Question

CaO and NaCl have the same crystal structure and approximately the same ionic radii. If U is the lattice energy of NaCl, the approximate lattice energy of CaO is:
A.$\dfrac{U}{2}$
B.U
C.2U
D.4U

Answer 1

Hint: Try to recall that lattice energy of a crystalline solid is a measure of the energy released when the ions are combined to make a compound product of charges present on each ion. Now, by using this you can easily find the correct option from the given ones.

Complete step by step solution:
It is known to you that lattice energy is a type of potential energy that is the energy required to break apart an ionic solid and convert its component atoms into gaseous ions.
The value of lattice energy is always positive since it will always be an endothermic reaction.
It is used to explain the stability of an ionic compound. It is a measure of cohesive force that binds the ions and is an estimate of the bond strength in an ionic compound.
The factors on which lattice energy depends is charge and size of ions.
Lattice energy is directly proportional to the product of charge on ions in a crystal and is inversely proportional to the size of ions.
Lattice energy of NaCl, $U = 1 \times 1 = 1$ since, charge on both ion is of magnitude 1.then, lattice energy of CaO $ = 2 \times 2 = 4 = 4U$ since, charge on each ion in CaO is of magnitude 2.
Therefore, from above we can conclude that option D is the correct option to the given question.

Note:
It should be remembered to you that lattice energy cannot be determined experimentally due to the difficulty in isolating the gaseous ions. The energy value can be determined by Born-Haber cycle or it can be calculated theoretically with an electrostatic examination of crystal structure.