Question

(a) Explain why the following ions have different bond angles: \(\mathrm{ClO}_{2}^{-}\) and \(\mathrm{NO}_{2}^{-}\). Predict the bond angle in each case. (b) Explain why the \(\mathrm{XeF}_{2}\) molecule is linear and not bent.

Short answer

The bond angles in ClO2- and NO2- ions differ due to the repulsion of lone electron pairs around the central atom. ClO2- has a smaller bond angle of around 109.5° because its central Cl atom has two lone pairs, while NO2- has a larger bond angle of approximately 120° as there is only one lone pair on its central N atom. XeF2 is a linear molecule because it has a trigonal bipyramidal electronic geometry with 3 lone pairs and 2 bonding pairs, resulting in no influence from bonding electron pairs on its bond angle.

Step-by-step solution

Electronic geometry and Molecular geometry

To explain the difference in bond angles between ions ClO2- and NO2-, we must first determine their electronic geometry and molecular geometry. Electronic geometry is the distribution of all electrons (bonding and non-bonding) in the structure, while molecular geometry is the distribution of only the bonding pairs.

Step 1a: Analyzing \(\mathrm{ClO}_{2}^{-}\) ion

Let's start with the electronic configuration of ClO2-. 1. Cl: Group 7A, 7 valence electrons 2. O: Group 6A, 6 valence electrons 3. Plus 1 extra electron for the negative charge Total valence electrons: \(7 (Cl) + 2*6 (O) + 1 = 20\) Now, let's draw the Lewis structure. Using the 20 valence electrons, we can come up with the following Lewis structure: Cl - O - O * Cl has 3 lone pairs and 1 bonding pair (1 single bond with O). * Each O atom has 2 lone pairs and 1 bonding pair (1 single bond with Cl or the other O). The electronic geometry of ClO2- is trigonal planar, as it has 3 electron groups (1 single bond with O and 2 lone pairs) around the central Cl atom. Since both oxygen atoms are bonded to the chloride atom, the molecular geometry would be bent or V-shaped.

Step 1b: Analyzing \(\mathrm{NO}_{2}^{-}\) ion

Now let's analyze the electronic configuration of NO2-. 1. N: Group 5A, 5 valence electrons 2. O: Group 6A, 6 valence electrons 3. Plus 1 extra electron for the negative charge Total valence electrons: \(5 (N) + 2*6 (O) + 1= 18\) Now, let's draw their Lewis structure using the 18 valence electrons: O - N - O * N has 1 lone pair and 2 bonding pairs (1 single bond with each O). * Each O atom has 2 lone pairs and 1 bonding pair (1 single bond with N). The electronic geometry of the NO2- ion is trigonal planar, with 3 electron groups (1 lone pair and 2 single bonds with O) around the central N atom. Since both oxygen atoms are bonded to the nitrogen atom, the molecular geometry would be bent or V-shaped.

Explanation and prediction of bond angles

Now that we know the electronic and molecular geometries of both ions, we can explain the difference in their bond angles. In ClO2-, there are 3 electron groups around Cl (1 bonding pair and 2 lone pairs), and in NO2-, there are 3 electron groups around N (2 bonding pairs and 1 lone pair). The electron repulsion between lone pairs in both ions influences the bond angles. In the case of ClO2-, there are two lone pairs, which creates greater repulsion, and for NO2-, there's only one. This causes a larger bond angle (approximately 120°) in NO2- and a smaller bond angle (around 109.5°) in ClO2-.

