Problem 13 - Chemistry

Question

Calculate the net energy change in kilojoules per mole that takes place on formation of \(\mathrm{MgF}_{2}(s)\) from the elements: \(\mathrm{Mg}(s)+\mathrm{F}_{2}(g) \longrightarrow \mathrm{MgF}_{2}(s)\). The following information is needed: Heat of sublimation for \(\mathrm{Mg}(s)=147.7 \mathrm{~kJ} / \mathrm{mol}\) \(E_{\mathrm{ea}}\) for \(\mathrm{F}(\mathrm{g})=-328 \mathrm{~kJ} / \mathrm{mol}\) Bond dissociation energy for \(\mathrm{F}_{2}(g)=158 \mathrm{~kJ} / \mathrm{mol}\) \(E_{\mathrm{il}}\) for \(\mathrm{Mg}(\mathrm{g})=737.7 \mathrm{~kJ} / \mathrm{mol}\) Electrostatic interactions in \(\mathrm{MgF}_{2}(s)=-2957 \mathrm{~kJ} / \mathrm{mol} \quad E_{\mathrm{i} 2}\) for \(\mathrm{Mg}(g)=1450.7 \mathrm{~kJ} / \mathrm{mol}\)

Step-by-Step Solution

Answer

The net energy change is -1198.9 kJ/mol.

Step 1: Convert the Magnesium to Gas Phase

Calculate the energy required to convert solid magnesium to gaseous magnesium using its heat of sublimation. This step requires 147.7 kJ/mol since magnesium changes from solid to gas.

Step 2: Ionize the Gaseous Magnesium

Convert gaseous magnesium to \( ext{Mg}^{+} \) and \( ext{Mg}^{2+} \) by providing ionization energies. The first ionization energy (\( E_{il} = 737.7 \text{ kJ/mol} \)) and the second ionization energy (\( E_{i2} = 1450.7 \text{ kJ/mol} \)) are required. The total energy for ionization is \[ 737.7 + 1450.7 = 2188.4 \ ext{kJ/mol. } \]

Step 3: Dissociate F2 Molecule

Calculate the energy to break one mole of \( F_2 \) into two moles of fluorine atoms, using its bond dissociation energy. The energy needed is \[ rac{1}{2} \times 158 = 79 \ ext{kJ/mol per } \ ext{fluorine atom.} \]

Step 4: Add Electron to F Atom

Provide electron affinity energy when forming \( ext{F}^- \). Since there are two fluorine atoms, total energy change due to electron affinity is \[ 2 \times (-328) = -656 \ ext{kJ/mol.} \]

Step 5: Form the Ionic Compound with Lattice Energy

Calculate the energy related to forming \( ext{MgF}_2 \) from gaseous ions by considering the lattice energy, which is given as \(-2957 \ ext{kJ/mol}\).

Step 6: Summation of All Energies

Add all previous energy changes from Steps 1 to 5 to find the net energy change: \1. Sublimation = 147.7 kJ/mol2. Ionization = 2188.4 kJ/mol3. \( F_2 \) Dissociation = 79 kJ/mol4. Electron Affinity = -656 kJ/mol5. Lattice Energy = -2957 kJ/molThe total energy change is \[ 147.7 + 2188.4 + 79 - 656 - 2957 = -1198.9 \ ext{kJ/mol.} \]

Key Concepts

Heat of Sublimation

The heat of sublimation is the energy required to convert a solid substance directly into a gas. This process occurs without passing through the liquid state. For magnesium, the heat of sublimation is 147.7 kJ/mol, which is the amount of energy needed for this conversion. When magnesium transitions from a solid to a gaseous state, it's essential to overcome the attractive forces between the magnesium atoms in the solid phase.

• This energy is always absorbed from the surroundings, making it an endothermic process.
• The value is different for each element and depends on factors like atomic structure and bonding.

Heat of sublimation is a crucial initial step in the formation of certain compounds where the metal needs to be in the gaseous state.

Ionization Energy

Ionization energy refers to the energy required to remove one or more electrons from an atom or ion. For magnesium, two ionization energies are needed to convert into Mg²⁺: the first ionization energy is 737.7 kJ/mol, and the second is 1450.7 kJ/mol.

• The first ionization energy is the energy to remove the first electron, transforming the neutral Mg atom into Mg⁺.
• The second ionization involves removing a second electron, forming Mg²⁺.
• Total energy for both ionizations is crucial for transition metal chemistry.

These energies indicate that removing a second electron is more difficult due to increased attraction between the remaining electrons and nucleus.

Bond Dissociation Energy

Bond dissociation energy measures the strength of a chemical bond. For fluorine, this is the energy needed to split an F₂ molecule into two individual fluorine atoms. The bond dissociation energy for F₂ is 158 kJ/mol.

• The dissociation process involves dividing this energy equally between each atom, as only one bond is broken.
• For each fluorine atom, the energy used is 79 kJ/mol (half the dissociation energy of F₂).
• This endothermic process provides the necessary atoms for further reactions.

Such an energy requirement ensures that only enough energy as needed is applied, maintaining balance in chemical reactions.

Electron Affinity

Electron affinity is the energy change when an electron is added to a gaseous atom to form an anion. For fluorine, this process releases energy, indicating that it is exothermic. Each fluorine atom captures an electron, forming F⁻ ions, and releasing an energy of -328 kJ/mol per atom.

• The negative sign shows energy is released as the atom becomes more stable.
• For two fluorine atoms, total energy released is -656 kJ/mol.
• This released energy helps stabilize the newly formed anions.

Electron affinities are significant in determining an element's ability to form negative ions, greatly influencing compound stability and formation.

Lattice Energy

Lattice energy is the energy released when gaseous ions form an ionic compound. For MgF₂, the lattice energy is -2957 kJ/mol, a large value reflecting the strong ionic bonds between Mg²⁺ and F⁻ ions.

• The negative value signifies energy release upon formation of solid from gaseous ions, exothermic.
• It is directly proportional to the charge of the ions and inversely proportional to the ionic radii.
• High lattice energies indicate stable ionic solids due to strong electrostatic forces.

Lattice energy is essential for predicting solubility and stability of ionic compounds. It helps assess the feasibility of forming particular compounds, especially when combined with other energy considerations.