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The correct order of hydration enthalpies is
(A) K$$^+$$
(B) Rb$$^+$$
(C) Mg$$^{2+}$$
(D) Cs$$^+$$
(E) Ca$$^{2+}$$
Choose the correct answer from the options below:
Hydration enthalpy depends on the charge density of the ion: higher charge and smaller ionic radius lead to greater (more negative) hydration enthalpy.
The ions given are (A) K$$^+$$ (charge = +1, ionic radius = 138 pm), (B) Rb$$^+$$ (charge = +1, ionic radius = 152 pm), (C) Mg$$^{2+}$$ (charge = +2, ionic radius = 72 pm), (D) Cs$$^+$$ (charge = +1, ionic radius = 167 pm) and (E) Ca$$^{2+}$$ (charge = +2, ionic radius = 100 pm).
Divalent cations have much higher hydration enthalpies than monovalent cations due to their greater charge density.
Between the divalent ions, Mg$$^{2+}$$ is smaller than Ca$$^{2+}$$, so Mg$$^{2+}$$ has greater hydration enthalpy: C > E.
Among the monovalent ions, smaller size means greater hydration enthalpy: K$$^+$$ > Rb$$^+$$ > Cs$$^+$$, i.e., A > B > D.
The complete order is:
$$\text{Mg}^{2+} > \text{Ca}^{2+} > \text{K}^+ > \text{Rb}^+ > \text{Cs}^+$$
That is: C > E > A > B > D.
The correct answer is Option D.
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