Question

Use the following data to estimate \(\Delta H_{\mathrm{f}}^{\circ}\) for potassium chloride. $$ \mathrm{K}(s)+\frac{1}{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{KCl}(s) $$ $$ \begin{array}{lr} \text { Lattice energy } & -690 . \mathrm{kJ} / \mathrm{mol} \\ \text { Ionization energy for } \mathrm{K} & 419 \mathrm{~kJ} / \mathrm{mol} \\\ \text { Electron affinity of Cl } & -349 \mathrm{~kJ} / \mathrm{mol} \\ \text { Bond energy of } \mathrm{Cl}_{2} & 239 \mathrm{~kJ} / \mathrm{mol} \\ \text { Enthalpy of sublimation for } \mathrm{K} & 64 \mathrm{~kJ} / \mathrm{mol} \end{array} $$

Short answer

The estimated standard enthalpy of formation for potassium chloride is \(-443 \,\mathrm{kJ/mol}\).

Step-by-step solution

Write down the given data

We start by writing the given data in their respective symbols: - Lattice energy: \(U_{\mathrm{lattice}} = -690 \,\mathrm{kJ/mol}\) - Ionization energy of K: \(IE_{\mathrm{K}} = 419 \,\mathrm{kJ/mol}\) - Electron affinity of Cl: \(EA_{\mathrm{Cl}} = -349 \,\mathrm{kJ/mol}\) - Bond energy of Cl: \(BE_{\mathrm{Cl_2}} = 239 \,\mathrm{kJ/mol}\) - Enthalpy of sublimation for K: \(\Delta H_{\mathrm{sub}}^{\mathrm{K}} = 64 \,\mathrm{kJ/mol}\)

Apply Hess's Law

Using Hess's Law, we can determine the enthalpy change for the formation of KCl from its constituent elements by adding up the individual energy changes: $$\Delta H_{\mathrm{f}}^{\circ}(\mathrm{KCl}) = \Delta H_{\mathrm{sub}}^{\mathrm{K}} + \frac{1}{2} \cdot BE_{\mathrm{Cl_2}} + IE_{\mathrm{K}} + EA_{\mathrm{Cl}} + U_{\mathrm{lattice}}$$

Calculate the enthalpy change

Now, we can plug in the given values for each term into the equation from step 2: $$\Delta H_{\mathrm{f}}^{\circ}(\mathrm{KCl}) = 64\,\mathrm{kJ/mol} + \frac{1}{2} \cdot 239\,\mathrm{kJ/mol} + 419\,\mathrm{kJ/mol} - 349\,\mathrm{kJ/mol} - 690\,\mathrm{kJ/mol}$$

Solve for the enthalpy of formation

Simplifying the equation, we get: $$\Delta H_{\mathrm{f}}^{\circ}(\mathrm{KCl}) = 64 + \frac{1}{2} \cdot 239 + 419 - 349 - 690$$ Calculating the value, we find: $$\Delta H_{\mathrm{f}}^{\circ}(\mathrm{KCl}) = -443\,\mathrm{kJ/mol}$$ So, the estimated standard enthalpy of formation for potassium chloride is \(-443 \,\mathrm{kJ/mol}\).

Key concepts

Hess's Law

Hess's Law is a powerful principle in chemistry that helps us calculate the enthalpy change of a chemical reaction. It states that the total enthalpy change during a chemical reaction is the same, regardless of the pathway the reaction takes. This is because enthalpy is a state function, meaning its value depends only on the initial and final states, not on how the reaction proceeds between them.

To utilize Hess's Law effectively, you sum up individual energy changes of a series of steps leading to the overall reaction. In the exercise, we used Hess's Law to estimate the enthalpy of formation for potassium chloride (KCl). By adding up the lattice energy, ionization energy, electron affinity, and other relevant data, we arrived at the total enthalpy change for KCl's formation.

• Hess's Law facilitates calculating enthalpy changes indirectly.
• It relies on the fact that enthalpy is a state function.

Understanding Hess's Law enables you to predict reaction energetics, making it a crucial tool for solving thermodynamic problems.

Lattice Energy

Lattice energy is the energy released when ions in the gaseous state come together to form an ionic solid. It's a measure of the strength of the forces holding the ions together in a crystal lattice. In simpler terms, lattice energy shows how much energy is needed to separate the ions in an ionic solid or how much is released when ions bond.

In the context of the exercise, for potassium chloride (KCl), the lattice energy is negative because energy is released when gaseous potassium and chloride ions form solid KCl. Lattice energy is usually expressed in kJ/mol and can influence the stability and solubility of ionic compounds.

• Lattice energy relates to ionic bond strength.
• High lattice energy implies strong ionic bonds and typically less solubility.
• Lattice energy is exothermic, meaning energy is released.

This concept is critical when evaluating the energetics of ionic compound formation.

Ionization Energy

Ionization energy is the energy required to remove an electron from a gaseous atom or ion. When an atom loses its electron, it becomes a positively charged ion, called a cation. Ionization energy helps us understand an element’s reactivity, as elements with lower ionization energies tend to lose electrons easily and form cations.

In our exercise, we looked at the ionization energy of potassium (K), which plays a crucial role in the formation of KCl. Potassium needs to lose an electron to become a K⁺ ion that will bond with Cl⁻. Ionization energy is usually measured in kJ/mol and varies across the periodic table, generally increasing across a period and decreasing down a group.

• Ionization energy influences an element's ability to form bonds.
• It provides insights into periodic trends and element reactivity.
• Low ionization energy indicates easier electron removal.

Understanding ionization energy helps in predicting how different elements interact during chemical reactions.

Electron Affinity

Electron affinity is the energy change when an electron is added to a gaseous atom, forming an anion. It's typically measured in kJ/mol and can be either positive or negative, depending on whether energy is absorbed or released. Negative electron affinity indicates energy release when an atom gains an electron, which often happens with nonmetals.

In the exercise, electron affinity relates to chlorine (Cl) gaining an electron to become Cl⁻, an essential step in forming potassium chloride (KCl). The negative value signifies an exothermic process where energy is released as the electron is added.

• Electron affinity reflects an atom’s tendency to gain electrons.
• Nonmetals usually have higher (more negative) electron affinities.
• Electron affinity values help predict compound stability.

This concept assists in understanding the energetics involved in the formation of ionic compounds such as KCl, where electron exchange is fundamental.