Question

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

Short answer

The order of polarity for the given molecules is: \(\mathrm{CF}_{2} \mathrm{H}_{2} > \mathrm{CCl}_{2} \mathrm{H}_{2} > \mathrm{CH}_{4} > \mathrm{CF}_{2} \mathrm{Cl}_{2} > \mathrm{CCl}_{4}\). This order is determined by analyzing the molecular geometry and electronegativity differences of the atoms in each molecule. The polar molecules have asymmetric geometries and larger electronegativity differences, while the nonpolar molecules have symmetrical geometries and smaller or canceled out electronegativity differences.

Step-by-step solution

Determine Molecular Geometry for each molecule

For each molecule, we will use the VSEPR (Valence Shell Electron Pair Repulsion) theory to predict their molecular geometry: \(\mathrm{CH}_{4}\): Tetrahedral \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\): Tetrahedral \(\mathrm{CF}_{2} \mathrm{H}_{2}\): Tetrahedral \(\mathrm{CCl}_{4}\): Tetrahedral \(\mathrm{CCl}_{2} \mathrm{H}_{2}\): Tetrahedral

Analyzing Electronegativity Differences

Now, we will analyze the electronegativity values of the atoms bonded and look for any differences. 1. \(\mathrm{CH}_{4}\) - Carbon (C) to Hydrogen (H) difference: 2.55 - 2.20 = 0.35 2. \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\) - Carbon (C) to Fluorine (F) difference: 3.98 - 2.55 = 1.43 - Carbon (C) to Chlorine (Cl) difference: 3.16 - 2.55 = 0.61 3. \(\mathrm{CF}_{2} \mathrm{H}_{2}\) - Carbon (C) to Fluorine (F) difference: 3.98 - 2.55 = 1.43 - Carbon (C) to Hydrogen (H) difference: 2.55 - 2.20 = 0.35 4. \(\mathrm{CCl}_{4}\) - Carbon (C) to Chlorine (Cl) difference: 3.16 - 2.55 = 0.61 5. \(\mathrm{CCl}_{2} \mathrm{H}_{2}\) - Carbon (C) to Chlorine (Cl) difference: 3.16 - 2.55 = 0.61 - Carbon (C) to Hydrogen (H) difference: 2.55 - 2.20 = 0.35

Determine Polarity of each molecule

Now, let's analyze each molecule individually considering both shape and electronegativity differences: 1. \(\mathrm{CH}_{4}\): Symmetrical sp³ hybrid orbitals; the slight electronegativity difference is canceled out due to the symmetric arrangement - Nonpolar. 2. \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\): Symmetrical sp³ hybrid orbitals; the electronegativity differences are canceled out due to the symmetric arrangement - Nonpolar. 3. \(\mathrm{CF}_{2} \mathrm{H}_{2}\): Asymmetric sp³ hybrid orbitals; higher electronegativity difference between C and F than between C and H - Polar. 4. \(\mathrm{CCl}_{4}\): Symmetrical sp³ hybrid orbitals; the electronegativity differences are canceled out due to the symmetric arrangement - Nonpolar. 5. \(\mathrm{CCl}_{2} \mathrm{H}_{2}\): Asymmetric sp³ hybrid orbitals; higher electronegativity difference between C and Cl than between C and H - Polar.

Arrange molecules from most to least polar

Now that we know each molecule's polarity, we can arrange them from most to least polar: 1. \(\mathrm{CF}_{2} \mathrm{H}_{2}\) - Most polar (asymmetric and highest electronegativity difference) 2. \(\mathrm{CCl}_{2} \mathrm{H}_{2}\) - Next in polarity (asymmetric) 3. \(\mathrm{CH}_{4}\) - Nonpolar (symmetrical, small electronegativity difference) 4. \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\) - Nonpolar (symmetrical) 5. \(\mathrm{CCl}_{4}\) - Least polar (symmetrical) So, the order of polarity is: \(\mathrm{CF}_{2} \mathrm{H}_{2} > \mathrm{CCl}_{2} \mathrm{H}_{2} > \mathrm{CH}_{4} > \mathrm{CF}_{2} \mathrm{Cl}_{2} > \mathrm{CCl}_{4}\).