Question

There are exceptions to the predictions of VSEPR. Consider \(\mathrm{CH}_{3}\), known as a methyl radical. (a) Create a dot diagram for the methyl radical. How is it fundamentally different from other dot diagrams you have done? (b) Use VSEPR to predict the shape of the methyl radical and draw it with that shape (treat the odd electron as a single electron group). (c) The methyl radical is known to be planar with \(120^{\circ} \mathrm{H}-\mathrm{C}-\mathrm{H}\) angles. What steric number is being employed here, and what is the carbon atom doing with respect to the odd electron in determining molecular shape? (d) The \(\mathrm{CF}_{3}\) radical does obey VSEPR. Draw it according to its VSEPR-predicted shape. What steric number is being employed here? (e) The \(\mathrm{C}-\mathrm{H}\) bond is shorter than the \(\mathrm{C}-\mathrm{F}\) bond. When bonds are short, the atoms at the ends of the bonds can bang into each other (this is called steric congestion) unless a geometry is adopted to get around this. Use this knowledge to explain why \(\mathrm{CH}_{3}\) violates VSEPR, but \(C F_{3}\) does not.

Short answer

The methyl radical (CH₃) has an odd electron in its dot diagram, making it fundamentally different from other diagrams. VSEPR predicts a tetrahedral shape, but it actually has a planar geometry with a 120° C–H–C bond angle and a steric number of 3. CH₃ violates VSEPR due to steric congestion and shorter C–H bonds; adopting a planar geometry avoids atom collisions. On the other hand, CF₃ follows VSEPR's tetrahedral prediction due to longer C–F bonds, which reduce steric congestion.

Step-by-step solution

(a) Drawing the Dot Diagram for CH₃

To draw a dot diagram, place the central atom (Carbon) in the middle and surround it with the hydrogen atoms. Since Carbon has 4 valence electrons and each hydrogen atom has 1 valence electron, Carbon shares 1 electron with each H atom and has an unpaired electron (the lone odd electron) creating a total of 4 electron groups. The structure becomes fundamentally different from others as it has an odd electron (unpaired) in its structure, unlike other dot diagrams. The dot diagram for CH₃ is : H | H–C–H •

(b) VSEPR Prediction for CH₃ Shape

Using VSEPR theory to predict the shape of the methyl radical, the odd electron is considered a single electron group. Since the molecule has 4 electron groups (3 H-C bonds and 1 unpaired electron), the VSEPR theory predicts a tetrahedral geometry for the CH₃ radical. This predicted shape should have the angles C-H-C equal to 109.5°.

(c) Planar Geometry and Steric Number

The methyl radical is observed to be planar and have C–H–C angles of 120°, which contrasts with the VSEPR prediction. In this case, the steric number is 3 (as there are 3 electron groups around the central atom), and the carbon atom is using the odd electron to keep all of them in a planar configuration.

(d) VSEPR Predicted Shape for CF₃ and Steric Number

Using VSEPR theory, with the C atom as the central atom, the CF₃ radical has 4 electron groups (3 C–F bonds and 1 unpaired electron). The VSEPR prediction gives a tetrahedral geometry for the CF₃ radical— similar to what was predicted for CH₃—and a steric number of 4.

(e) Explanation of CH₃ Violating VSEPR and CF₃ Obeying VSEPR

The violation of VSEPR in CH₃ can be explained by considering the bond lengths and steric congestion. The C–H bond is shorter than the C–F bond. As a result, the hydrogen atoms in CH₃ are closer to each other, which can lead to steric congestion (atom collisions) if the tetrahedral geometry predicted by VSEPR were followed. By adopting a planar geometry, the CH₃ radical avoids steric congestion, allowing hydrogen atoms to be further apart. In contrast, the CF₃ radical has longer C–F bonds, which reduce the likelihood of steric congestion and allows the molecule to follow VSEPR's tetrahedral geometry prediction.

Key concepts

Methyl Radical Structure

The methyl radical (CH₃) is a chemical species characterized by having an unpaired electron. This odd electron sets the methyl radical apart from molecules with all paired electrons. In the structure of CH₃, the carbon atom is at the center, with three hydrogen atoms covalently bonded to it. The presence of this unpaired electron can influence the molecular geometry of the radical in a way that deviates from standard predictions.

In traditional dot diagrams, electrons around a central atom are typically paired, but in the case of the methyl radical, the single unpaired electron gives rise to a dot diagram with an electron count that does not adhere to the octet rule. This is the fundamental difference when comparing the methyl radical's dot diagram to those of fully paired electron systems.

Steric Number

The steric number is a crucial concept that helps us understand molecular shape. It refers to the total number of bonds and lone electron pairs (or odd electrons) surrounding a central atom. To determine the steric number, one simply counts the single, double, triple bonds, and lone electron groups (paired or unpaired) around the central atom. For example, in the methyl radical, there are three hydrogen atoms bonded to carbon and one unpaired electron, leading to a steric number of 4.

However, the steric number doesn't always dictate the molecular geometry perfectly. While a steric number of 4 would typically predict a tetrahedral shape according to VSEPR theory, the methyl radical is known to adopt a planar molecular geometry. This indicates that practical steric considerations can override simple steric number predictions, leading to exceptions in VSEPR theory.

Planar Molecular Geometry

Molecular geometry is fundamentally the three-dimensional arrangement of atoms in a molecule. Planar molecular geometry, as seen in the methyl radical, implies that all atoms in the molecule lie in a single plane. This planar structure of CH₃ is indicated by the observed 120° bond angles between the hydrogen atoms. Despite a steric number that would usually predict a tetrahedral shape, the methyl radical adopts a trigonal planar arrangement.

Such planar geometries are often associated with a steric number of 3, which includes three bonding pairs or electron groups around the central atom with no lone pairs. It's fascinating to note that in some cases, like that of the methyl radical, the planar structure can be favored due to certain dynamics in the molecule, such as the need to minimize steric congestion.

Steric Congestion

Steric congestion refers to the crowding of atoms within a molecule resulting from electron repulsions among bonds that are too close together. This concept is paramount in understanding why molecules adopt specific shapes and why there may be exceptions to VSEPR theory predictions.

In the case of the methyl radical, adopting a tetrahedral geometry would result in greater steric congestion because of the shorter C–H bond lengths, making it more energetically unfavorable. Therefore, the molecule takes on a planar geometry to minimize these repulsions, allowing for more space between the hydrogen atoms, despite the initial steric number suggesting a tetrahedral shape. In contrast, species like the CF₃ radical do not experience this level of congestion due to longer bond lengths, hence adhering to the geometry predicted by the VSEPR theory.