Analysis of a compound indicates that it contains \(77.55 \%\) Xe and \(22.45 \%\) F by mass. (a) What is the empirical formula for this compound? (Assume this is also the molecular formula in responding to the remaining parts of this exercise). (b) Write a Lewis structure for the compound. (c) Predict the shape of the molecules of the compound. (d) What hybridization is consistent with the shape you predicted?

Understanding percent composition is crucial for determining the empirical formula of a compound. It represents the percent by mass of each element within a compound. To find these percentages, the mass of each element in a sample is divided by the total mass of the sample, then multiplied by 100%. In the given exercise, the compound's percent composition is provided, which serves as the basis for calculating the empirical formula. This allows us to relate the mass percentages directly to moles of elements, leading to the ratio of atoms in the compound.

For instance, given percentages for Xe and F can be used to calculate the moles of each element in a hypothetical 100 g sample. This process simplifies the stoichiometric conversion and aids in determining the simplest ratio of atoms, which reflects the compound's empirical formula.

Molar mass is a fundamental concept in chemistry, signifying the mass of one mole of a substance. It is typically expressed in grams per mole (g/mol) and is calculated by summing the atomic masses of each element in a chemical formula. For instance, Xe has a molar mass of 131.29 g/mol, and F has 19.00 g/mol. Knowing these values enables students to convert the mass percentage of elements in a compound to the number of moles, which is essential for empirical formula calculations. As illustrated in the exercise solution, the molar mass is used to determine how many moles of Xe and F are present in a sample, thereby facilitating the next steps in the process.

The Lewis structure is a visual representation of molecules depicting the arrangement of atoms and the distribution of electrons among them. It displays both bonding pairs of electrons, which form chemical bonds between atoms, and lone pairs of electrons that are not involved in bonding. The structure helps in predicting molecular geometry and the type of bonding within a molecule. In the exercise, drawing the Lewis structure begins by arranging the Xe atom as the central atom and distributing F atoms around it, accounting for the octet rule and the capability of Xe to have an expanded octet. A correct Lewis structure is crucial for both predicting molecular shape and determining atomic hybridization.

Molecular shape prediction is a process in which the three-dimensional arrangement of atoms in a molecule is determined. This arrangement is a direct consequence of the repulsions between both bonding pairs of electrons and lone pairs surrounding a central atom. The VSEPR theory assists in predicting the molecular shapes by considering these repulsive forces. Students can then link the number of bonded atoms and lone pairs to typical molecular geometries. For example, a molecule with four bonding pairs and no lone pairs on the central atom, such as CH4, is tetrahedral. In the case of the Xe compound in the exercise, the molecular shape can be deduced similarly once we know the number of bonds and lone pairs.

The VSEPR theory is an important tool in predicting molecular geometry. It states that electron pairs around a central atom will arrange themselves to minimize repulsion, which leads to specific molecular shapes. When applying VSEPR theory, both bonding and non-bonding electron pairs (lone pairs) are considered. The number and arrangement of these pairs of electrons around a central atom allow us to predict the molecular geometry, such as linear, trigonal-planar, tetrahedral, trigonal-bipyramidal, or octahedral. In the textbook problem, once the Lewis structure is determined, VSEPR theory is used to predict that XeF2 has a linear shape because there are three pairs of electrons around the Xe atom, two bonding pairs and one lone pair.

Atomic hybridization is the concept of mixing atomic orbitals to create new hybrid orbitals for bonding. The type of hybridization correlates with the molecule's geometry, which can be inferred from the VSEPR theory. To determine the hybridization state of the central atom, one must count its bonding pairs and lone pairs of electrons. These will correspond to specific hybrid orbitals, such as sp (linear), sp2 (trigonal-planar), sp3 (tetrahedral), sp3d (trigonal-bipyramidal), or sp3d2 (octahedral). In the given exercise, by predicting the shape of the XeF2 molecule using the VSEPR theory, we can conclude that the Xe atom undergoes sp3d hybridization, accommodating its three electron pairs in a linear arrangement.