MCQEasyJEE 2023Trends in Atomic Radius & Ionisation Energy

JEE Chemistry 2023 Question with Solution

Ion having highest hydration enthalpy among the given alkaline earth metal ions is:

  • A

    Be2+\mathrm{Be}^{2+}

  • B

    Ba2+\mathrm{Ba}^{2+}

  • C

    Ca2+\mathrm{Ca}^{2+}

  • D

    Sr2+\mathrm{Sr}^{2+}

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: The ions are Be2+\mathrm{Be}^{2+}, Ba2+\mathrm{Ba}^{2+}, Ca2+\mathrm{Ca}^{2+} and Sr2+\mathrm{Sr}^{2+}.

Find: Which ion has the highest hydration enthalpy.

Hydration enthalpy depends on the charge density of the ion. Highly charged and smaller-sized metal ions have higher hydration enthalpy.

All the given ions have the same charge, namely +2+2. Therefore, hydration enthalpy will be greater for the ion with the smallest size.

Down the alkaline earth metal group, ionic size increases, so hydration enthalpy decreases. Hence the order is:

Be2+>Mg2+>Ca2+>Sr2+>Ba2+\mathrm{Be}^{2+} > \mathrm{Mg}^{2+} > \mathrm{Ca}^{2+} > \mathrm{Sr}^{2+} > \mathrm{Ba}^{2+}

Therefore, the ion having the highest hydration enthalpy is Be2+\mathrm{Be}^{2+}. The correct option is A.

Charge Density View

Given: All ions belong to alkaline earth metals and each has charge +2+2.

Find: The ion with maximum hydration enthalpy.

Hydration enthalpy is the energy released when a gaseous ion gets surrounded by water molecules to form a hydrated ion. Its magnitude increases with increasing charge density.

This can be expressed qualitatively as:

Hydration enthalpychargesize\text{Hydration enthalpy} \propto \frac{\text{charge}}{\text{size}}

Since the charge is the same for all given ions, we compare only their sizes:

Hydration enthalpy1size\text{Hydration enthalpy} \propto \frac{1}{\text{size}}

As we move down the group from beryllium to barium, ionic size increases. So the smallest ion, Be2+\mathrm{Be}^{2+}, has the greatest hydration enthalpy.

Hence, Be2+\mathrm{Be}^{2+} shows the highest hydration enthalpy, so the correct option is A.

Common mistakes

  • Comparing only the charge and ignoring ionic size. All given ions have the same charge +2+2, so size becomes the deciding factor. Compare charge density, not charge alone.

  • Assuming heavier ions have higher hydration enthalpy. This is incorrect because hydration enthalpy decreases as ionic size increases down the group. Use smaller ion \Rightarrow higher hydration enthalpy.

  • Confusing hydration enthalpy with ease of hydration in terms of atomic mass or metallic character. The correct basis here is the size of the gaseous ion and its charge density.

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