Problem 26 - Chemistry: The Central Science in SI Units, Global Edition

Question

Which of the following trends in lattice energy is due to differences in ionic radii? (a) \(\mathrm{LiF}>\mathrm{NaF}>\mathrm{CsF},(\mathbf{b}) \mathrm{CaO}>\mathrm{KCl}\) (c) \(\mathrm{PbS}>\mathrm{Li}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

The correct answer is (a): LiF > NaF > CsF, as this trend in lattice energy is predominantly determined by the differences in ionic radii, with smaller radii leading to higher lattice energy.

Step 1: Understanding ionic radii trends

In order to find which trend is based on the differences in ionic radii, it is essential to know the general trends of the ionic radii in the periodic table. Typically, the atomic radii or ionic radii increase as one moves down a group and decrease as one moves from left to right across a period.

Step 2: Analyze option (a)

In option (a), the compounds given are LiF, NaF, and CsF. They are all from Group 1 and have the same charge of +1 for the cations and -1 for the F anions. As Li, Na, and Cs are from the same group, we can see that the ionic radii will increase as we move down the group. However, when the ionic radii increase, the lattice energy will decrease. Therefore, the trend in option (a) is determined by the differences in ionic radii. Due to smaller radii, LiF has the highest lattice energy, followed by NaF and CsF.

Step 3: Analyze option (b)

In option (b), the compounds given are CaO and KCl. Ca and K are from different groups and their corresponding anions (O and Cl) also belong to different groups. So, we cannot confidently determine the trend based solely on the ionic radii.

Step 4: Analyze option (c)

In option (c), the compounds given are PbS and Li2O. Pb and Li belong to different groups, and their corresponding anions (S and O) also belong to different groups. So, similar to option (b), we cannot confidently determine the trend based solely on the ionic radii.

Step 5: Determine the correct answer

Based on the analysis of each option, option (a) is the only trend that is predominantly determined by the differences in ionic radii. So, the correct answer is (a): LiF > NaF > CsF.

Key Concepts

Ionic Radii

Ionic radii describe the size of ions in ionic compounds. As you move down a group in the periodic table, ionic radii increase. This is due to the addition of more electron shells as we go from one element to the next at the bottom. For instance, in Group 1 of the periodic table, lithium (Li), sodium (Na), and cesium (Cs) are all alkali metals that can form positively charged cations. The ionic radius for Li\(^+\) is smaller compared to Na\(^+\) and Cs\(^+\). This difference in size affects the lattice energy of the compounds they form, such as LiF, NaF, and CsF. The smaller the cation, like Li\(^+\), the closer the ions can get to each other, leading to higher lattice energy.

Periodic Table Trends

The periodic table provides an organized view of the elements, showcasing trends that help us predict and understand various chemical properties. Two key trends are the changes in atomic and ionic radii. As you move across a period from left to right, atomic and ionic radii tend to decrease due to an increase in the effective nuclear charge. This means electrons are pulled closer to the nucleus. Conversely, as you move down a group, the atomic and ionic radii increase due to more electron shells being added. These trends help predict properties like reactivity and lattice energy in ionic compounds. Observing these patterns allows chemists to understand how elements will behave chemically, such as how ions might influence the lattice energy of compounds they form.

Ionic Compounds

Ionic compounds are formed through the transfer of electrons between a metal and a non-metal. This interaction results in the formation of positively charged cations and negatively charged anions. A key character of ionic compounds is the lattice structure they form, where these ions are held together by strong ionic bonds. The stability and properties such as melting and boiling points, as well as solubility, can often be attributed to this lattice structure. Lattice energy, an integral part of understanding ionic compounds, is the measure of the strength of these bonds and is influenced by the size and charge of the ions involved. Smaller ions with higher charges generally result in greater lattice energy, which is seen in compounds like LiF having higher lattice energy than NaF and CsF because of the smaller size of Li\(^+\).

Group Trends in Chemistry

Group trends in chemistry refer to the patterns and behaviors of elements within the same column of the periodic table. These trends arise from similar electron configurations and can help us understand how an element will react with others. Typical group trends include the increase in atomic size and ionic radii as you move down a group. For example, the alkali metals (Group 1) show increasing atomic and ionic radii as you move from lithium to cesium. Understanding these trends also explains certain observable properties, such as an increase in reactivity as you go down the group for alkali metals. Additionally, these trends help anticipate how changes in ionic radii can affect the lattice energy in ionic compounds, such as why LiF exhibits higher lattice energy compared to NaF and CsF.