Problem 4 - Chemistry: The Central Science in SI Units, Global Edition

Question

The molecule shown here is difluoromethane (CH_2F2), which is used as a refrigerant called R-32. (a) Based on the structure, how many electron domains surround the \(\mathrm{C}\) 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 earbon atom toward a hydrogen atom? [Sections 9.2 and 9.3\(]\)

Step-by-Step Solution

Answer

The difluoromethane (CH2F2) molecule has 4 electron domains surrounding its carbon atom. It also has a nonzero dipole moment, making it a polar molecule. The overall dipole moment vector points from the carbon atom to a point midway between the fluorine atoms (option ii).

Step 1: Determine the number of electron domains surrounding the carbon (C) atom

The number of electron domains surrounding an atom is the total number of lone pairs and bonded atoms. In the difluoromethane (CH2F2) molecule, the carbon atom is bonded to two hydrogen atoms and two fluorine atoms. Since carbon has no lone pairs, the electron domains surrounding the carbon atom are those formed by the two hydrogen and two fluorine atoms. Number of electron domains = Number of bonded atoms = 2 hydrogen atoms + 2 fluorine atoms = 4 electron domains

Step 2: Determine if the molecule has a nonzero dipole moment

To determine if the molecule has a nonzero dipole moment, we need to consider the individual bond dipoles and their orientation in the molecular structure. The bond between carbon and fluorine (C-F) is polar, as fluorine is highly electronegative. Hence, there will be a bond dipole moment vector pointing from the carbon atom to each fluorine atom. On the other hand, the bond between carbon and hydrogen (C-H) is less polar, but still has a small bond dipole moment vector pointing from the carbon atom to each hydrogen atom. Due to CH2F2's tetrahedral shape, the molecule is asymmetric, so the dipoles don't cancel each other out, resulting in a nonzero net dipole moment. Hence, the molecule has a nonzero dipole moment and is polar.

Step 3: Determine the overall dipole moment vector direction

Since CH2F2 is polar, we now need to describe the overall dipole moment vector direction. Given the options in the exercise: (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 (iv) from the carbon atom toward a hydrogen atom The bond dipoles of the C-F bonds are larger than the bond dipoles of the C-H bonds. Therefore, the overall dipole moment vector is influenced more by the C-F bond dipoles and points in the direction closest to the fluorine atoms. Since there are two fluorine atoms, the overall dipole moment vector will point from the carbon atom to a point midway between the fluorine atoms. Thus, the correct option is (ii) from the carbon atom to a point midway between the fluorine atoms.

Key Concepts

Electron Domains

Electron domains are crucial for understanding the 3D arrangement of atoms in a molecule. For any given atom, electron domains include all regions where electrons are likely found, including both bonds and lone electron pairs. In difluoromethane ( CH_2F_2 ), the carbon atom has four electron domains. Each electron domain is created by a single bond to one of the other atoms in the structure:

• Two are formed by bonds with hydrogen atoms.
• Two are from bonds with fluorine atoms.

Because carbon has no lone pairs here, it has a total of 4 electron domains, making it important for its geometric structure. Understanding electron domains helps in predicting the molecular shape, which is tetrahedral in this case.

Tetrahedral Molecular Geometry

Tetrahedral molecular geometry is a common shape adopted by molecules where a central atom is surrounded by four electron domains. These domains arrange themselves to minimize repulsion, achieving maximum distance between them. In difluoromethane, carbon adopts a tetrahedral molecular geometry due to its four bonded atoms, which are two hydrogen atoms and two fluorine atoms. This means:

• The bond angles between any two adjacent bonds are approximately 109.5°.
• Each bond points towards the vertices of an imaginary tetrahedron.

Tetrahedral geometry affects how diffusing electric fields interact with the molecule, which can influence its polarity. In turn, this impacts whether molecules like CH_2F_2 exhibit behaviors like creating dipole moments.

Dipole Moment

A dipole moment occurs when there is a separation of electrical charge across a molecule, leading to a molecular "pull" in one direction. This property becomes crucial when discussing molecular polarity. In difluoromethane, the polarity largely results from its tetrahedral arrangement and the electronegativity of the fluorine atoms:

• Fluorine is much more electronegative than hydrogen, leading to polar covalent bonds with carbon.
• The dipole moments of the C-F bonds are more significant than those of the C-H bonds.
• The molecule is not symmetric in its dipole distribution due to varied electronegativity at different ends.

CH_2F_2 is polar since the combined dipole vectors from the C-F bonds lead to a nonzero net dipole moment. The dipole moment vector points toward a blend of directions influenced heavily by the positions of the fluorine atoms, specifically from the carbon atom towards a point midway between them. Understanding how molecular shape and electronegativity contribute to dipole moments can help predict a molecule's behavior, especially in electromagnetic contexts and solvents.