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Chapter 12: Problem 10

Suppose you want to dissolve some \(\mathrm{MgCl}_{2}\) in water. (a) How do we know that magnesium cations have a \(+2\) charge? (b) \(\Delta E_{\text {solute separation }}\) for \(\mathrm{MgCl}_{2}\) is much more positive than \(\Delta E_{\text {solute separation }}\) for \(\mathrm{NaCl}\). Explain what this means and why it might be so. (c) \(\mathrm{MgCl}_{2}\) is more soluble in water than \(\mathrm{NaCl}\). Explain how this is possible in light of the information given in (b).

Short Answer

Expert verified
(a) Magnesium cations have a +2 charge because Mg is in Group 2 of the periodic table, where elements tend to lose two electrons to achieve a stable octet electron configuration. (b) The more positive solute separation energy for MgCl鈧� than for NaCl means that more energy is required to separate Mg虏鈦� and Cl鈦� ions in the MgCl鈧� lattice compared to separating Na鈦� and Cl鈦� ions in NaCl. This is due to the stronger electrostatic attraction between the Mg虏鈦� and Cl鈦� ions, as Mg虏鈦� has a higher charge than Na鈦�. (c) MgCl鈧� can be more soluble in water than NaCl because its higher hydration energy compensates for its higher solute separation energy. The higher charge of Mg虏鈦� compared to Na鈦� results in stronger interaction with water molecules, leading to higher hydration energy and promoting dissolution.

Step by step solution

01

(a) Magnesium Cations Charge

Magnesium (Mg) is an alkaline earth metal, and it is in the second group in the periodic table. Elements in Group 2 generally lose two electrons to achieve a stable octet electron configuration which is the fully filled s and p orbitals of the previous energy level. When magnesium loses two electrons, it forms a cation with a charge of +2, which we can represent as Mg虏鈦�. Therefore, magnesium cations have a +2 charge.
02

(b) Solute Separation Energies Comparison

The positive value of solute separation energy for MgCl鈧� than that of NaCl means that the energy required to separate Mg虏鈦� and Cl鈦� ions in the MgCl鈧� lattice is higher compared to the energy needed to separate Na鈦� and Cl鈦� ions in the NaCl lattice. This is because Mg虏鈦� has a higher charge compared to Na鈦�, which leads to stronger electrostatic attraction between Mg虏鈦� and Cl鈦� ions. Therefore, more energy is needed to separate the MgCl鈧� ions in the lattice.
03

(c) Solubility of MgCl鈧� vs NaCl

Despite the higher solute separation energy for MgCl鈧�, it can still be more soluble in water than NaCl. This is because the hydration energy of MgCl鈧�, or the energy released when Mg虏鈦� and Cl鈦� ions interact with water molecules, is also higher than the hydration energy of NaCl. The hydration energy comes from the electrostatic attraction between the charged ions and the oppositely charged ends of the water molecules (Oxygen end being negative and hydrogen end being positive). The higher charge of Mg虏鈦� compared to Na鈦� results in stronger interaction with water molecules, leading to higher hydration energy. The overall energy change for the dissolution process is the difference between the hydration energy and solute separation energy. If the hydration energy is significantly larger than the solute separation energy, more negative overall energy change will occur, promoting dissolution. In the case of MgCl鈧�, the higher hydration energy compensates for the higher solute separation energy, making it more soluble in water than NaCl.

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Key Concepts

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

Magnesium Cations Charge
Magnesium cations exhibit a charge of +2, a fundamental concept in chemistry. This charge emerges because magnesium, located in Group 2 of the periodic table, loses two electrons to attain a stable electron configuration. Similar to its Periodic Table Group 2 companions, magnesium aims for the 'octet rule'鈥攁 condition where it achieves a stable arrangement of 8 electrons in its outer shell, akin to the noble gases.

The electron shedding allows magnesium to stabilize with a noble gas electronic structure. Upon releasing these electrons, the resulting magnesium ion reflects this exchange with a charge denoted by Mg虏鈦�. This +2 charge significantly influences the properties of the ion, including how it interacts with other ions and molecules in a solution, such as water.
Solubility in Water
The solubility of a substance in water is closely tied to the interactions between the solute particles and the solvent molecules. Generally, solute particles must disrupt their existing bonds or attractions to dissolve in a solvent. In water, polar molecules, which have a charge distribution across their structure, readily dissolve ions due to the equivalent polarity of water.

Water's ability to dissolve ionic compounds, like magnesium chloride (MgCl鈧�), comes from its polar nature, where the oxygen side is slightly negative and the hydrogen side slightly positive. This polarity enables water to surround and interact with the positive magnesium ions and negative chloride ions, facilitating the dissolution process even when an ionic lattice is held together with significant energy, as is with MgCl鈧�.
Hydration Energy
Hydration energy is the energy released when ions are solvated by water molecules. This is a crucial aspect that plays into the solubility of substances like MgCl鈧�. When an ionic compound dissolves in water, the water molecules align around the ions based on their charge orientation, the negative oxygen towards the positive ions, and the positive hydrogen towards the negative ions.

The higher the charge of the ion, the greater the attraction for the water molecules, and consequently, the greater the hydration energy released. For Mg虏鈦� ions, with their higher +2 charge, water molecules can release a substantial amount of energy upon interaction, which can be substantial when considering the solubility of magnesium-containing compounds in water.
Periodic Table Group 2 Elements
The elements of Group 2 in the periodic table are known as the alkaline earth metals, and they share common properties due to their similar electron configurations. These elements include beryllium, magnesium, calcium, strontium, barium, and radium. Key characteristics involve their propensity to lose two electrons and form cations with a +2 charge.

Understanding Group 2 elements' behaviors provides insights into their chemical reactivity and bonding patterns. These bi-valent cations exhibit trends in properties such as hardness, melting points, and reactivity with water. Magnesium, being one of these elements, displays predictable properties, including solubility trends and the formation of Mg虏鈦� in solutions, that follow from its position in this group.
Electrostatic Attraction
Electrostatic attraction is a force that draws ions with opposite charges towards each other. It is fundamental to many chemical processes, including the formation of ionic lattices and the interaction of ions with solvent molecules in solutions.

In the context of solubility, the electrostatic attraction between ions in a compound like MgCl鈧� contributes to the energy needed to separate the ions - referred to as solute separation energy. Likewise, the electrostatic attraction between the water molecules and the ions defines the hydration energy. For example, the stronger electrostatic attraction between water molecules and Mg虏鈦� ions due to the higher charge of magnesium is responsible for the high solubility of MgCl鈧� in water despite its high solute separation energy.

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