Arrange the following molecules from most to least polar and explain your order: $\mathrm{CH}_{4}, \mathrm{CF}_{2} \mathrm{C} \mathrm{l}_{2}, \mathrm{CF}_{2} \mathrm{H}_{2}, \mathrm{CCl}_{4},\( and \)\mathrm{CCl}_{2} \mathrm{H}_{2}$.

The first step to determine the polarity of the given molecules is to find the electronegativity differences between bonded atoms. We will be comparing Carbon (C), Hydrogen (H), and Chlorine (Cl) in these molecules. Electronegativity values: C: 2.5 H: 2.1 F: 3.98 Cl: 3.16 Now, compute the electronegativity differences for the bonded atoms in each molecule: \(\mathrm{CH}_{4}: \Delta_\mathrm{C-H} = |2.5 - 2.1| = 0.4\) \(\mathrm{CF}_{2} \mathrm{C} \mathrm{l}_{2}: \Delta_\mathrm{C-F} = |2.5 - 3.98| = 1.48, \Delta_\mathrm{C-Cl} = |2.5 - 3.16| = 0.66\) \(\mathrm{CF}_{2} \mathrm{H}_{2}: \Delta_\mathrm{C-F} = 1.48, \Delta_\mathrm{C-H} = 0.4\) \(\mathrm{CCl}_{4}: \Delta_\mathrm{C-Cl} = 0.66\) \(\mathrm{CCl}_{2} \mathrm{H}_{2}: \Delta_\mathrm{C-Cl} = 0.66, \Delta_\mathrm{C-H} = 0.4\)

The next step is to identify the molecular geometry of each molecule. This is important because even if there are bonds with electronegativity differences, the molecule may still be nonpolar if the molecular geometry is symmetric, and the dipoles cancel out. \(\mathrm{CH}_{4}\): Tetrahedral \(\mathrm{CF}_{2} \mathrm{C} \mathrm{l}_{2}:\) Tetrahedral \(\mathrm{CF}_{2} \mathrm{H}_{2}:\) Tetrahedral \(\mathrm{CCl}_{4}:\) Tetrahedral \(\mathrm{CCl}_{2} \mathrm{H}_{2}:\) Tetrahedral

Now we'll use the molecular geometry and electronegativity differences to determine the polarity of each molecule. \(\mathrm{CH}_{4}\): Nonpolar, since the molecular geometry is symmetric and dipoles cancel out. \(\mathrm{CF}_{2} \mathrm{C} \mathrm{l}_{2}:\) Polar, the molecule has asymmetric distribution of dipoles. \(\mathrm{CF}_{2} \mathrm{H}_{2}:\) Polar, the molecule has asymmetric distribution of dipoles. \(\mathrm{CCl}_{4}:\) Nonpolar, since the molecular geometry is symmetric and dipoles cancel out. \(\mathrm{CCl}_{2} \mathrm{H}_{2}:\) Polar, the molecule has asymmetric distribution of dipoles.

Now we can arrange the molecules from most to least polar based on the polarity determined in the previous step. The most polar molecule should have the greatest electronegativity difference and asymmetry due to the unequal sharing of electrons and resulting in a net nonzero dipole moment. 1. \(\mathrm{CF}_{2} \mathrm{C} \mathrm{l}_{2}\): Polar (greatest electronegativity difference) 2. \(\mathrm{CF}_{2} \mathrm{H}_{2}\): Polar (larger electronegativity difference than \(\mathrm{CCl}_{2} \mathrm{H}_{2}\)) 3. \(\mathrm{CCl}_{2} \mathrm{H}_{2}:\) Polar (asymmetric distribution of dipoles) 4. \(\mathrm{CH}_{4}\): Nonpolar (symmetric geometry) 5. \(\mathrm{CCl}_{4}\): Nonpolar (symmetric geometry) So, the order of molecules from most to least polar is \(\mathrm{CF}_{2} \mathrm{C} \mathrm{l}_{2} \gt \mathrm{CF}_{2} \mathrm{H}_{2} \gt \mathrm{CCl}_{2} \mathrm{H}_{2} \gt \mathrm{CH}_{4} \gt \mathrm{CCl}_{4}\).