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Chapter 12: Problem 71

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) \(\mathrm{NaF}<\mathrm{KF}<\mathrm{RbF}<\mathrm{CsF}\)

Short Answer

Expert verified
The correct order for increasing lattice energy is (a).

Step by step solution

01

Understand Lattice Energy

Lattice energy is the amount of energy released when ions in the gas phase form an ionic lattice. It depends primarily on two factors: the charge on the ions and the size of the ions. Greater charge increases lattice energy, and smaller ionic radius increases lattice energy due to the closer proximity of ions.
02

Analyze Option (a)

For arrangement (a), compare the ionic radii of the Group 2 ions in the sulfates: Ba2+, Sr2+, Ca2+, Mg2+. As we go from BaSO4 to MgSO4, the cation size decreases, increasing lattice energy. Thus, this order shows increasing lattice energy.
03

Analyze Option (b)

In arrangement (b), we deal with Group 2 carbonates: MgCO3, CaCO3, SrCO3, BaCO3. Here, as cation size increases down the group, lattice energy should decrease. This sequence is incorrect for increasing lattice energy.
04

Analyze Option (c)

Arrange by halide size: LiF, LiCl, LiBr, LiI. As we move from fluoride to iodide, halide ions increase in size, and lattice energy decreases due to the increased distance between ions. This order is incorrect for increasing lattice energy.
05

Analyze Option (d)

In arrangement (d), the ionic compound order is: NaF, KF, RbF, CsF. As the alkali metal ion size increases, lattice energy decreases due to increased ionic distance. This ordering reflects decreasing lattice energy, thus incorrect for increasing energy.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Ionic Radius
The ionic radius is a measure of the size of an ion in a crystal lattice. It is important to know because it affects the interactions between ions. In a crystal lattice, ions are close together and their sizes determine how tightly they can pack. Smaller ions can get closer to each other, which increases the attraction between them. This means that a smaller ionic radius generally results in higher lattice energy. When considering lattice energy, we often focus on the cations in the ionic compounds. As you move down a group in the periodic table, the ionic radius of cations increases. This is due to the addition of electron shells, which increases the distance between the nucleus and the outermost electrons. The larger the ion, the lower the attraction between the ions, resulting in lower lattice energy. Therefore, knowing the ionic radius is crucial in determining the lattice energy of ionic compounds.
Characteristics of Group 2 Cations
Group 2 cations, also known as alkaline earth metals, include ions like barium (\(\mathrm{Ba^{2+}}\)), strontium (\(\mathrm{Sr^{2+}}\)), calcium (\(\mathrm{Ca^{2+}}\)), and magnesium (\(\mathrm{Mg^{2+}}\)). These cations play a significant role in determining the lattice energy of their compounds. As we move down the group from magnesium to barium, the ionic radii of these cations increase.
  • Magnesium has the smallest radius and often the highest lattice energy when paired with the same anion.
  • Barium, being the largest, tends to have the lowest lattice energy.
This trend is due to the increasing number of electronic shells that make the ions larger with added electrons and shielding effects. These factors decrease the effective nuclear charge experienced by the outermost electrons, making it easier for the ion size to grow. This influences the positioning and strength of attraction in ionic lattices, directly impacting the lattice energy.
Formation and Importance of an Ionic Lattice
An ionic lattice is a repeating three-dimensional arrangement of ions. It forms when positive and negative ions attract each other to minimize their energy. The lattice structure helps maximize attraction and minimize repulsion among ions, leading to a stable compound with significant lattice energy release. The strength of an ionic lattice largely depends on:
  • The charge of the ions: Higher charge results in stronger electrostatic forces and higher lattice energy.
  • The size of the ions: Smaller ions can come closer to each other, increasing lattice energy due to tighter packing.
In these lattices, all ions touch their neighbors, forming a dense and strong structure. This systematically aligns the ions into a pattern based on size and charge, optimizing the attractive forces throughout the lattice. Understanding this concept is crucial for predicting the properties of ionic compounds, such as solubility, hardness, and melting points.
Properties and Behavior of Ionic Compounds
Ionic compounds consist of positive and negative ions held together by electrostatic forces in an ionic lattice. This configuration gives them distinct properties like high melting points, electrical conductivity in molten form, and brittleness. Key properties of ionic compounds include:
  • High melting and boiling points due to the strong ionic bonds in the lattice.
  • Conductivity when dissolved in water or melted, as the ions are free to move and carry an electric current.
  • Typically appearing as crystalline solids, owing to the orderly arrangement of ions.
  • Brittleness, since any shift in the lattice pushes like-charged ions closer, causing repulsion and breakage.
The formation, stability, and characteristics of ionic compounds are directly influenced by lattice energy. Thus, a solid understanding of lattice energy and its determinants, such as ionic radius and group trends, provides insight into the behavior and applications of various ionic compounds.

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Most popular questions from this chapter

Which of the following statements is true about effective nuclear charge? (a) \(\mathrm{Z}_{\text {eff }}\) decreases from top to bottom (b) \(\mathrm{Z}_{\text {eff }}\) increases from top to bottom (c) \(Z_{\text {eff }}\) increases as we move from left to right in periodic table (d) \(Z_{e f f}=Z \times \sigma\) (here \(\sigma\) is screening constant)

Ionic radius (in A) of \(\mathrm{As}^{3+}, \mathrm{Sb}^{3+}\) and \(\mathrm{Bi}^{3+}\) follow the order (a) \(\mathrm{As}^{3+}>\mathrm{Sb}^{3+}>\mathrm{Bi}^{3+}\) (b) \(\mathrm{Sb}^{3+}>\mathrm{Bi}^{3+}>\mathrm{As}^{3+}\) (c) \(\mathrm{Bi}^{3+}>\mathrm{As}^{3+}>\mathrm{Sb}^{3+}\) (d) \(\mathrm{Bi}^{3+}>\mathrm{Sh}^{3+}>\mathrm{As}^{3+}\)

Which one of the following groupings represents a collection of isoelectronic species? (At. number of Cs \(=55, \mathrm{Br}=35\) ) (a) \(\mathrm{Na}^{+}, \mathrm{Ca}^{2+}, \mathrm{Mg}^{2+}\) (b) \(\mathrm{N}^{3-}, \mathrm{F}^{-}, \mathrm{Na}^{+}\) (c) \(\mathrm{Be}, \mathrm{Al}^{3+}, \mathrm{F}^{-}\) (d) \(\mathrm{Ca}^{2+}, \mathrm{Cs}^{+}, \mathrm{Br}\)

Properties that are directly or indirectly related to the electronic configuration of the elements and show a regular gradation when we move from left to right in a period or form top to bottom in a group are called periodic properties. Some of these properties are ionization energy, electron affinity and electronegativity Which of the following is arranged in the order of decreasing electropositive character ? (a) \(\mathrm{Fe}, \mathrm{Mg}, \mathrm{Cu}\) (b) \(\mathrm{Mg}, \mathrm{Cu}, \mathrm{Fe}\) (c) \(\mathrm{Mg}, \mathrm{Fe}, \mathrm{Cu}\) (d) \(\mathrm{Cu}, \mathrm{Fe}, \mathrm{Mg}\)

The outermost configuration of the most electronegative elements is (a) \(\mathrm{ns}^{2} \mathrm{np}^{3}\) (b) \(\mathrm{ns}^{2} \mathrm{np}^{6}\) (c) \(\mathrm{ns}^{2} \mathrm{np}^{4}\) (d) \(\mathrm{ns}^{2} \mathrm{np}^{3}\)
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