Question

We can define average bond enthalpies and bond lengths for ionic bonds, just like we have for covalent bonds. Which ionic bond is predicted to have the smaller bond enthalpy, \(\mathrm{Li}-\mathrm{F}\) or \(\mathrm{Cs}-\mathrm{F}\) ?

Short answer

The \(\mathrm{Cs}-\mathrm{F}\) bond is predicted to have a smaller bond enthalpy than the \(\mathrm{Li}-\mathrm{F}\) bond, as the bond length of \(\mathrm{Cs}-\mathrm{F}\) is larger due to the increase in ionic radius of \(\mathrm{Cs}^+\) compared to \(\mathrm{Li}^+\), and bond enthalpy decreases with increasing bond length.

Step-by-step solution

Understand the relationship between bond length and bond enthalpy

In general, as the bond length increases, the bond enthalpy decreases. This is because the atoms are farther apart, and the interaction between the ions is weaker, leading to a lower amount of energy needed to break the bond. Keeping this relationship in mind, we can compare the bond lengths of \(\mathrm{Li}-\mathrm{F}\) and \(\mathrm{Cs}-\mathrm{F}\) to determine which bond has a lower bond enthalpy.

Examine the factors that determine bond lengths in ionic compounds

The bond length in ionic compounds is determined by the sum of the ionic radii of the two ions involved in the bond. The ionic radii of cations and anions decrease across a period and increase down a group in the periodic table. Since lithium (Li) and cesium (Cs) are both in Group 1, and fluorine (F) is in Group 17, we can use these trends to predict which bond will have a smaller bond enthalpy.

Compare the ionic radii of \(\mathrm{Li}^+\) and \(\mathrm{Cs}^+\)

Li and Cs are both Group 1 elements, with Cs being below Li in the periodic table. As we move down a group, the ionic radii increase due to the addition of electron shells. Therefore, the ionic radius of \(\mathrm{Cs}^+\) is larger than the ionic radius of \(\mathrm{Li}^+\).

Compare the bond lengths of \(\mathrm{Li}-\mathrm{F}\) and \(\mathrm{Cs}-\mathrm{F}\)

Since the ionic radius of \(\mathrm{Cs}^+\) is larger than the ionic radius of \(\mathrm{Li}^+\), and both compounds have a \(\mathrm{F}^-\) anion with the same ionic radius, the bond length of \(\mathrm{Cs}-\mathrm{F}\) will be larger than the bond length of \(\mathrm{Li}-\mathrm{F}\).

Determine which bond has a smaller bond enthalpy

Recall that as the bond length increases, the bond enthalpy decreases. Since the bond length of \(\mathrm{Cs}-\mathrm{F}\) is greater than the bond length of \(\mathrm{Li}-\mathrm{F}\), the bond enthalpy of \(\mathrm{Cs}-\mathrm{F}\) is predicted to be smaller than that of \(\mathrm{Li}-\mathrm{F}\).

Conclusion

Based on the relationship between bond lengths and bond enthalpies, as well as the trends in ionic radii in the periodic table, the ionic bond with a smaller bond enthalpy is the \(\mathrm{Cs}-\mathrm{F}\) bond.

Key concepts

Ionic Bonds

Ionic bonds are a type of chemical bond formed between two ions with opposite charges. These bonds arise when an electron from the outer shell of an atom, typically a metal, is transferred to another atom, commonly a non-metal. This electron exchange results in the formation of two ions: a positively charged cation and a negatively charged anion. The electrostatic force of attraction between these oppositely charged ions holds the ions together. This force is what constitutes an ionic bond.

The strength of an ionic bond, known as bond enthalpy, is influenced by several factors, such as the charge of the ions and the distance between the ion centers. A strong ionic bond typically involves ions with high charges and short distances between their centers. Thus, understanding the nature of ionic bonds helps explain interactions at a molecular level.

Bond Length

Bond length is the distance between the nuclei of two bonded atoms. In ionic compounds, this distance is determined by the sum of the ionic radii of the bonded ions. The bond length significantly affects the bond's characteristics, such as bond strength or enthalpy.

• As bond length increases, the bond enthalpy generally decreases.
• Shorter bonds are stronger and require more energy to break.
• Factors like ionic size and charges influence bond length.

Understanding bond length is crucial for predicting the behavior and stability of ionic compounds. By examining bond length, particularly in ionic bonds like \(\mathrm{Li}-\mathrm{F}\) and \(\mathrm{Cs}-\mathrm{F}\), chemists can predict which bonds are stronger or weaker.

Ionic Radii

Ionic radii refer to the effective distance from the nucleus to the outermost electron of an ion. This measure is crucial in determining the physical and chemical properties of ionic compounds. As ions combine to form compounds, their radii influence both bond length and enthalpy.

Ionic radii are not fixed and can vary depending on several factors:

• Size of the electron cloud.
• Position in the periodic table.
• Charge of the ion.

For example, the ionic radius of \(\mathrm{Cs}^+\) is larger than that of \(\mathrm{Li}^+\) due to its position lower down in Group 1 of the periodic table. Larger ionic radii often lead to longer bond lengths and thus, lower bond enthalpies, which is important in understanding their reactivity and formation potential.

Periodic Table Trends

The periodic table is structured in a way that illustrates clear trends in elemental properties, which are crucial for predicting ionic behaviors. One such trend is the change in ionic radii:

• Ionic radii often decrease across a period from left to right.
• Ionic radii increase going down a group.

Another important trend involves electronegativity, which affects how strongly atoms attract bonding electrons. In the context of ionic bonds, these trends can predict bond strengths and lengths. For instance, moving down Group 1, elements like lithium and cesium exhibit increasing ionic radii. This trend helps predict that \(\mathrm{Cs}-\mathrm{F}\), with a larger ionic radius than \(\mathrm{Li}-\mathrm{F}\), will have a longer bond length and correspondingly a smaller bond enthalpy, highlighting the consistency of periodic trends in chemical properties.