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Chapter 12: Problem 23

Ten grams of the hypothetical ionic compounds \(\mathrm{XZ}\) and \(Y Z\) are each placed in a separate \(2.0\) - \(L\) beaker of water. \(X Z\) completely dissolves, whereas YZ is insoluble. The energy of hydration of the \(\mathrm{Y}^{+}\) ion is greater than the \(\mathrm{X}^{+}\) ion. Explain this difference in solubility.

Short Answer

Expert verified
\(XZ\) dissolves because its hydration energy exceeds its lattice energy, unlike \(YZ\).

Step by step solution

01

Examine Solubility

When the compound \(XZ\) is placed in water and completely dissolves, it means the interactions between the ions \(X^{+}\) and \(Z^{-}\) with water molecules are stronger than the lattice energy holding the ions together. In contrast, when \(YZ\) is insoluble, the lattice energy is stronger than their interaction with water.
02

Understanding Lattice Energy

Lattice energy is the energy required to separate the ions in a solid ionic compound. If \(YZ\) has a high lattice energy, it means that a large amount of energy is required to break the ionic bonds between \(Y^{+}\) and \(Z^{-}\). This is a reason why \(YZ\) might not dissolve in water, as hydration energy must be higher than lattice energy for dissolution to occur.
03

Hydration Energy Comparison

Hydration energy is the energy released when ions interact with water molecules. Although the \(Y^{+}\) ion has a greater hydration energy than \(X^{+}\), \(YZ\) does not dissolve because the overall hydration energy (sum for both \(Y^{+}\) and \(Z^{-}\)) does not outweigh the lattice energy. Conversely, for \(XZ\), the overall hydration energy exceeds the lattice energy, leading to solubility.
04

Conclusion on Solubility Difference

The key reason for the difference in solubility between \(XZ\) and \(YZ\) lies in the balance of lattice and hydration energies. Although \(Y^{+}\) has a greater individual hydration energy, the insolubility of \(YZ\) is due to its higher lattice energy relative to the total hydration energy.

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Key Concepts

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

Lattice Energy
Lattice energy is crucial to understanding the stability of ionic compounds. It refers to the energy required to separate the ions in a solid ionic compound into gaseous ions. In simpler terms, it's the glue that holds the ions together in a crystal lattice.

Let's break it down:
  • Energy Requirement: A high lattice energy means more energy is needed to pull the ions apart. This usually means the compound is more stable and less likely to dissolve.
  • Influences: The magnitude of lattice energy depends on both the charge and the size of the ions. Higher charges and smaller ions result in a higher lattice energy due to stronger electrostatic attractions.
Understanding lattice energy helps us explain why certain compounds, like the hypothetical compound YZ, remain insoluble in water. If the lattice energy is too high, the compound won't easily dissolve since breaking those ionic bonds would require considerable energy.
Hydration Energy
Hydration energy comes into play when ionic compounds dissolve in water. It's the energy released when ions are surrounded and stabilized by water molecules.

Here's what you need to know:
  • Energy Release: When ions dissolve in water, they release energy upon interacting with the polar water molecules. This released energy can help overcome the lattice energy, leading to dissolution.
  • Role of Ion Characteristics: Smaller ions and those with higher charges tend to have higher hydration energies because they attract water molecules more strongly.
In the exercise, even though the Y+ ion has a higher hydration energy than the X+ ion, it wasn't enough to surpass YZ's lattice energy. Thus, YZ did not dissolve, while XZ did because the hydration energy of both X+ and Z- ions together was enough to exceed the lattice energy.
Ionic Compounds
Ionic compounds are fascinating due to their unique properties and formation mechanisms. They are composed of positively charged ions (cations) and negatively charged ions (anions) held together by ionic bonds.

Consider these points:
  • Formation: Ionic compounds form when electrons transfer from one element to another, creating a pair of ions with opposite charges that attract each other.
  • Characteristics: They often form crystalline solids with high melting points and conduct electricity when dissolved in water or molten.
Such characteristics are evident in compounds like XZ and YZ from our exercise. The nature of the ionic bonds (and thus, lattice energy) plays a significant role in whether these ionic compounds will dissolve in water or not.
Dissolution Process
The dissolution process is key to understanding why some ionic compounds dissolve in water while others don't. It involves breaking apart the ionic bonds within the solid and forming new interactions with water molecules.

Here's a simple breakdown:
  • Step 1 - Solute Separation: The first step is overcoming the lattice energy, which requires the ionic solid to break apart into its individual ions.
  • Step 2 - Solvent Interaction: These free ions then interact with the water molecules solidly enough to form hydration shells, releasing energy in the process.
  • Necessary Condition: For dissolution to occur, the energy released from hydration must exceed the energy needed to break the lattice, making the process energetically favorable.
This explains why XZ dissolves in the exercise while YZ does not. Even though Y+ has good hydration energy, YZ's lattice energy takes too much to overcome compared to what is released during hydration, leading to its insolvency.

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Most popular questions from this chapter

A natural gas mixture consists of \(90.0\) mole percent \(\mathrm{CH}_{4}\) (methane) and \(10.0 \mathrm{~mole}\) percent \(\mathrm{C}_{2} \mathrm{H}_{6}\) (ethane). Suppose water is saturated with the gas mixture at \(20^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) total pressure, and the gas is then expelled from the water by heating. What is the composition in mole fractions of the gas mixture that is expelled? The solubilities of \(\mathrm{CH}_{4}\) and \(\mathrm{C}_{2} \mathrm{H}_{6}\) at \(20^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) are \(0.023 \mathrm{~g} / \mathrm{L} \mathrm{H}_{2} \mathrm{O}\) and \(0.059 \mathrm{~g} / \mathrm{L} \mathrm{H}_{2} \mathrm{O}\), respectively.

A solution contains \(0.0653 \mathrm{~g}\) of a compound in \(8.31 \mathrm{~g}\) of ethanol. The molality of the solution is \(0.0368 \mathrm{~m} .\) Calculate the molecular weight of the compound.

Give the type of colloid (aerosol, foam, emulsion, sol, or gel) that each of the following represents. a. rain cloud b. milk of magnesia c. soapsuds d. silt in water

A \(0.0140-\mathrm{g}\) sample of an ionic compound with the formula \(\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}_{3}\) was dissolved in water to give \(25.0 \mathrm{~mL}\) of solution at \(25^{\circ} \mathrm{C}\). The osmotic pressure was determined to be \(119 \mathrm{mmHg}\). How many ions are obtained from each formula unit when the compound is dissolved in water?

Explain the process of reverse osmosis to produce drinkable water from ocean water.
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