Final answer:
To estimate the lattice energy of the hypothetical salt XY, with ions similar in size to Na+ and Cl- but with higher charges, we calculate it to be nine times that of NaCl, resulting in an estimated lattice energy of -7083 kJ/mol.
Step-by-step explanation:
Estimating the lattice energy of a hypothetical ionic compound XY, where X3+ and Y3- have similar sizes to Na+ and Cl- respectively, requires understanding how ionic charges and ionic radii affect lattice energy. The lattice energy of NaCl is -787 kJ/mol. According to the information provided, if the ions have the same radius but different charges, we can expect a significant increase in lattice energy due to the stronger electrostatic force between ions with higher charges.
Given that lattice energy is proportional to the product of the charges of the ions, we can estimate the lattice energy for XY by considering the increase in charge from +1 and -1 for NaCl to +3 and -3 for XY. The increase in the charge product (from 1*1 to 3*3) suggests that the lattice energy for XY would be (3/1)^2 times greater than that of NaCl.
Therefore, the estimated lattice energy for XY is (-787 kJ/mol) * (3/1)^2 = -787 * 9 = -7083 kJ/mol (negative sign indicates energy is released).