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) \(\mathrm{LiF}<\mathrm{LiCl}<\mathrm{LiBr}<\mathrm{Lil}\) (d) \(\mathrm{NaF}<\mathrm{KF}<\mathrm{RbF}<\mathrm{CsF}\)

Step-by-Step Solution

Answer

Options (a) and (c) show the correct order of increasing lattice energy.

Step 1: Understanding Lattice Energy

Lattice energy is the energy required to separate the ions in an ionic solid into gaseous ions. Generally, lattice energy increases with the magnitude of the charge on the ions and decreases with increasing ionic radii.

Step 2: Analyzing Option (a)

For the series 2 ext{"BaSO ext{4}< ext{SrSO extashv{4}< extCaSO eleased {4}7< extmgSO eopen4}8 ", as the cation size decreases from Ba to Mg, lattice energy increases. So option (a) is consistent with increasing lattice energy.

Step 3: Analyzing Option (b)

In the series 2 ext{"MgCOegin{3}< extCaCO inishedr{3} ext{3}< extbayCo extReopen}6, the lattice energy would decrease from Mg to Ba due to increasing ionic size, so this is incorrectly ordered in terms of increasing lattice energy.

Step 4: Analyzing Option (c)

For 2 ext{"LiF warrior^< extLiClbeacon{< extlidir option b< indxI8rouch96 ", the lattice energy should decrease from LiF to LiI as halide ion size increases. This matches the pattern given.

Step 5: Analyzing Option (d)

In the sequence 2 ext{"NaFbeagle< extKFbeacon{< extRbFsue87< CsFeacon ", lattice energy is expected to decrease as cation size increases from Na to Cs, supporting this arrangement.

Key Concepts

Ionic Radii

Ionic radii refer to the size of an ion in a crystal lattice, which plays a critical role in determining the lattice energy of ionic compounds. As a general rule, larger ions result in lower lattice energy because they cannot pack together as tightly. The distance between ions increases with increasing ionic radii, reducing the electrostatic force of attraction. Consider ionic compounds like

• BaSO extsubscript{4}
• SrSO extsubscript{4}
• CaSO extsubscript{4}
• MgSO extsubscript{4}

In these examples, magnesium has the smallest ionic radius, which allows ions to pack closer together and increases the lattice energy. This is the logic behind why lattice energy increases as ionic radii decrease.

Charge on Ions

The charge on ions is a pivotal factor influencing lattice energy. The greater the magnitude of the charges on the ions, the stronger is the force of attraction between them. This directly contributes to higher lattice energy, because more energy is required to separate the ions. For example, ions with a higher charge density have a strong electrostatic attraction. Consider:

• LiF: The lithium ion and fluoride ion both possess a charge of +1 and -1, respectively.
• MgSO extsubscript{4}: The magnesium ion has a +2 charge that greatly enhances lattice energy compared to singly charged ions.

Here, the stronger attraction in MgSO extsubscript{4} due to higher charges results in much higher lattice energy compared to LiF.

Ionic Solids

Ionic solids are formed by the electrostatic forces between positively charged cations and negatively charged anions. These solids have distinctive properties like high melting and boiling points due to their significant lattice energies. The arrangement of ions in ionic solids is generally a repeating lattice structure, which is crucial for understanding how different factors affect lattice energy.

• Lattice energy is generally higher in ionic solids with small, highly-charged ions.
• The crystal structures can vary, affecting how ions are arranged, but the overarching principle of charge balance and ionic radii still applies.

In ionic solids like

• NaF
• KF

As the cation increases in size from Na to K, lattice energy decreases which is a typical behavior observed in ionic compounds.

Cation Size

The size of the cation plays a significant role in the lattice energy of ionic compounds. Smaller cations can approach anions more closely, resulting in stronger electrostatic attractions and thus higher lattice energy. Consider the series:

• BaSO extsubscript{4} < SrSO extsubscript{4} < CaSO extsubscript{4} < MgSO extsubscript{4}

Here, the cation size is decreasing from barium to magnesium. As the size of the cation decreases, the ions can get closer, which increases the attraction between them and lead to higher lattice energy. This trend is integral to predicting lattice energy and related properties of ionic compounds.

Ion Separation

Ion separation is a critical concept when discussing lattice energy. It refers to the distance between the centers of two ions in a crystal lattice. The closer two ions are, the stronger the force of attraction between them, which increases lattice energy. Separation of ions is determined by both ionic radii and the type of ions involved.

• As the ionic radii increase, such as from LiF to LiI, or from NaF to CsF, ions are further apart, which decreases the lattice energy.
• Smaller ions or ions with higher charges will have less separation, which enhances lattice energy.

To understand lattice energy, examining how ion separation influences electrostatic interactions offers deep insights into the properties of ionic compounds.