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\(]\)

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 ```

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.

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.

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).