Question

\(\mathrm{CaO}\) and \(\mathrm{NaCl}\) have same crystal structure and nearly the same ionic radii. If \(X\) is the lattice energy of \(\mathrm{NaCl}\), the lattice energy of \(\mathrm{CaO}\) is very nealy (a) \(\mathrm{X}\) (b) \(2 \mathrm{X}\) (c) \(4 \mathrm{X}\) (d) \(\mathrm{X} / 4\)

Short answer

The lattice energy of CaO is nearly 4X.

Step-by-step solution

Understanding Lattice Energy

Lattice energy is the energy released when ions are combined to form a crystalline lattice. It is dependent on the charges of the ions and the distance between them.

Analyzing Ionic Charges

For NaCl, the ionic charges are +1 for Na and -1 for Cl. For CaO, the charges are +2 for Ca and -2 for O. The lattice energy is proportional to the product of the charges of the cation and anion.

Calculate Relative Lattice Energy for NaCl

The lattice energy formula is proportional to the product of the ionic charges: \(z^+ \cdot z^-\). In NaCl, \(z^+ = +1\) and \(z^- = -1\), so the product is \((+1) \cdot (-1) = -1\).

Calculate Relative Lattice Energy for CaO

In CaO, \(z^+ = +2\) and \(z^- = -2\), so the product is \((+2) \cdot (-2) = -4\). The magnitude of the product is 4 times that of NaCl.

Compare Lattice Energies

Comparing the products from NaCl and CaO, the lattice energy of CaO is four times that of NaCl because the ionic products differ by a factor of 4.

Key concepts

Ionic Charges

Ionic charges play a crucial role in determining the lattice energy of ionic compounds. In simple terms, the ionic charge is the electrical charge an atom acquires when it loses or gains electrons to form ions.
When it comes to ionic compounds like calcium oxide ( CaO ) and sodium chloride ( NaCl ), understanding their ionic charges is vital. Sodium ( Na ) and chloride ( Cl ) ions in NaCl have charges of +1 and -1, respectively. Meanwhile, in CaO , calcium ( Ca ) takes on a charge of +2 and oxygen ( O ) gets a charge of -2.
These charges are not arbitrary; they reflect the atom's need to achieve a stable electron configuration. The greater the charge on the ions, the stronger the electrostatic attraction between them. This results in a higher lattice energy, which is the energy required to break the ions apart from their lattice positions or, inversely, released when the lattice structure is formed.

• Ionic charge affects lattice energy significantly.
• The greater the absolute charge on ions, the stronger the electrostatic interaction.

Crystal Structure

The crystal structure of an ionic compound refers to the orderly arrangement of its ions in a three-dimensional space. Both CaO and NaCl possess a similar crystal structure, typically referred to as a "face-centered cubic" (FCC) lattice. In this configuration, each ion is surrounded by ions of the opposite charge, optimizing the electrostatic forces.
This specific structure supports minimal repellence between like-charged ions. By keeping ions of opposite charges in close proximity while maintaining maximum distance from similar charges, these compounds achieve structural stability and significant lattice energy. The similarity in crystal structure between CaO and NaCl means that differences in their lattice energies are mainly due to their ionic charges rather than the geometric packing pattern.

• Crystal structures contribute to ionic stability.
• Both CaO and NaCl use a face-centered cubic (FCC) lattice.

Ionic Radii

Ionic radii refer to the effective size of an ion in a crystal lattice, and they play a notable role in influencing lattice energy. Although CaO and NaCl have nearly the same ionic radii, meaning the physical sizes of the composing ions are similar, this doesn't solely determine their lattice energies.
The size of the ions affects the distance between them in the lattice. If the ionic radii are large, ions are spread out further apart, leading to a decrease in lattice energy due to weaker electrostatic forces. However, in our examples, since the ionic radii are almost the same, the charge difference primarily affects the lattice energy.
In summary, while ionic radii influence the overall energy dynamic by affecting distance, it is less impactful than ionic charges in this particular comparison of CaO and NaCl .

• Ionic radius affects the distance between ions.
• Despite similar radii, charge difference is more significant for lattice energy.

Cation and Anion Interaction

The interaction between cations and anions forms the basis of ionic bonding and is directly responsible for the lattice energy within a crystal. Cations are positively charged, whereas anions carry a negative charge. In the lattice structure, strong attractive forces exist between them.
For NaCl , sodium ( Na^+ ) interacts with chloride ( Cl^- ), and for CaO , calcium ( Ca^{2+} ) interacts with oxide ( O^{2-} ). The charges on these ions affect the strength of the interaction—the greater the product of the charges, the stronger the attraction and, therefore, the higher the lattice energy.
As seen in the problem solution, CaO with its higher charge products (+2 and -2) compared to NaCl (+1 and -1) results in four times stronger cation-anion interaction and thus four times greater lattice energy.

• Cation and anion interactions determine lattice energy strength.
• Higher charges lead to more substantial interactions and higher energy.