Question

Use the following data to estimate \(\Delta E\) for the reaction: $$\mathrm{Ba}(s)+\mathrm{Br}_{2}(g) \longrightarrow \mathrm{BaBr}_{2}(s) \quad \Delta E=?$$ Lattice energy First ionization energy of Ba Second ionization energy of Ba Electron affinity of Br Bond energy of \(\mathrm{Br}_{2}\) Enthalpy of sublimation of Ba \(-1985 \mathrm{kJ} / \mathrm{mol}\) \(503 \mathrm{kJ} / \mathrm{mol}\) \(965 \mathrm{kJ} / \mathrm{mol}\) -325 kJ/mol \(193 \mathrm{kJ} / \mathrm{mol}\) \(178 \mathrm{kJ} / \mathrm{mol}\)

Short answer

The change in energy (\(\Delta E\)) for the reaction is -796 kJ/mol.

Step-by-step solution

Energy required for formation of Ba\(^{2+}\) from Ba

To form Ba\(^{2+}\), we need to remove two electrons from the Barium atom, one at a time. The first electron removal requires an energy of 503 kJ/mol (first ionization energy of Ba), and the second electron removal requires an energy of 965 kJ/mol (second ionization energy of Ba). But, as Barium is in solid form, we must first make it gaseous by providing energy equal to the enthalpy of sublimation of Ba (178 kJ/mol). So, the total energy required for the formation of Ba\(^{2+}\): Energy = Enthalpy of sublimation + First ionization energy + Second ionization energy Energy = 178 kJ/mol + 503 kJ/mol + 965 kJ/mol = 1646 kJ/mol

Energy required for formation of 2Br\(^{-}\) from Br\(_2\)

To form two Br\(^{-}\) ions, we need to add one electron to each bromine atom, which requires energy which is equal to the electron affinity of Br (-325 kJ/mol). Before that, we must break the bond between two bromine atoms (Br\(_2\)), which requires the bond energy of Br\(_2\) (193 kJ/mol). So, the total energy required for the formation of two Br\(^{-}\) ions: Energy = Bond energy + 2 × Electron affinity Energy = 193 kJ/mol + 2 × (-325 kJ/mol) = -457 kJ/mol

Lattice energy for the formation of BaBr\(_2\)

The lattice energy for the formation of BaBr\(_2\) from Ba\(^{2+}\) and Br\(^{-}\) ions is given as -1985 kJ/mol.

Calculate the change in energy (\(\Delta E\)) for the reaction

To find the change in energy, we need to calculate the difference between the sum of the energies of the products (lattice energy) and the sum of the energies of the reactants (energies from Steps 1 and 2). Therefore, \(\Delta E\) = Lattice energy - (Energy in Step 1 + Energy in Step 2) \(\Delta E\) = -1985 kJ/mol - (1646 kJ/mol - 457 kJ/mol) \(\Delta E\) = -1985 kJ/mol -1189 kJ/mol = -796 kJ/mol The change in energy (\(\Delta E\)) for the reaction is -796 kJ/mol.

Key concepts

Lattice Energy

Lattice energy is a measure of the strength of the forces holding ionic compounds together. It's the energy released when gaseous ions come together to form an ionic solid. For the reaction Barium plus Bromine equals solid Barium Bromide, the lattice energy is -1985 kJ/mol, indicating that a significant amount of energy is released when these ions form the ionic lattice of Barium Bromide. This highly exothermic process shows how lattice energy is a critical factor in the stability of ionic compounds.

Lattice Formation and Its Energy Implications

The energy release during lattice formation is a clear indicator of the exothermic nature of this step in forming an ionic compound. It is crucial to consider lattice energy when predicting the feasibility and strength of the resulting compound. For students, visualizing the ionic lattice and understanding that the negative sign denotes the release of energy can help solidify their grasp of this concept.

Ionization Energy

Ionization energy is the energy needed to remove an electron from an atom in its gaseous state. It plays a vital role in understanding the reactivity and binding capabilities of elements. In our example, Barium's first ionization energy is 503 kJ/mol, which pertains to removing the first electron. The second ionization energy, 965 kJ/mol, is higher because it is more challenging to remove an electron from a positively charged ion than a neutral atom.

The Role of Multiple Ionization Energies

Considering both the first and second ionization energies is essential as they cumulatively represent the energy cost to form Bada{2+} from solid Barium. These values suggest that forming ions is an endothermic process, meaning it absorbs energy from the surroundings.

Electron Affinity

Electron affinity measures the energy change when an electron is added to a neutral atom in the gaseous state. A negative value, such as the -325 kJ/mol for Bromine, indicates that energy is released when the atom gains an electron to form an anion. This process is typically exothermic for non-metals, which are keen to gain electrons and achieve a more stable electron configuration.

Understanding Electron Gain

Electron affinity can vary widely among different elements, affecting how they combine during chemical reactions. For instance, when Bromine becomes an anion, it releases energy, showing its propensity to form negative ions readily.

Enthalpy of Sublimation

The enthalpy of sublimation is the energy required to change a substance from solid to gaseous state without passing through a liquid state. For Barium, it is given as 178 kJ/mol, signifying the energy required to sublimate one mole of solid Barium into its gaseous constituent atoms. This value is important for reactions involving elements that need to transition from solid to gas before engaging in chemical bonding.

From Solid to Gas

The role of the enthalpy of sublimation in the overall energy balance of a reaction is often overlooked but is critical when evaluating the energy profile of metal-involved reactions, particularly those forming ionic compounds from solid metal.

Bond Energy

Bond energy is the energy needed to break a chemical bond in a mole of substance under standard conditions. Regarding Br₂, the bond energy is 193 kJ/mol. It reflects the energy input required to break the bond between the two bromine atoms to form separate bromine radicals ready to combine with other elements. This is also an endothermic process that requires an input of energy.

Bonds and Energy

The concept of bond energy is pivotal when considering reaction mechanisms and energy changes, as breaking bonds is a necessary step before new bonds can form in products. Understanding the energetic costs of bond dissociation aids in predicting reaction behavior.

Chemical Thermodynamics

Chemical thermodynamics deals with the study of energy changes during chemical reactions. It helps predict whether a reaction is energetically feasible and what might be the extent of energy exchange with the surroundings. In our example, we used principles of chemical thermodynamics to calculate delta E as -796 kJ/mol, indicating the reaction's spontaneity and that it releases energy - in this case, heat - to the surroundings.

Reaction Energetics and Spontaneity

By harnessing the concepts of ionization energy, electron affinity, lattice energy, bond energy, and enthalpy of sublimation, we can predict that the formation of Barium Bromide is favorable since it releases a considerable amount of energy. This approach is fundamental in chemical thermodynamics to assess the energy profile and spontaneity of chemical processes.