Problem 76 - Chemistry The Central Science

Question

(a) Why does xenon react with fluorine, whereas neon does not? (b) Using appropriate reference sources, look up the bond lengths of \(\mathrm{Xe}-\mathrm{F}\) bonds in several molecules. How do these numbers compare to the bond lengths calculated from the atomic radii of the elements?

Step-by-Step Solution

Answer

(a) Xenon reacts with fluorine due to its larger atomic size, which allows it to accommodate additional electrons and form stable compounds like XeF2, XeF4, and XeF6. In contrast, neon's full electron shell is firmly held by the nucleus, preventing it from reacting with fluorine. (b) Experimental bond lengths for Xe-F in several molecules, such as XeF2 (\(1.94~\mathrm{Å}\)), XeF4 (\(1.92~\mathrm{Å}\)), and XeF6 (\(1.98~\mathrm{Å}\)), are close to the theoretical bond length calculated from the atomic radii of the elements (\(1.95~\mathrm{Å}\)), indicating that the approximation using atomic radii is reasonably accurate in predicting the bond lengths of these xenon fluoride compounds.

Step 1: Discuss reactivity of xenon and neon

To begin, let's first discuss the reactivity of xenon (Xe) and neon (Ne) with fluorine (F). Both Xe and Ne are noble gases, known for their lack of reactivity due to their full outer electron shell. However, Xe is an exception to this general trend in noble gases because it has a larger atomic size which allows it to accommodate additional electrons and form stable compounds. Xe forms various compounds with fluorine, such as XeF2, XeF4, and XeF6. In contrast, neon's full electron shell is firmly held by the nucleus and doesn't provide sufficient energy to accommodate additional electrons, which means it remains unreactive with fluorine.

Step 2: Research Xe-F bond lengths in molecules

Using appropriate reference sources, look up Xe-F bond lengths in several xenon fluoride compounds. Some examples are: 1. XeF2: \(1.94~\mathrm{Å}\) (Angstrom) 2. XeF4: \(1.92~\mathrm{Å}\) 3. XeF6: \(1.98~\mathrm{Å}\) These bond lengths may vary slightly depending on the source, but they should be in similar ranges.

Step 3: Calculate bond lengths from atomic radii

Next, we will calculate the theoretical bond lengths for Xe-F bonds using atomic radii of Xe and F. The atomic radii for Xe and F are approximately: - Xe: \(1.31~\mathrm{Å}\) - F: \(0.64~\mathrm{Å}\) To calculate the bond length, add the atomic radii of the two atoms involved in the bond: Theoretical Xe-F bond length = Atomic radius of Xe + Atomic radius of F = \(1.31~\mathrm{Å} + 0.64~\mathrm{Å} = 1.95~\mathrm{Å}\)

Step 4: Compare experimental values to theoretical bond lengths

Now, let's compare the bond lengths found in Step 2 to the theoretical bond length calculated in Step 3. 1. XeF2: Experimental \(1.94~\mathrm{Å}\), Theoretical \(1.95~\mathrm{Å}\) 2. XeF4: Experimental \(1.92~\mathrm{Å}\), Theoretical \(1.95~\mathrm{Å}\) 3. XeF6: Experimental \(1.98~\mathrm{Å}\), Theoretical \(1.95~\mathrm{Å}\) As observed, the experimental bond lengths for Xe-F bonds in different molecules are close to the theoretical bond length calculated from the atomic radii of the elements. This indicates that the approximation using atomic radii is reasonably accurate in predicting the bond lengths of these xenon fluoride compounds.

Key Concepts

Noble Gases

Noble gases are a unique group in the periodic table, including helium, neon, argon, krypton, xenon, and radon. These elements are known for their stability and lack of reactivity. This is because they have complete valence electron shells, which makes it energetically unfavorable for them to lose or gain electrons. However, certain noble gases, like xenon, can participate in chemical reactions under specific conditions.

Xenon, with its larger atomic size, can be induced to react, especially with the highly electronegative element fluorine. This is due to the ability of xenon to accommodate additional electrons, forming stable compounds such as XeF2, XeF4, and XeF6. On the other hand, lighter noble gases like neon have a more strongly held valence shell, making them essentially inert under normal conditions.

Fluorine Compounds

Fluorine is the most electronegative element on the periodic table, which makes it highly reactive. When paired with xenon, it forms several interesting fluorine compounds. These compounds, such as

• XeF2 (xenon difluoride),
• XeF4 (xenon tetrafluoride),
• and XeF6 (xenon hexafluoride),

show fascinating chemical properties due to their unique structure and bond formation.

Fluorine's high reactivity is the driving force that allows the formation of these compounds, even with a seemingly non-reactive element like xenon. The compounds exhibit different geometries and bond angles, influenced by the number of fluorine atoms involved and the resulting electron pair repulsions.

Bond Lengths

Bond lengths are a fundamental aspect of understanding molecular structure. They are the average distance between the nuclei of two bonded atoms. For xenon-fluorine compounds, bond lengths help us visualize the spatial arrangement of atoms in the molecule.

Experimental measurements of Xe-F bond lengths have shown values such as:

• XeF2: approximately 1.94 Å,
• XeF4: around 1.92 Å,
• XeF6: about 1.98 Å.

These small differences in bond lengths can be attributed to changes in bond angles and molecular geometry as more fluorine atoms are added. Comparing these values to those predicted by atomic radii calculations helps chemists understand the limitations and accuracy of theoretical models.

Atomic Radii

The atomic radius is a measure of the size of an atom, typically the distance from the nucleus to the outer boundary of the electron cloud. It varies across the periodic table due to atomic number and electronic configuration. In noble gases, atomic radii increase down the group.

When predicting bond lengths like those of xenon-fluorine, chemists use the atomic radii of xenon (approximately 1.31 Å) and fluorine (around 0.64 Å). By adding these radii, the expected Xe-F bond length is approximately 1.95 Å.

Such calculations provide a critical baseline for expectations concerning molecular dimensions. Variations between calculated and experimental bond lengths can arise from effects like electronegativity and bond angle variations driven by molecular geometry.