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Chapter 1: Problem 20

When calcium chloride \(\left(\mathrm{CaCl}_{2}\right)\) dissolves in water, the temperature of the water increases dramatically. Which of the following must be true regarding the enthalpy of solution? (A) The lattice energy in \(\mathrm{CaCl}_{2}\) exceeds the bond energy within the water molecules. (B) The hydration energy between the water molecules and the solute ions exceeds the lattice energy within \(\mathrm{CaCl}_{2}\) . (C) The strength of the intermolecular forces between the solute ions and the dipoles on the water molecules must exceed the hydration energy. (D) The hydration energy must exceed the strength of the intermolecular forces between the water molecules.

Short Answer

Expert verified
The correct answer is Option (B) : The hydration energy between the water molecules and the solute ions exceeds the lattice energy within \(\mathrm{CaCl}_{2}\) .

Step by step solution

01

Understanding key concepts

In a solution process, there are two principal types of energy changes: lattice energy, which is the energy required to separate a mole of a solid ionic compound into its gaseous ions, and hydration energy, the energy released when new bonds are made between the ions and water molecules.
02

Analyzing each option

Option (A) talks about lattice energy exceeding the bond energy within water molecules but we are interested in the exchange between the solute and the solvent not within the solvent itself, hence discard this option. Option (B) suggests that the hydration energy (energy released due to interaction of water with solute ions) is greater than the lattice energy (energy used to break the solid solute into ions); which falls in line with our concept of an exothermic solution process. Thus this seems a reasonable choice. Option (C) refers to the strength of intermolecular forces between the solute ions and the dipoles on the water molecules exceeding the hydration energy; but in reality, it's the hydration energy that corresponds to these forces, hence discard this. Option (D) relates the hydration energy with the strength of intermolecular forces between water molecules which doesn't make sense for the same reason as for option (A).
03

Concluding

Analyzing each option in relevance with the nature of the exothermic dissolution of calcium chloride, the most reasonable option that accurately describes the enthalpy of the solution is Option (B) because the energy released during hydration is greater than the energy used up to break the lattice of the solid.

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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 a crucial concept in understanding the dissolving process of ionic compounds like calcium chloride (\(\text{CaCl}_2\)) in water. It's the energy needed to break an ionic solid's lattice into its gaseous ions.
This energy is often quite high because the ions in the lattice are strongly attracted to one another due to electrostatic forces.
In simpler terms, imagine the lattice of \(\text{CaCl}_2\) as a tightly packed structure of positive calcium ions and negative chloride ions. Separating them requires substantial energy, known as lattice energy. This is because each positive ion is surrounded by negative ions and vice versa, creating strong attractions.
Breaking these strong attractions requires a significant input of energy, which is why lattice energy is considered when evaluating the solubility of ionic compounds.
Hydration Energy
Hydration energy is the energy released when ions interact with water molecules during the dissolution process.
When \(\text{CaCl}_2\) dissolves in water, each calcium and chloride ion is surrounded by water molecules which stabilize the ions through interactions. This process releases energy.
  • The water molecules are polar, having a partial positive charge near the hydrogen atoms and a partial negative charge near the oxygen atom.
  • This polarity allows water molecules to surround and "snuggle up to" the ions, effectively stabilizing them in solution.
The energy released during this interaction is the hydration energy. When this energy is greater than the lattice energy, the overall process becomes energetically favorable, which leads to the dissolving of the ionic compound.
Exothermic Process
An exothermic process is one where energy is released in the form of heat. When \(\text{CaCl}_2\) dissolves in water and the temperature of the water increases, it indicates an exothermic reaction has occurred.
In such processes:
  • The total energy released when water molecules interact with the solute (hydration energy) is greater than the energy required to break apart the solute's lattice (lattice energy).
  • This net release of energy is felt as a rise in temperature, making the surrounding environment warmer.
Thus, for calcium chloride when it dissolves, the warming of water confirms that the hydration energy exceeds the lattice energy.
Intermolecular Forces
Intermolecular forces are forces of attraction or repulsion which act between neighboring particles. They are significantly involved when an ionic solid like \(\text{CaCl}_2\) dissolves in water.
  • The interplay of these forces determines the stability and solubility of the dissolved ions.
  • Water, a highly polar solvent, capitalizes on its polarity to exert dipole-dipole attractions toward the \(\text{Ca}^{2+}\) and \(\text{Cl}^-\) ions.
These forces are responsible for stabilizing the ions in solution. The stronger these interactions, the more energy is released as hydration energy. This process results in the ions being efficiently dispersed throughout the water, leading to the observed dissolution and subsequent rise in water temperature associated with exothermic processes.

