Question

The molecule shown here is difluaromethane \(\left(\mathrm{CH}_{2} \mathrm{~F}_{2}\right)\) which is used as a refrigerant called 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, in what direction will the overall dipole moment vector point in the molecule? [Sections \(9.2\) and 9.3]

Short answer

(a) The carbon atom in difluoromethane (\(\mathrm{CH}_{2}\mathrm{F}_{2}\)) has 4 electron domains, as it forms bonds with 2 hydrogen atoms and 2 fluorine atoms. (b) The molecule has a nonzero dipole moment, making it a polar molecule due to the difference in electronegativities between carbon-hydrogen and carbon-fluorine bonds. (c) The overall dipole moment vector points towards the fluorine atoms in the molecule.

Step-by-step solution

Draw the Lewis structure of \(\mathrm{CH}_{2}\mathrm{F}_{2}\)

To draw the Lewis structure of \(\mathrm{CH}_{2}\mathrm{F}_{2}\), start by counting the total valence electrons that the molecule has: - Carbon (C) has 4 valence electrons. - Each hydrogen (H) has 1 valence electron, so two hydrogens will have 2 valence electrons. - Each fluorine (F) has 7 valence electrons, so two fluorines will have 14 valence electrons. Together, this molecule has 4 + 2 + 14 = 20 valence electrons. The carbon atom will be the central atom, and the hydrogen and fluorine atoms will surround it. Now, distribute the electrons around the atoms in such a way that the octet rule is satisfied. The final structure would look like this: H-C-F | F In this structure, carbon forms single bonds with both hydrogen atoms and a single bond with each fluorine atom.

Calculate the electron domains surrounding the carbon atom

Next, determine the electron domains around the carbon atom in the \(\mathrm{CH}_{2}\mathrm{F}_{2}\) molecule. An electron domain includes bonding electrons and non-bonding (lone pair) electrons. In the case of \(\mathrm{CH}_{2}\mathrm{F}_{2}\), we can see that the carbon atom is bonded to 2 hydrogen atoms and 2 fluorine atoms, with no lone pairs. Therefore, there are a total of 4 electron domains surrounding the carbon atom.

Determine the molecular geometry and dipole moment

Now that we know the electron domain geometry around the carbon atom, we can determine the molecular shape and dipole moment. Since there are 4 electron domains and no lone pairs on carbon, the molecule has a tetrahedral geometry. However, the molecule has two different atoms (hydrogen and fluorine) attached to carbon. Due to the difference in electronegativities between carbon and these two atoms, the bonds between carbon-hydrogen (C-H) and carbon-fluorine (C-F) have distinct polarities. Thus, the molecule has a nonzero dipole moment, making it a polar molecule.

Determine the direction of the dipole moment vector

The overall dipole moment vector of the \(\mathrm{CH}_{2}\mathrm{F}_{2}\) molecule will be the vector sum of each bond's individual dipole moment. The dipole moments of carbon-fluorine bonds will be stronger than the carbon-hydrogen bonds due to a higher difference in electronegativity. Therefore, these vectors will dominate the direction of the overall dipole moment. The overall dipole moment vector would point towards the fluorine atoms. In conclusion: (a) The carbon atom in the \(\mathrm{CH}_{2}\mathrm{F}_{2}\) molecule is surrounded by 4 electron domains. (b) The molecule has a nonzero dipole moment, making it a polar molecule. (c) The overall dipole moment vector will point towards the fluorine atoms in the molecule.

Key concepts

Dipole Moment

A dipole moment arises in a molecule when there is an unequal distribution of electron density. Think of it as a tug-of-war game between atoms. In this game, more electronegative atoms, like fluorine in our example, tend to "pull" electrons towards themselves. This results in the creation of a partially negative charge at the fluorine atom and a partially positive charge at the other connected atoms, in this case, carbon.

The \(\mathrm{CH}_{2}\mathrm{F}_{2}\) molecule has polar bonds due to the difference in electronegativity between the carbon-fluorine (C-F) and carbon-hydrogen (C-H) bonds. The carbon-fluorine bonds are particularly polar because fluorine, being highly electronegative, strongly attracts the shared electrons. When different atoms like hydrogen and fluorine surround the carbon atom, the symmetries cancel out if they're equal, but since fluorine attracts more strongly than hydrogen, this creates a net dipole moment.

For the overall dipole moment in this molecule, it's as if all the small dipole vectors from individual bonds add up. Here, the direction of this vector points towards the more electronegative fluorine atoms. Hence, \(\mathrm{CH}_{2}\mathrm{F}_{2}\) becomes a polar molecule, with a non-zero dipole moment.

Electron Domains

Understanding electron domains is crucial to predicting a molecule's shape. In simple terms, an electron domain can be thought of as any region where electrons are likely to be found, including in bonds or lone pairs around a central atom. These domains can help us lay out the structure of the molecule.

In the difluoromethane molecule \(\mathrm{CH}_{2}\mathrm{F}_{2}\), carbon is the central atom which forms bonds with two hydrogen atoms and two fluorine atoms. Although there are no lone pairs around the carbon, each bond counts as an electron domain. Thus, carbon in this structure has a total of four electron domains.

• Bond between carbon and hydrogen: 1 electron domain each
• Bond between carbon and fluorine: 1 electron domain each

These four electron domains organize themselves geometrically to minimize repulsion between them, resulting in the classic tetrahedral shape. This arrangement is vital, as it directly influences the molecular geometry and properties like polarity.

Lewis Structure

The Lewis structure is essentially the blueprint of a molecule. It's a visual representation that shows the arrangement of atoms, bonds, and lone pairs of electrons. Using Lewis structures enables us to understand the electron distribution within a molecule, fulfilling the octet rule wherever possible for stability.

For \(\mathrm{CH}_{2}\mathrm{F}_{2}\), start by summing up the valence electrons of each atom. Carbon contributes 4, each hydrogen contributes 1, and each fluorine brings 7, making a total count of 20 valence electrons. The carbon atom will sit at the center, given that it can make the most bonds. Hydrogen atoms, being less electronegative, typically surround carbon.

• Carbon and both hydrogens form single bonds
• Carbon and both fluorines form single bonds

This configuration helps carbon achieve an octet and flourishes the molecule with a stable form. In the diagram, each line represents a pair of shared electrons forming a covalent bond. Through this structure, one can visually count up to four bonding domains around carbon, confirming the four-electron domain prediction for the tetrahedral geometry.