Question

Two different compounds have the formula \(\mathrm{XeF}_{2} \mathrm{Cl}_{2} .\) Write Lewis structures for these two compounds, and describe how measurement of dipole moments might be used to distinguish between them.

Short answer

The two different compounds with the formula XeF2Cl2 have the following Lewis structures: 1. First isomer: ``` F Cl \ / Xe / \ F Cl ``` 2. Second isomer: ``` Cl F \ / Xe / \ Cl F ``` Both structures have distorted tetrahedral geometry. The first isomer has a smaller net dipole moment due to the partial cancellation of the Xe-F bond dipoles, while the second isomer has a larger net dipole moment. By measuring the dipole moments, we can distinguish between these two compounds: the compound with a smaller dipole moment would be the first isomer and the one with a larger dipole moment would be the second isomer.

Step-by-step solution

Determine the valence electrons

In order to draw the Lewis structure for each compound, we first need to determine the valence electrons. For Xenon (Xe), there are 8 valence electrons; for Fluorine (F), there are 7 valence electrons; and for Chlorine (Cl), there are also 7 valence electrons.

Draw the first possible Lewis structure

The Lewis structure of the first isomer can be obtained as follows: 1. Place Xe in the center as it is the least electronegative. 2. Place the four atoms F, F, Cl, Cl around Xe with the least electronegative atoms (Fluorine) either opposite or adjacent to each other. 3. Link each atom to the central atom (Xe) using single bonds, using two valence electrons (one from Xe and one from each of the F and Cl atoms). 4. Fill the remaining valence electrons around each atom to satisfy the octet rule. The first possible Lewis structure is: ``` F Cl \ / Xe / \ F Cl ```

Draw the second possible Lewis structure

The Lewis structure of the second isomer can be obtained by switching the positions of fluorine and chlorine atoms: ``` Cl F \ / Xe / \ Cl F ```

Determine the molecular geometry and polarity

In both Lewis structures, the central atom (Xe) has a tetrahedral arrangement with four single bonds (the Xe-F and Xe-Cl bond pairs). In both structures, the molecular geometry is distorted tetrahedral. The bond dipoles of Xe-F and Xe-Cl are not equal due to the different electronegativities of F and Cl. In the first structure, XeF2Cl2, the two Xe-F bond dipoles partially cancel the effect of each other as they are opposite to each other, but the overall molecule still has a net dipole moment due to the remaining Xe-Cl bond dipoles. In the second structure, XeF2Cl2, all bond dipoles contribute to the molecular dipole, resulting in a molecule with a larger net dipole moment.

Compare dipole moments to distinguish the compounds

From step 4, we know that the molecular dipole moments of the two isomers are different. A measurement of their dipole moments would reveal this difference and allow us to distinguish between the two compounds. A compound with a larger dipole moment would be identified as the second isomer, while the one with the smaller dipole moment would be the first isomer.

Key concepts

Valence Electrons

Valence electrons play a crucial role in the formation of Lewis structures as they participate in chemical bonding. Each atom in a molecule contributes its valence electrons to form bonds with other atoms.

• Xenon (Xe) has 8 valence electrons.
• Fluorine (F) and Chlorine (Cl) each have 7 valence electrons.

These electrons are represented as "dots" around the element's symbol, indicating areas where bonds can form. Knowing the number of valence electrons helps ensure that each atom achieves a stable electron configuration, often following the octet rule whereby atoms seek to have eight electrons in their valence shell.

Molecular Geometry

Understanding molecular geometry is essential for predicting how molecules will interact with light and with each other. In the case of \(\mathrm{XeF}_{2}\mathrm{Cl}_{2}\), the central atom Xe is surrounded in a tetrahedral arrangement, albeit distorted. This means four atoms surround Xe at the corners of a tetrahedron.

• The angles between the bonding pairs cause the structure to slightly deviate from the perfect tetrahedral shape.
• In both isomers, Xe is bonded to two fluorine and two chlorine atoms.

The rearrangement of these atoms in space affects not only the shape but also the physical properties like polarity, making molecular geometry a key concept in understanding molecular behavior.

Dipole Moments

Dipole moments occur due to differences in electronegativity between atoms, resulting in unequal sharing of electrons.

• Fluorine, being more electronegative than chlorine, attracts electrons more strongly.
• This causes a "pull" on the electrons in the Xe-F bonds compared to the Xe-Cl bonds.

In the case of the two isomers of \(\mathrm{XeF}_{2}\mathrm{Cl}_{2}\), the arragnement of these bonds leads to different dipole moments. An isomer where opposing dipoles cancel out results in a lower net dipole moment. In contrast, an isomer with bond dipoles aligned in one general direction results in a higher net dipole moment. Measuring these dipole moments allows chemists to distinguish between isomers based on their polarity.

Isomers

Isomers are compounds with the same molecular formula, but different arrangements of atoms. In \(\mathrm{XeF}_{2}\mathrm{Cl}_{2}\), two possible isomers exist based on how the F and Cl atoms are positioned around Xe.

• The first isomer has fluorine atoms across from each other, and chlorine atoms opposite to each other.
• The second isomer swaps one fluorine with one chlorine, leading to different dipole interactions.

These different spatial arrangements result in unique properties, particularly affecting the molecular dipole moments. Each isomer will exhibit distinct physical behaviors, which can be critical for specific chemical applications. Identifying isomers requires careful analysis of their molecular geometry and their interaction with other molecules or electromagnetic fields.