Problem 62 - Chemistry An Atoms First Approach

Question

Use the following data formagnesium fluoride to estimate \(\Delta E\) for the reaction: $$\mathrm{Mg}(s)+\mathrm{F}_{2}(g) \longrightarrow \mathrm{MgF}_{2}(s) \quad \Delta E=?$$ Lattice energy First ionization energy of \(\mathrm{Mg}\) Second ionization energy of \(\mathbf{M g}\) Electron affinity of \(\mathbf{F}\) Bond energy of \(\mathrm{F}_{2}\) Energy of sublimation for \(\mathrm{Mg}\) \(-2913 \mathrm{kJ} / \mathrm{mol}\) \(735 \mathrm{kJ} / \mathrm{mol}\) \(1445 \mathrm{kJ} / \mathrm{mol}\) \(-328 \mathrm{kJ} / \mathrm{mol}\) \(154 \mathrm{kJ} / \mathrm{mol}\) 150\. kJ/mol

Step-by-Step Solution

Answer

The change in energy, ΔE, for the reaction $$\mathrm{Mg}(s)+\mathrm{F}_{2}(g) \longrightarrow \mathrm{MgF}_{2}(s)$$ is 6053 kJ/mol.

Step 1: Write down the given energy values

We are given the following energy values for magnesium fluoride: - Lattice energy = -2913 kJ/mol - First ionization energy of Mg = 735 kJ/mol - Second ionization energy of Mg = 1445 kJ/mol - Electron affinity of F = -328 kJ/mol - Bond energy of F₂ = 154 kJ/mol - Energy of sublimation for Mg = 150 kJ/mol

Step 2: Determine the total energy for forming Mg²⁺ from Mg

To find the total energy needed for forming Mg²⁺ from Mg, we'll add the first and second ionization energies of Mg: $$\text{Total energy for forming Mg}^{2+} = \text{First ionization energy of Mg} + \text{Second ionization energy of Mg}$$ $$= 735 \mathrm{kJ/mol} + 1445 \mathrm{kJ/mol}$$ $$= 2180 \mathrm{kJ/mol}$$

Step 3: Determine the total energy for forming 2 F⁻ from F₂

To find the total energy for forming 2 F⁻ from F₂, we'll consider the bond energy of F₂ and the electron affinity of F: $$\text{Total energy for forming 2 F}^- = \text{Bond energy of F}_{2} - 2 \times (\text{Electron affinity of F})$$ $$= 154 \mathrm{kJ/mol} - 2 \times (-328 \mathrm{kJ/mol})$$ $$= 154 \mathrm{kJ/mol} + 656 \mathrm{kJ/mol}$$ $$= 810 \mathrm{kJ/mol}$$

Step 4: Calculate ΔE for the reaction

To calculate ΔE for the reaction, we'll consider the total energy for forming Mg²⁺, 2 F⁻, the lattice energy of MgF₂, and the energy of sublimation for Mg: $$\Delta E = \text{Total energy for forming Mg}^{2+} + \text{Total energy for forming 2 F}^- - \text{Lattice energy} + \text{Energy of sublimation for Mg}$$ $$= 2180 \mathrm{kJ/mol} + 810 \mathrm{kJ/mol} - (-2913 \mathrm{kJ/mol}) + 150 \mathrm{kJ/mol}$$ $$= 2180 \mathrm{kJ/mol} + 810 \mathrm{kJ/mol} + 2913 \mathrm{kJ/mol} + 150 \mathrm{kJ/mol}$$ $$= 6053 \mathrm{kJ/mol}$$ So, the change in energy, ΔE, for the reaction is 6053 kJ/mol.

Key Concepts

Ionization Energy

Ionization energy is the energy required to remove an electron from an atom or ion in its gaseous state. When an atom loses an electron, it becomes a positively charged ion, known as a cation. The first ionization energy refers to the energy needed to remove the first electron, and each subsequent ionization energy (second, third, etc.) is higher because it is more difficult to remove an electron from a positively charged ion than a neutrally charged atom. For instance, magnesium (Mg) must undergo two ionization steps to achieve the Mg²⁺ needed for forming magnesium fluoride (MgF₂). The first ionization of Mg requires 735 kJ/mol, while the second requires a much higher energy of 1445 kJ/mol due to the increased nuclear attraction on the remaining electrons.

Electron Affinity

Electron affinity is the energy change that occurs when an atom in the gas phase accepts an electron to form an anion. This process can release energy, making electron affinity values negative. For example, fluorine (F) has a high electron affinity because it readily accepts electrons to fill its outer electron shell, releasing energy in the process. The electron affinity of F is -328 kJ/mol, indicating that energy is released when each F atom gains an electron, thus two F atoms gaining electrons would release twice this amount, contributing to the overall energy changes in a chemical reaction.

Bond Energy

Bond energy refers to the amount of energy required to break a bond between two atoms in a molecule in the gas phase. The bond energy is a measure of bond strength within a chemical bond. In the case of fluorine (F₂), the bond energy is 154 kJ/mol. To break the chemical bond in a single molecule of F₂ to produce two separate F atoms, 154 kJ/mol of energy is consumed. This energy must be taken into account when calculating the total energy changes during the formation of compounds like magnesium fluoride.

Energy of Sublimation

The energy of sublimation is the energy required for a substance to transition from a solid to a gas without passing through the liquid phase. This process involves overcoming the lattice forces that hold the solid together. For magnesium (Mg), the energy of sublimation is 150 kJ/mol. During the formation of magnesium fluoride, we must consider the sublimation of solid magnesium, as it contributes to the total energy input necessary for the reaction. This ensures that all states are considered, with magnesium going from solid to gaseous before it reacts with fluorine gas to become MgF₂.

Enthalpy Change Calculation

Enthalpy change calculation involves determining the overall energy change of a reaction, often represented as ΔH under constant pressure or ΔE when considering internal energy. In reactions like the formation of magnesium fluoride, we calculate ΔE by adding the total ionization energies of Mg, the energy of forming F⁻ ions from F₂, and the energy of sublimation for Mg, then subtracting the lattice energy of MgF₂. Lattice energy is the energy released when ions bond to form a solid. It is typically a negative value, indicating an exothermic process. The enthalpy change for the formation of MgF₂ also considers the energy needed to break the F₂ bond.