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Most popular questions from this chapter

Use the following information to answer questions 1-5. \(\begin{array}{ll}{\text { Reaction } 1 : \mathrm{N}_{2} \mathrm{H}_{4}(l)+\mathrm{H}_{2}(g) \rightarrow 2 \mathrm{NH}_{3}(g)} & {\Delta H=?} \\ {\text { Reaction } 2 : \mathrm{N}_{2} \mathrm{H}_{4}(l)+\mathrm{CH}_{4} \mathrm{O}(l) \rightarrow \mathrm{CH}_{2} \mathrm{O}(g)+\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)} & {\Delta H=-37 \mathrm{kJ} / \mathrm{mol}_{\mathrm{rxn}}} \\ {\text { Reaction } 3 : \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{NH}_{3}(g)} & {\Delta H=-46 \mathrm{kJ} / \mathrm{mol}_{\mathrm{rxn}}} \\ {\text { Reaction } 4 : \mathrm{CH}_{4} \mathrm{O}(l) \rightarrow \mathrm{CH}_{2} \mathrm{O}(g)+\mathrm{H}_{2}(g)} & {\Delta H=-65 \mathrm{kJ} / \mathrm{mol}_{\mathrm{rxn}}}\end{array}\) If reaction 2 were repeated at a higher temperature, how would the reaction's value for \(\Delta G\) be affected? (A) It would become more negative because entropy is a driving force behind this reaction. (B) It would become more positive because the reactant molecules would collide more often. (C) It would become more negative because the gases will be at a higher (D) It will stay the same; temperature does not affect the value for \(\Delta G\) .

The following reaction is found to be at equilibrium at 25掳C: \(2 \mathrm{SO}_{3}(g) \leftrightarrow \mathrm{O}_{2}(g)+2 \mathrm{SO}_{2}(g) \quad \Delta H=-198 \mathrm{kJ} / \mathrm{mol}\) Which of the following would cause the reverse reaction to speed up? (A) Adding more \(\mathrm{SO}_{3}\) (B) Raising the pressure (C) Lowering the temperature (D) Removing some \(\mathrm{SO}_{2}\)

How many moles of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) must be added to 500 milliliters of water to create a solution that has a 2 -molar concentration of the Na' ion? (Assume the volume of the solution does not change). (A) 0.5 \(\mathrm{mol}\) (B) 1 \(\mathrm{mol}\) (C) 2 \(\mathrm{mol}\) (D) 5 \(\mathrm{mol}\)

The following reaction is found to be at equilibrium at 25掳C: \(2 \mathrm{SO}_{3}(g) \leftrightarrow \mathrm{O}_{2}(g)+2 \mathrm{SO}_{2}(g) \quad \Delta H=-198 \mathrm{kJ} / \mathrm{mol}\) What is the expression for the equilibrium constant, \(K_{\mathrm{c}} ?\) (A) \(\frac{\left[\mathrm{SO}_{3}\right]^{2}}{\left[\mathrm{O}_{2}\right]\left[\mathrm{SO}_{2}\right]^{2}}\) (B) \(\frac{2\left[\mathrm{SO}_{3}\right]}{\left[\mathrm{O}_{2}\right] 2\left[\mathrm{SO}_{2}\right]}\) (C) \(\frac{\left[\mathrm{O}_{2}\right]\left[\mathrm{SO}_{2}\right]^{2}}{\left[\mathrm{SO}_{3}\right]^{2}}\) (D) \(\frac{\left[\mathrm{O}_{2}\right] 2\left[\mathrm{SO}_{2}\right]}{2\left[\mathrm{SO}_{3}\right]}\)

$$\begin{array}{|c|c|}\hline \text { Time (Hours) } & {[\mathrm{A}] M} \\\ \hline 0 & {0.40} \\ \hline 1 & {0.20} \\ \hline 2 & {0.10} \\ \hline 3 & {0.05} \\ \hline\end{array}$$ Reactant A underwent a decomposition reaction. The concentration of A was measured periodically and recorded in the chart above. Based on the data in the chart, which of the following is the rate law for the reaction? (A) Rate \(=k[\mathrm{A}]\) (B) Rate \(=k[\mathrm{A}]^{2}\) (C) Rate \(=2 k[\mathrm{A}]\) (D) Rate \(=\frac{1}{2} k[\mathrm{A}]\)
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