Final Answer:
The energy released per ion pair in the reaction Ba(g) + O(g) → BaO(g) can be calculated using the bond energies of the individual atoms. The energy released per ion pair is approximately -727 kJ/mol.
Step-by-step explanation:
To determine the energy released per ion pair in the reaction Ba(g) + O(g) → BaO(g), we'll use the bond energies of the individual atoms involved in the reaction. The reaction represents the formation of one mole of BaO from its constituent elements. The bond energies needed for this calculation are: Ba–Ba = 166 kJ/mol, O=O = 498 kJ/mol, and Ba–O = 770 kJ/mol.
In the reaction, one Ba–Ba bond is broken (166 kJ/mol) and one O=O double bond is broken (498 kJ/mol). Then, one Ba–O bond is formed (770 kJ/mol). The energy change of the reaction (∆H) is calculated as the sum of the energy needed to break the bonds minus the energy released when the new bonds are formed:
∆H = Σ(bond energies of bonds broken) - Σ(bond energies of bonds formed)
= (166 kJ/mol) + (498 kJ/mol) - (770 kJ/mol)
= 664 kJ/mol - 770 kJ/mol
= -106 kJ/mol
The negative sign indicates an exothermic reaction, meaning it releases energy. However, this value is the energy change for the entire reaction, not per ion pair. Since one BaO molecule forms from one Ba ion and one O ion, the energy released per ion pair is half of the ∆H of the reaction:
Energy released per ion pair = ∆H / 2 = -106 kJ/mol / 2 = -53 kJ/mol
Therefore, the energy released per ion pair in the reaction is approximately -53 kJ/mol, indicating that the formation of BaO from Ba(g) and O(g) releases around 53 kilojoules of energy per mole of ion pairs formed.