Problem 71 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following arrangements show the correct order of increasing lattice energy? (a) \(\mathrm{BaSO}_{4}<\mathrm{SrSO}_{4}<\mathrm{CaSO}_{4}<\mathrm{MgSO}_{4}\) (b) \(\mathrm{MgCO}_{3}<\mathrm{CaCO}_{3}<\mathrm{SrCO}_{3}<\mathrm{BaCO}_{3}\) (c) \(\mathrm{LiF}<\mathrm{LiCl}<\mathrm{LiBr}<\) Lil (d) \(\mathrm{NaF}<\mathrm{KF}<\mathrm{RbF}<\mathrm{CsF}\)

Step-by-Step Solution

Answer

The correct order is (a): BaSO4 < SrSO4 < CaSO4 < MgSO4.

Step 1: Understanding Lattice Energy

Lattice energy is the energy released when ions combine to form a crystalline lattice. It is influenced by the charge of the ions and the size of the ions. Smaller ions and higher charged ions generally lead to higher lattice energies.

Step 2: Analyze Metal Sulfates (Option A)

In option (a), the sulfate compounds are listed with Ba, Sr, Ca, and Mg as the metal ions. Since lattice energy increases with smaller cation size, and Ba > Sr > Ca > Mg in terms of ionic size, the order MgSO4 > CaSO4 > SrSO4 > BaSO4 reflects increasing lattice energy.

Step 3: Examine Carbonates (Option B)

In option (b), carbonates are listed with Mg, Ca, Sr, and Ba. The increasing order of the size of ions from Mg to Ba does lead to decreasing lattice energy, hence the correct order from lowest to highest lattice energy would be BaCO3 < SrCO3 < CaCO3 < MgCO3, opposite of what is presented.

Step 4: Review Lithium Halides (Option C)

Option (c) lists lithium halides. For these, increasing ionic size in the order LiI > LiBr > LiCl > LiF suggests that lattice energy should decrease. The list should be LiI < LiBr < LiCl < LiF for increasing lattice energy, contrary to the option given.

Step 5: Evaluate Alkali Fluorides (Option D)

In option (d), fluoro compounds are listed with Na, K, Rb, and Cs. The ionic size increases from Na to Cs, suggesting lattice energy should decrease from NaF to CsF. Hence, NaF has the highest lattice energy, followed by KF, RbF, and CsF, contrary to the list provided.

Key Concepts

Ionic Size

Ionic size is a critical factor affecting lattice energy. Lattice energy is higher when the ions are smaller because smaller ions can come closer together. This means the electrostatic force, which binds them, becomes stronger. When ions are large, they can't pack as closely, weakening the attractions between them.

In terms of ordering, for ions like those present in lattice structures:

• Smaller ions generally lead to stronger lattice energy.
• Larger ions tend to decrease lattice energy due to increased distance between charges.

Understanding ionic size is essential when predicting and comparing the lattice energies of different compounds.

Ionic Charge

The charge of ions plays a crucial role in determining lattice energy. More highly charged ions will exert a greater electrostatic force on one another, increasing the energy released when they form a crystal lattice.

Consider these points:

• Lattice energy is directly proportional to the magnitude of the charge on the ions. Higher charges generally mean stronger attractions.
• Ions with +2 or -2 charges, for instance, will result in higher lattice energy than those with +1 or -1 because of increased force of attraction.

When analyzing compounds, always examine both the ionic sizes and charges to understand lattice energy thoroughly.

Crystal Lattice

A crystal lattice refers to the arrangement of ions in a solid. It is this very formation that determines the physical properties of ionic compounds.

Key features of a crystal lattice include:

• It represents a systematic, repeating pattern extending in all three spatial dimensions.
• This organization maximizes attractive forces while minimizing repulsion, enhancing stability.

When ions form a crystal lattice, a significant amount of energy is released as lattice energy, which further stabilizes the structure.

Metal Sulfates

Metal sulfates like BaSO₄, SrSO₄, CaSO₄, and MgSO₄ provide an excellent context for exploring lattice energy. These compounds feature sulfate ions alongside various metal cations. The size and charge of these metal ions significantly impact their lattice energies.

For these compounds:

• As you move from larger ions (Ba) to smaller ions (Mg), the lattice energy increases due to the decreased ionic size.
• This size difference influences how tightly the sulfate ions can pack, affecting the overall stability and energy of the lattice.

Analyzing metal sulfates offers clear examples of the relationship between ionic size and lattice energy.

Carbonates

Carbonates, such as e.g., MgCO₃, CaCO₃, SrCO₃, and BaCO₃ , display fascinating variations in lattice energy primarily due to differences in metal ion size. In examining these carbonates:

• The increasing size from Mg to Ba leads to a decrease in lattice energy.
• The larger the metal ion, the less tightly the carbonate ions are held together, reducing stability and lattice energy.

Therefore, understanding how ionic size within carbonates affects lattice energy helps predict the order of stability and reactivity in these compounds.

Lithium Halides

Lithium halides illustrate how lattice energy changes with varying halide ions paired with lithium. These salts—such as LiF, LiCl, LiBr, and LiI—show different lattice energies based on ionic size.

• When looking from LiI to LiF, the ionic size decreases, leading to stronger attractions between ions and increased lattice energy.
• LiF has the highest lattice energy because of the small ion sizes and resulting strong interactions.

Studying these differences helps clarify how lithum's ionic relationships with different halides impact their properties.

Alkali Fluorides

Alkali fluorides feature combinations like NaF, KF, RbF, and CsF. In these salts, as the cation size increases from Na to Cs, lattice energy systematically decreases due to weaker attractions between larger ions.

Consider these points:

• NaF, being the smallest, has the highest lattice energy due to shorter ion-to-ion distances.
• As you progress to CsF, the lattice energy decreases owing to the reduced electrostatic interactions caused by larger ionic sizes.

Understanding alkali fluorides offers valuable insights into how both cation size and lattice energy interplay in these compounds.