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Chapter 12: Problem 43

Which of the following ions would be expected to have the greater energy of hydration, \(\mathrm{Mg}^{2+}\) or \(\mathrm{Al}^{3+}\) ?

Short Answer

Expert verified
\(\mathrm{Al}^{3+}\) has greater hydration energy due to its higher charge and smaller size.

Step by step solution

01

Understand Energy of Hydration

The energy of hydration refers to the energy released when ions interact with water molecules. Hydration energy is influenced by factors such as the charge of the ion and the size of the ion.
02

Compare Ionic Charge

Higher charges on the ion generally lead to greater hydration energy because the ion can more strongly attract water molecules. - The ion \(\mathrm{Al}^{3+}\) has a charge of +3. - The ion \(\mathrm{Mg}^{2+}\) has a charge of +2.
03

Evaluate Ionic Size

Hydration energy also depends on ionic size; smaller ions can pack more closely with water molecules, leading to higher hydration energy. Since both ions are from similar periods, focus mostly on their charges.
04

Determine Which has Greater Hydration Energy

Among \(\mathrm{Mg}^{2+}\) and \(\mathrm{Al}^{3+}\), Al has a higher charge and is likely smaller, which results in stronger attraction to water molecules and higher hydration energy.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ionic Charge
The concept of ionic charge is crucial in understanding the energy of hydration. An ion's charge refers to the number of electrons lost or gained compared to the neutral atom. A higher ionic charge increases an ion's ability to attract the opposite partial charges on water molecules. For example, the
  • The \( \mathrm{Al}^{3+} \) ion has a charge of +3 and attracts water molecules more effectively.
  • The \( \mathrm{Mg}^{2+} \) ion, with a +2 charge, also does attract water molecules, albeit less strongly.
The greater the ionic charge, the stronger the attraction to water, which enhances the hydration energy. This is because each water molecule in proximity with the charged ion contributes to the system's stabilization, releasing energy.
Ionic Size
Ionic size plays a key role in determining hydration energy. Smaller ions are able to get closer to water molecules. This proximity allows for stronger electrostatic interactions between the ion and the dipoles of water molecules. When comparing \( \mathrm{Mg}^{2+} \) and \( \mathrm{Al}^{3+} \):
  • \( \mathrm{Al}^{3+} \) is smaller than \( \mathrm{Mg}^{2+} \) because its higher charge pulls its electrons in tighter.
  • Smaller ions, like \( \mathrm{Al}^{3+} \), exhibit stronger attraction to water dipoles.
This makes aluminum ions have a higher energy of hydration. In general, smaller ionic sizes favor higher hydration energies due to their compactness and ability to closely interact with water molecules.
Hydration Energy
Hydration energy quantifies the energy released when ions become surrounded by water molecules. It involves the dynamic process where water molecules create a hydration shell around the ion. Two main factors鈥攊onic charge and ionic size鈥攊nfluence this process:
  • Ions with higher charges, such as \( \mathrm{Al}^{3+} \), lead to greater hydration energy.
  • Smaller ions can pack closely with water molecules, also increasing hydration energy.
Hydration energy plays a critical role in many chemical reactions, particularly in aqueous solutions. It is a driving force for ion dissolution and stability in water, dictating reactions' spontaneity and equilibrium.
Water Molecule Attraction
At the heart of hydration energy lies the attraction between ions and water molecules. Water molecules are polar, meaning they have partial positive and negative charges, which allows them to be attracted to ions.
  • A positive ion like \( \mathrm{Mg}^{2+} \) will attract the negative ends of water molecules.
  • The stronger the attraction, the more energy will be released during hydration.
In cases such as \( \mathrm{Al}^{3+} \), which have a higher positive charge, the attraction to water molecules is even stronger. This stronger attraction leads to an increased hydration energy. Understanding these interactions is vital for predicting ionic behaviors in solutions.

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Most popular questions from this chapter

If \(1-\mathrm{mol}\) samples of urea, a nonelectrolyte, sodium chloride, and calcium chloride are each dissolved in equal volumes of water in separate containers: a. Which solution would have the highest boiling point? b. Which solution would have the highest freezing point?

The lattice enthalpy of sodium chloride, \(\Delta H^{\circ}\) for $$\mathrm{NaCl}(s) \longrightarrow \mathrm{Na}^{+}(g)+\mathrm{Cl}^{-}(g)$$ is \(787 \mathrm{~kJ} / \mathrm{mol} ;\) the heat of solution in making up \(1 \mathrm{M} \mathrm{NaCl}(a q)\) is \(+4.0 \mathrm{~kJ} / \mathrm{mol}\). From these data, obtain the sum of the heats of hydration of \(\mathrm{Na}^{+}\) and \(\mathrm{Cl}^{-}\). That is, obtain the sum of \(\Delta H^{\text {values for }}\) $$\begin{aligned}&\mathrm{Na}^{+}(g) \longrightarrow \mathrm{Na}^{+}(a q) \\ &\mathrm{Cl}^{+}(g) \longrightarrow \mathrm{Cl}^{-}(a q)\end{aligned}$$ If the heat of hydration of \(\mathrm{Cl}^{-}\) is \(-338 \mathrm{~kJ} / \mathrm{mol}\), what is the heat of hydration of \(\mathrm{Na}^{+}\) ?

An aqueous solution is \(20.0 \%\) by mass of sodium thiosulfate pentahydrate, \(\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O} .\) What is the molarity of \(\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\) in this solution at \(20^{\circ} \mathrm{C} ?\) The density of this solution at \(20^{\circ} \mathrm{C}\) is \(1.174 \mathrm{~g} / \mathrm{mL}\)

A starch has a molar mass of \(3.20 \times 10^{04} \mathrm{~g} / \mathrm{mol}\). If \(0.759 \mathrm{~g}\) of this starch is dissolved in \(112 \mathrm{~mL}\) of solution, what is the osmotic pressure, in torr, at \(25.00^{\circ} \mathrm{C} ?\)

Ethanol, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\), is known as grain alcohol and is the alcohol found in alcoholic beverages. Calculate the mole fraction of ethanol in a solution that contains \(4.76 \mathrm{~g}\) of ethanol dissolved in \(50.0 \mathrm{~g}\) of water.
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