Problem 4 - Chemistry The Central Science

Question

The molecule shown here is diffuoromethane \(\left(\mathrm{CH}_{2} \mathrm{F}_{2}\right),\) which is used as a refrigerant called \(\mathrm{R}-32\) . (a) Based on the structure, how many electron domains surround the C atom in this molecule? (b) Would the molecule have a nonzero dipole moment? (c) If the molecule is polar, which of the following describes the direction of the overall dipole moment vector in the molecule: (i) from the carbon atom toward a fluorine atom, (ii) from the carbon atom to a point midway between the fluorine atoms, (iii) from the carbon atom to a point midway between the hydrogen atoms, or (iv) from the carbon atom toward a hydrogen atom? [Sections 9.2 and 9.3\(]\)

Step-by-Step Solution

Answer

(a) In difluoromethane (CH2F2), the C atom is surrounded by 4 electron domains. (b) The molecule has a nonzero dipole moment, indicating it is polar. (c) The overall dipole moment vector points from the carbon atom to a point midway between the fluorine atoms (direction ii).

Step 1: Draw the Lewis structure of the molecule

Start by drawing the Lewis structure of the given molecule, difluoromethane (CH2F2). Place the carbon atom in the center and the two hydrogen and two fluorine atoms around it. Connect the carbon atom with each of the surrounding atoms using single bonds. The Lewis structure is as follows: ``` F | H - C - H | F ```

Step 2: Identify the hybridization and geometry of the carbon atom

To find the hybridization of the carbon atom in the molecule, count the number of electron domains around the carbon atom. In this molecule, the carbon atom has 4 electron domains: two bonded hydrogen atoms and two bonded fluorine atoms. As there are four electron domains, the hybridization of the carbon atom is sp3, which results in tetrahedral geometry.

Step 3: Calculate the dipole moment of the molecule

To determine if the molecule has a nonzero dipole moment (meaning it's polar), we need to evaluate the net dipole moment considering the individual dipole moments of each bond. The carbon-fluorine bond is polar because fluorine is more electronegative than carbon, thus pulling electron density towards itself. The carbon-hydrogen bond is also polar, but to a lesser extent compared to the C-F bond because of the smaller electronegativity difference between carbon and hydrogen. However, in tetrahedral geometry, the bond angle between the two fluoride atoms is 109.5 degrees. Due to this, the individual dipole moments of the two C-F bonds don't cancel each other out, and neither do the two C-H bonds. Therefore, the molecule has a nonzero dipole moment.

Step 4: Determine the overall dipole moment vector direction

As the molecule is polar with a nonzero dipole moment, we need to find the direction of the overall dipole moment vector. Since fluorine is more electronegative than hydrogen, the overall dipole moment vector will be towards the more electronegative atoms, fluorine. To be more specific, the overall dipole moment vector will be pointing from the carbon atom to a point midway between the fluorine atoms. This corresponds to direction (ii) in the question. #Final answer# (a) The C atom in difluoromethane (CH2F2) is surrounded by 4 electron domains. (b) The molecule has a nonzero dipole moment, indicating it is polar. (c) The overall dipole moment vector points from the carbon atom to a point midway between the fluorine atoms (direction ii).

Key Concepts

Lewis Structure

The Lewis structure is a visual representation of a molecule that shows how electrons are arranged around each atom. For difluoromethane (CH extsubscript{2}F extsubscript{2}), we begin by placing the carbon atom in the center of the structure because it is the least electronegative element capable of forming multiple bonds. Surround the carbon atom with two hydrogen (H) atoms and two fluorine (F) atoms.

• Carbon (C) forms four single covalent bonds, pairing with two hydrogens and two fluorines.
• Each hydrogen atom forms one single bond with carbon, and each fluorine forms one single bond with carbon.
• Carbon, having four valence electrons, shares one electron each with hydrogen and fluorine atoms to satisfy the octet rule.

Effectively, the structure shows a central carbon atom with single bonds extending to two hydrogen atoms and two fluorine atoms. The visual aspect of the Lewis structure aids understanding molecular geometry and polarity.

Molecular Geometry

Molecular geometry describes the three-dimensional arrangement of atoms in a molecule. In the case of difluoromethane, we need to consider the tetrahedral arrangement dictated by carbon's hybridization:

• The carbon atom has sp extsuperscript{3} hybridization because it utilizes four orbitals for bonding.
• These orbitals create a tetrahedral geometry, meaning the bond angles are approximately 109.5 degrees.
• This geometry positions the two hydrogen atoms and two fluorine atoms at the vertices of a tetrahedron with the carbon at the center.

The tetrahedral shape is key to understanding the molecule's overall dipole moment, as it influences how bond dipoles interact with one another. Thus, understanding molecular geometry is crucial for predicting the behavior of molecules, such as their polarity and reactivity.

Dipole Moment

The dipole moment is a measure of the overall polarity of a molecule, resulting from differences in electronegativity between bonded atoms. In difluoromethane:

• The C-F bond has a significant dipole moment due to the high electronegativity of fluorine compared to carbon.
• While the C-H bonds also have some polarity, they are less polar than C-F bonds because of the smaller difference in electronegativity.
• The distribution of these dipoles impacts the molecule's polarity, as the dipoles don't completely cancel due to their geometric arrangement.

Since the molecule has an asymmetric shape with strong C-F bonds, it possesses a nonzero net dipole moment, making it a polar molecule. The understanding of dipole moments helps in predicting both physical properties and reactions that the molecule may undergo.

Electron Domains

Electron domains are regions where electrons are likely to be found in a molecule and influence both the shape and hybridization of the central atom. For difluoromethane:

• The molecular diagram shows the carbon atom surrounded by four electron domains: two from C-H bonds and two from C-F bonds.
• Each bond pair counts as one electron domain, so the carbon atom in CH extsubscript{2}F extsubscript{2} has four electron domains surrounding it.
• This arrangement aligns with a tetrahedral electron domain geometry, directing the sp extsuperscript{3} hybridization.

Understanding electron domains helps in envisaging the spatial arrangement of atoms and the resulting molecular geometry. This concept is important in predicting molecular shapes, bond angles, and hybridization patterns in more complex molecules.