Question

Consider \(\mathrm{CH}_{3}^{+}\) and \(\mathrm{C} \mathrm{H}_{3}^{-}\). Using these as examples, explain why it is necessary to draw a correct Lewis dot diagram before trying to predict the shape of a molecule. Use the concept of steric number in your explanation.

Short answer

Drawing the correct Lewis dot diagrams is crucial for predicting the shape of a molecule, as it allows us to understand the distribution of electrons in the molecule, including the number of bonded atoms and any lone pairs of electrons. This information is used to calculate the steric number, which is key in determining the molecular geometry. In the case of \(\mathrm{CH}_{3}^{+}\) and \(\mathrm{CH}_{3}^{-}\), their Lewis dot diagrams and steric numbers are different, leading to different molecular geometries (trigonal planar for \(\mathrm{CH}_{3}^{+}\) and tetrahedral for \(\mathrm{CH}_{3}^{-}\)). This highlights the importance of correctly drawing the Lewis dot diagrams and using the concept of steric number to predict the shape of molecules.

Step-by-step solution

Draw the Lewis dot structures for \(\mathrm{CH}_{3}^{+}\) and \(\mathrm{CH}_{3}^{-}\)

For \(\mathrm{CH}_{3}^{+}\), carbon has 4 valence electrons, but due to the positive charge, it has only 3. Hydrogen has 1 valence electron each. Therefore, carbon can form bonds with three hydrogen atoms, leaving no lone pair electrons: \[ \mathrm{H} \] \[ |/ \] \[ \mathrm{C}^{+} \] \[ | \] \[ \mathrm{H} \] For \(\mathrm{CH}_{3}^{-}\), carbon has 4 valence electrons, and due to the negative charge, it has a total of 5 valence electrons. Hydrogen has 1 valence electron each. Carbon forms bonds with three hydrogen atoms and has one lone pair electron: \[ \mathrm{H} \] \[ |/ \] \[ \mathrm{C}^{-} :\] \[ | \] \[ \mathrm{H} \]

Calculate the steric numbers for both molecules

The steric number is calculated as the sum of the number of bonded atoms and lone pairs of electrons: Steric Number = Number of bonded atoms + Number of lone pairs For \(\mathrm{CH}_{3}^{+}\): Steric Number = 3 (number of bonded hydrogen atoms) + 0 (no lone pairs) = 3 For \(\mathrm{CH}_{3}^{-}\): Steric Number = 3 (number of bonded hydrogen atoms) + 1 (one lone pair of electrons) = 4

Determine the molecular geometry based on steric numbers

Using the steric numbers calculated in the previous step, we can now predict the molecular geometries: For \(\mathrm{CH}_{3}^{+}\), the steric number is 3, which corresponds to a trigonal planar geometry. For \(\mathrm{CH}_{3}^{-}\), the steric number is 4, which corresponds to a tetrahedral geometry.

Explain the significance of Lewis dot diagrams and steric numbers in predicting molecular shapes

Drawing the correct Lewis dot diagrams is crucial for predicting the shape of a molecule, as it allows us to understand the distribution of electrons in the molecule, including the number of bonded atoms and any lone pairs of electrons. This information is used to calculate the steric number, which is key in determining the molecular geometry. In the case of \(\mathrm{CH}_{3}^{+}\) and \(\mathrm{CH}_{3}^{-}\), we can see that even though they both have similar chemical formulas, their Lewis dot diagrams and steric numbers are different, leading to different molecular geometries. This highlights the importance of correctly drawing the Lewis dot diagrams and using the concept of steric number to predict the shape of molecules.

Key concepts

Lewis Dot Structures

Lewis Dot Structures represent a visualization of the valence electrons in a molecule, depicted as dots around the chemical symbols of the elements. These structures are a fundamental starting point for understanding the chemical bonding and arrangement of atoms within a compound. For instance, when drawing the Lewis Dot Structure for a molecule such as \( \mathrm{CH}_{3}^{+} \), we must consider the number of valence electrons for the carbon atom, which typically has four. However, due to the positive charge, one electron is missing, leaving it with only three valence electrons to share. This interaction with the hydrogen atoms, which each contribute one valence electron, will dictate the bonding pattern.

In contrast, \( \mathrm{CH}_{3}^{-} \) has an extra electron due to the negative charge, thus carbon has five valence electrons to work with. Creating the correct Lewis Dot Structure is crucial for the next stages of predicting molecular shape and understanding reactivity and bonding characteristics.

Molecular Geometry Prediction

Predicting the molecular geometry of a compound is essential for deducing its properties and behavior. The three-dimensional arrangement is determined primarily by the steric number, which reflects the regions of electron density around a central atom. We calculate the steric number by adding together the number of atoms bonded to the central atom and the number of lone pairs of electrons. For example, in \( \mathrm{CH}_{3}^{+} \), with a steric number of 3, we predict a trigonal planar geometry, which impacts properties such as the angles between bonds and the molecule's reactivity.

Similarly, \( \mathrm{CH}_{3}^{-} \) with a steric number of 4, reveals a tetrahedral to the observer, changing the perspective on potential interactions with other molecules. It is the precise Lewis Dot Structure that allows us to calculate the steric number, thus linking the two core concepts together.

Valence Electrons

Valence electrons are the electrons in the outermost shell of an atom, and they play a pivotal role in chemical bonding. An atom's chemical behavior is largely determined by these electrons as they participate in the formation of chemical bonds. In the case of carbon, its four valence electrons facilitate the formation of strong covalent bonds. When a molecule like \( \mathrm{CH}_{3}^{+} \) is formed, it’s the absence of one of these valence electrons that gives rise to the molecule's positive charge, while the presence of an additional electron in \( \mathrm{CH}_{3}^{-} \) results in a negative charge. Counting valence electrons is the first step in drawing Lewis Dot Structures and ultimately in predicting molecular geometry. This count guides us in determining how atoms in a molecule will share electrons to achieve a full octet, or eight electrons, to emulate the electron configuration of the nearest noble gas.

Chemical Bonding

Chemical bonding is the force that holds atoms together in molecules. These bonds arise from the attraction between the positively charged nuclei of atoms and the negatively charged electrons shared or transferred between them. The type and number of bonds that form depend on the elements involved and their valence electrons. In molecules such as \( \mathrm{CH}_{3}^{+} \) and \( \mathrm{CH}_{3}^{-} \) the carbon atom forms covalent bonds with hydrogen atoms by sharing its valence electrons with the hydrogen’s own valence electron. The nature of the charge on the carbon atom affects the number of bonds it can form and indicates the presence or absence of lone pairs of electrons, which further influence the molecular geometry. Understanding chemical bonding is integral to appreciating how molecules come together and react, forming the diverse range of substances we encounter.