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\(]\)

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

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.

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.