Question

Hydration enthalpy of which of the following ions is highest?

• A. Mg$^{2+}$
• B. Na$^{+}$
• C. Ca$^{2+}$
• D. K$^{+}$

Hint:

Hydration enthalpy increases (becomes more negative) with increasing charge on the ion.
Hydration enthalpy increases (becomes more negative) with decreasing size of the ion (for ions of the same charge).
Charge density (charge/size ratio) is a good indicator: higher charge density leads to higher hydration enthalpy.
Generally, M$^{2+}$ ions have much higher hydration enthalpies than M$^+$ ions.
For ions in the same group, hydration enthalpy decreases down the group as ionic size increases.

Answer 1

The Correct Option is A

Hydration enthalpy is the enthalpy change when one mole of gaseous ions dissolves in sufficient water to give an infinitely dilute solution. It is an exothermic process (negative enthalpy change), so "highest" usually refers to the largest magnitude (most negative value). Hydration enthalpy depends on two main factors: 1. Charge of the ion: Higher the charge on the ion, stronger the electrostatic attraction with polar water molecules, and thus greater (more negative) the hydration enthalpy. 2. Size of the ion: Smaller the ionic radius, higher the charge density, leading to stronger attraction with water molecules, and thus greater (more negative) the hydration enthalpy. Let's compare the given ions: \begin{itemize} \item Mg$^{2+$:} Charge = +2. Magnesium is in Period 3, Group 2. \item Na$^{+$:} Charge = +1. Sodium is in Period 3, Group 1. \item Ca$^{2+$:} Charge = +2. Calcium is in Period 4, Group 2. \item K$^{+$:} Charge = +1. Potassium is in Period 4, Group 1. \end{itemize} Comparing based on charge: Ions with +2 charge (Mg$^{2+}$, Ca$^{2+}$) will have significantly higher (more negative) hydration enthalpies than ions with +1 charge (Na$^{+}$, K$^{+}$) due to stronger ion-dipole interactions. So, we can narrow down the choice to Mg$^{2+}$ and Ca$^{2+}$. Comparing Mg$^{2+$ and Ca$^{2+}$ (both have +2 charge):} We need to compare their ionic sizes. Mg is in Period 3, Group 2. Ca is in Period 4, Group 2. Since Ca is below Mg in the same group, Ca$^{2+}$ has a larger ionic radius than Mg$^{2+}$ (Ca$^{2+}$ has an additional electron shell). Ionic radius: Mg$^{2+}$<Ca$^{2+}$. Since Mg$^{2+}$ is smaller than Ca$^{2+}$ and both have the same +2 charge, Mg$^{2+}$ has a higher charge density. Therefore, Mg$^{2+}$ will have a stronger interaction with water molecules and a higher (more negative) hydration enthalpy than Ca$^{2+}$. So, among the given ions, Mg$^{2+}$ has the highest hydration enthalpy (largest negative value). Order of hydration enthalpy magnitude: Mg$^{2+}$>Ca$^{2+}$>Na$^{+}$>K$^{+}$. (Na$^+$ vs K$^+$: Both +1 charge. Na$^+$ is smaller than K$^+$, so hydration enthalpy of Na$^+$>K$^+$). (Comparing Ca$^{2+}$ and Na$^+$: Ca$^{2+}$ has +2 charge, Na$^+$ has +1. Ca$^{2+}$ is larger than Na$^+$. High charge usually dominates. $\Delta H_{hyd}(\text{Ca}^{2+}) \approx -1577 \text{ kJ/mol}$, $\Delta H_{hyd}(\text{Na}^{+}) \approx -406 \text{ kJ/mol}$. So, Ca$^{2+}$ is much higher than Na$^+$). \[ \boxed{\text{Mg}^{2+}} \]