${\text{0}}{\text{.135mm}}$radius. So, the ion with radius ${\text{0}}{\text{.0065mm}}$and charge +2 will be the smallest and hence, it will have the highest value of enthalpy of hydration.

Note: Since charge density of ions decreases down a group and increases along a period, the hydration enthalpy will also decrease down a group and increase along a period. Also, the ion with highest charge density will have the smallest size before hydration but it will have the largest size after hydration due to the greatest extent of hydration. Moreover, the heavily hydrated ions have lesser ionic mobility, i.e., they move slower.