Question

The ionic compound MX from the metal M and nonmetal X in their standard states. Given that: ∆Hf = -150 kJ/mol, ∆Hsub = 300 kJ/mol, 1/2 ∆HBE = 350 kJ/mol, ∆HIE1+IE2 = 450 kJ/mol, and ∆HEA1+EA2 = -250 kJ/mol, what is the lattice energy of the compound MX?

A. 700 kJ/mol
B. -300 kJ/mol
C. -1000 kJ/mol
D. -1500 kJ/mol
E. -700 kJ/mol

Answer 1

Using the Born-Haber cycle and Hess's law, the lattice energy for the ionic compound MX is calculated to be +1500 kJ/mol, which indicates an endothermic process. However, if viewed as an exothermic process, the energy released would be -1500 kJ/mol (Option D).

Step-by-step explanation:

The lattice energy of the ionic compound MX can be calculated using the Born-Haber cycle, which relates various enthalpy changes during the formation of an ionic compound. According to the provided data, we have the enthalpy of formation (ΔHf), sublimation energy (ΔHsub), bond energy (ΔHBE), ionization energy (ΔHIE1+IE2), and electron affinity (ΔHEA1+EA2). To find the lattice energy (ΔHLattice) for the compound, we can apply Hess's law, which states that the total enthalpy change for a reaction is the same, no matter how many steps the reaction is carried out in. The lattice energy can be calculated using the formula:

ΔHLattice = ΔHsub + 1/2 ΔHBE + ΔHIE1+IE2 - ΔHEA1+EA2 - ΔHf

Substituting the values from the question, we get:

ΔHLattice = 300 kJ/mol + 350 kJ/mol + 450 kJ/mol - (-250 kJ/mol) - (-150 kJ/mol) = 1500 kJ/mol

Since lattice energy is typically considered the energy required to separate the ions, and given that separating ions is an endothermic process, the correct answer for the lattice energy of the compound MX is +1500 kJ/mol, which is not among the given choices. However, if we consider the lattice energy as the energy released (which would be an exothermic process) when ions form a solid lattice, the answer would then be -1500 kJ/mol (Option D).