Electronic geometry and molecular geometry of \(\mathrm{XeF}_{2}\)

Let's determine the electronic geometry and molecular geometry of XeF2. 1. Xe: Group 8A, 8 valence electrons 2. F: Group 7A, 7 valence electrons Total valence electrons: \(8 (Xe) + 2*7 (F) = 22\) Now, let's draw their Lewis structure using the 22 valence electrons: Xe - F - F * Xe has 3 lone pairs and 2 bonding pairs (1 single bond with each F). * Each F atom has 3 lone pairs and 1 bonding pair (1 single bond with Xe). The electronic geometry of XeF2 is trigonal bipyramidal, with 5 electron groups (3 lone pairs and 2 single bonds with F) around the central Xe atom. The molecular geometry would be linear since the two fluorine atoms are bonded to the xenon atom with no repulsion from bonding electron pairs. #Conclusion# ClO2- has a smaller bond angle (around 109.5°) due to the presence of two lone pairs on the central Cl atom, while NO2- has a larger bond angle (approximately 120°) because there's only one lone pair on the central N atom. On the other hand, XeF2 is linear because it has a trigonal bipyramidal electronic geometry with 3 lone pairs and 2 bonding pairs, resulting in no influence from bonding electron pairs on the bond angle.

Key concepts

Bond Angles

Bond angles are all about the spatial arrangement of atoms in molecules and polyatomic ions. They are formed wherever two bonds radiate from a single atom, and the measure of this angle tells us a lot about the molecule's shape and reactivity.

Let's consider the task at hand. In molecules like \(\mathrm{ClO}_{2}^{-}\) and \(\mathrm{NO}_{2}^{-}\), bond angles differ due to the presence of lone pairs of electrons, which occupy more space than bonding pairs due to their greater repulsion. According to the Valence Shell Electron Pair Repulsion (VSEPR) theory, electron pairs around a central atom spread out to maximize the distance between them, which in turn dictates the bond angles. This is why \(\mathrm{NO}_{2}^{-}\), with one lone electron pair, has a larger bond angle than \(\mathrm{ClO}_{2}^{-}\), which has two lone pairs pushing the bonded atoms closer together.

In the case of \(\mathrm{ClO}_{2}^{-}\), the two lone pairs force the atoms into a position that results in a bond angle of roughly 109.5°, deviating from the ideal trigonal planar angle of 120° because of that extra repulsion. Conversely, for \(\mathrm{NO}_{2}^{-}\), there is less electron repulsion, so its bond angle is closer to the trigonal planar ideal, hovering around 120°.

Lewis Structures

To predict molecular shape, polarity, reactivity, and more, chemistry students must first master drawing Lewis structures. These diagrams represent the valence electrons of atoms within a molecule, illustrating how the atoms are bonded together and whether they possess any non-bonding electron pairs or 'lone pairs'.

If we apply this to the \(\mathrm{XeF}_{2}\) molecule, we start by counting valence electrons: xenon has 8 and each fluorine has 7, totaling 22. When we draw it out, we place xenon in the middle with two fluorine atoms on opposite sides and follow by allocating lone pairs to fulfill the octet rule.

The resulting structure is a bit curious because xenon has three lone pairs and two single bonds, and you might expect these electrons to repel each other into a bent shape. However, the lone pairs are positioned in such a way that leaves the molecule linear. This is unusual but explainable by the VSEPR theory, which tells us that the best arrangement to minimize repulsion here leads to a straight line, confirming the linear structure.

Electron Group Repulsion

Diving deeper into the concept of electron group repulsion, which is the driving force behind the shapes of molecules and ions, we find that it's central to VSEPR theory. This principle states that electron pairs (bonding or non-bonding) around a central atom will arrange themselves as far away from each other as possible to minimize repulsion.

This is a critical factor in determining both the electronic and molecular geometry of the molecule or ion in question. In \(\mathrm{XeF}_{2}\), despite having five electron groups, the arrangement that minimizes repulsion leaves us with a linear shape. This is because the lone pairs of electrons are placed at the equatorial positions in a trigonal bipyramidal electron geometry which effectively 'cancels out' their repulsive effects, rendering the molecule linear.

Understanding electron group repulsion not only helps us predict the geometric shape of molecules but also their reactivity and interactions, both crucial for crafting complex chemical reactions and in the study of materials and medicines.