Answer :
Final answer:
The total heat of hydration for 1 mol of gas phase Li⁺ and Cl⁻ ions is -865.1 kJ, calculated by subtracting the lattice energy (828 kJ/mol) from the heat of solution (-37.1 kJ/mol).
Explanation:
To calculate the total heat of hydration for 1.00 mol of gas phase Li⁺ and Cl⁻ ions using the given heat of solution and lattice energy, we apply the concept that the total heat involved in forming an aqueous solution from an ionic solid can be thought of as the sum of the lattice energy (endothermic) and the heat of hydration (exothermic).
The given heat of solution for LiCl is -37.1 kJ/mol, which is the net heat change when one mole of LiCl is dissolved in water. It includes the lattice energy, an endothermic process to separate LiCl solid into Li⁺ and Cl⁻ ions (given as 828 kJ/mol), and the heat of hydration, an exothermic process where water molecules surround and stabilize the ions.
We can express this relationship as:
Heat of solution = Lattice energy + Heat of hydration
Rearranging this equation to solve for the heat of hydration, we have:
Heat of hydration = Heat of solution - Lattice energy
Substituting in the given values, we get:
Heat of hydration = (-37.1 kJ/mol) - (828 kJ/mol)
Heat of hydration = -865.1 kJ/mol (for 1.00 mol of gas phase ions)
Therefore, the total heat of hydration for 1.00 mol of Li⁺ and Cl⁻ ions is -865.1 kJ.
