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Chapter 13: Problem 3

How does the lattice energy of an ionic solid affect its solubility in water? [Section 13.1\(]\)

Short Answer

Expert verified
The lattice energy of an ionic solid affects its solubility in water by determining the strength of the electrostatic forces holding the ions together in the crystal lattice. If the lattice energy is high, indicating stronger attractive forces between ions, the solubility will be lower as it is more difficult for the solid to dissolve in water. Conversely, if the lattice energy is low, indicating weaker attractive forces between ions, the solubility will be higher as it is easier for the solid to dissolve in water. The solubility of an ionic solid in water depends on the balance between the lattice energy and the hydration energy, which is the energy released when the ions become surrounded by water molecules. If the hydration energy is greater than or equal to the lattice energy, the ionic solid will have high solubility, while low hydration energy compared to lattice energy results in low solubility.

Step by step solution

01

1. Define lattice energy

Lattice energy is the energy required to separate one mole of an ionic solid into its constituent gaseous ions. It is a measure of the strength of the electrostatic forces holding the ions together in the crystal lattice. A higher lattice energy indicates stronger attractive forces between ions, making it more difficult to separate them.
02

2. Define solubility

Solubility refers to the maximum amount of a solute (in this case, an ionic solid) that can dissolve in a given amount of solvent (in this case, water) to form a homogeneous solution. Solubility is influenced by factors such as temperature, pressure, and the nature of the solute and solvent.
03

3. Understand the solvation process

When an ionic solid dissolves in water, the ions in the solid become surrounded by water molecules, which forms a sphere of hydration around the ions. The energy released during this process is called hydration energy. The hydration energy is the sum of the ion-dipole interactions between the ions and the polar water molecules.
04

4. Examine the relationship between lattice energy and solubility

For an ionic solid to dissolve in water, the attractive forces between the ions in the solid (lattice energy) must be overcome by the attractive forces between the ions and water molecules (hydration energy). If the hydration energy is greater than or equal to the lattice energy, the ionic solid will dissolve in water, and the solubility will be high. On the other hand, if the hydration energy is less than the lattice energy, the ionic solid will not dissolve easily in water, resulting in low solubility.
05

5. Conclusion

In summary, the lattice energy of an ionic solid affects its solubility in water. If the lattice energy is high, meaning the ionic bonds are very strong, it will be more difficult for the solid to dissolve in water, and solubility will be lower. If the lattice energy is low, meaning the ionic bonds are weaker, it will be easier for the solid to dissolve in water, and solubility will be higher. Therefore, a higher lattice energy generally leads to a lower solubility, while a lower lattice energy leads to a higher solubility in water.

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Most popular questions from this chapter

(a) Why is there no colloid in which both the dispersed substance and the dispersing substance are gases? (b) Michael Faraday first prepared ruby-red colloids of gold particles in water that were stable indefinitely. To the unaided eye these brightly colored colloids are not distinguishable from solutions. How could you determine whether a given colored preparation is a solution or colloid?

The maximum allowable concentration of lead in drinking water is \(9.0 \mathrm{ppb}\). (a) Calculate the molarity of lead in a 9.0-ppb solution. What assumption did you have to make in your calculation? (b) How many grams of lead are in a swimming pool containing 9.0 ppb lead in \(60 \mathrm{~m}^{3}\) of water?

Describe how you would prepare each of the following aqueous solutions, starting with solid KBr: (a) \(0.75 \mathrm{~L}\) of \(1.5 \times 10^{-2} M \mathrm{KBr},\) (b) \(125 \mathrm{~g}\) of \(0.180 \mathrm{~m} \mathrm{KBr},\) (c) \(1.85 \mathrm{~L}\) of a solution that is \(12.0 \% \mathrm{KBr}\) by mass (the density of the solution is \(1.10 \mathrm{~g} / \mathrm{mL}\) ), (d) a \(0.150 \mathrm{M}\) solution of \(\mathrm{KBr}\) that contains just enough KBr to precipitate \(16.0 \mathrm{~g}\) of AgBr from a solution containing \(0.480 \mathrm{~mol}\) of \(\mathrm{AgNO}_{3}\)

The following table presents the solubilities of several gases in water at \(25^{\circ} \mathrm{C}\) under a total pressure of gas and water vapor of 1 atm. (a) What volume of \(\mathrm{CH}_{4}(g)\) under standard conditions of temperature and pressure is contained in \(4.0 \mathrm{~L}\) of a saturated solution at \(25^{\circ} \mathrm{C} ?\) (b) Explain the variation in solubility among the hydrocarbons listed (the first three compounds), based on their molecular structures and intermolecular forces. (c) Compare the solubilities of \(\mathrm{O}_{2}, \mathrm{~N}_{2}\), and \(\mathrm{NO},\) and account for the variations based on molecular structures and intermolecular forces. (d) Account for the much larger values observed for \(\mathrm{H}_{2} \mathrm{~S}\) and \(\mathrm{SO}_{2}\) as compared with the other gases listed. (e) Find several pairs of substances with the same or nearly the same molecular masses (for example, \(\mathrm{C}_{2} \mathrm{H}_{4}\) and \(\mathrm{N}_{2}\) ), and use intermolecular interactions to explain the differences in their solubilities. $$ \begin{array}{lc} \hline \text { Gas } & \text { Solubility }(\mathrm{m} M) \\ \hline \mathrm{CH}_{4}(\text { methane }) & 1.3 \\ \mathrm{C}_{2} \mathrm{H}_{6} \text { (ethane) } & 1.8 \\ \mathrm{C}_{2} \mathrm{H}_{4} \text { (ethylene) } & 4.7 \\ \mathrm{~N}_{2} & 0.6 \\ \mathrm{O}_{2} & 1.2 \\ \mathrm{NO} & 1.9 \\ \mathrm{H}_{2} \mathrm{~S} & 99 \\ \mathrm{SO}_{2} & 1476 \end{array} $$

(a) What is the molality of a solution formed by dissolving \(1.12 \mathrm{~mol}\) of \(\mathrm{KCl}\) in \(16.0 \mathrm{~mol}\) of water? (b) How many grams of sulfur \(\left(\mathrm{S}_{8}\right)\) must be dissolved in \(100.0 \mathrm{~g}\) naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\) to make a \(0.12 \mathrm{~m}\) solution?
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