Problem 5 - Chemistry An Atoms First Approach

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 \(\mathrm{CCl}_{2} \mathrm{H}_{2}\).

Step-by-Step Solution

Answer

The given molecules can be arranged in the decreasing order of polarity as follows: \(\mathrm{CF}_{2}\mathrm{Cl}_{2} > \mathrm{CF}_{2}\mathrm{H}_{2} > \mathrm{CCl}_{2}\mathrm{H}_{2} > \mathrm{CH}_{4} \approx \mathrm{CCl}_{4}\). This order is based on the molecular geometry, electronegativity difference, and overall dipole moment of each molecule. Molecules with higher electronegativity differences and non-symmetric geometries have higher polarity.

Step 1: Calculate electronegativity difference

For each molecule, we will determine the electronegativity difference between its bonded atoms since this factor influences the dipole moment. The higher the electronegativity difference, the more polar the bond.

Step 2: Analyze molecular geometry

Next, we will examine the geometry of each molecule, which determines the overall dipole moment. Linear or symmetric arrangements tend to cancel out the individual bond dipoles, leading to a nonpolar molecule.

Step 3: Determine the polarity of each molecule

Based on the electronegativity difference and molecular geometry, we can now determine the polarity of each molecule and rank them in descending order. Here's the breakdown for the given molecules: 1. \(\mathrm{CH}_{4}\): Tetrahedral geometry with no electronegativity difference since all the atoms are hydrogen, making this molecule nonpolar. 2. \(\mathrm{CF}_{2}\mathrm{Cl}_{2}\): Tetrahedral geometry with some electronegativity difference due to the presence of fluorine and chlorine atoms, making this molecule polar. 3. \(\mathrm{CF}_{2}\mathrm{H}_{2}\): Tetrahedral geometry with some electronegativity difference due to the presence of fluorine atoms, making this molecule polar. 4. \(\mathrm{CCl}_{4}\): Tetrahedral geometry with electronegativity difference due to the presence of chlorine atoms, but since the molecule is symmetric, the dipoles cancel out, making it nonpolar. 5. \(\mathrm{CCl}_{2}\mathrm{H}_{2}\): Tetrahedral geometry with some electronegativity difference due to the presence of chlorine atoms, making this molecule polar.

Step 4: Arrange the molecules in order of polarity

Now that we have analyzed the polarity of each molecule, we can arrange them in decreasing order of polarity: 1. \(\mathrm{CF}_{2}\mathrm{Cl}_{2}\) (Most polar) 2. \(\mathrm{CF}_{2}\mathrm{H}_{2}\) 3. \(\mathrm{CCl}_{2}\mathrm{H}_{2}\) 4. \(\mathrm{CH}_{4}\) and \(\mathrm{CCl}_{4}\) (Least polar; both have zero dipole moment) So, the final order from most to least polar is: \(\mathrm{CF}_{2}\mathrm{Cl}_{2} > \mathrm{CF}_{2}\mathrm{H}_{2} > \mathrm{CCl}_{2}\mathrm{H}_{2} > \mathrm{CH}_{4} \approx \mathrm{CCl}_{4}\).

Key Concepts

Electronegativity Difference

Electronegativity refers to an atom's ability to attract and hold onto electrons when it forms a chemical bond. In simple terms, some atoms are just greedier when it comes to electrons. Understanding electronegativity is crucial when determining the polarity of a molecule.

Each element has a specific electronegativity value, with fluorine being the most electronegative. The electronegativity difference between bonded atoms can predict the type of bond that will form: nonpolar covalent, polar covalent, or ionic. A large difference typically indicates ionic bonding, while a small difference points to a polar covalent bond, where electrons are unequally shared.

In the exercise provided, CF_2Cl_2 shows the most polarity due to the significant electronegativity differences between carbon, fluorine, and chlorine atoms. In contrast, methane (CH4) is nonpolar because the carbon-hydrogen bond has a relatively small electronegativity difference, causing an even distribution of charge.

Molecular Geometry

The spatial arrangement of atoms in a molecule, termed molecular geometry, is a pivotal aspect of understanding polarity. Molecules with symmetrical geometries, like tetrahedrons or squares, can often cancel out their individual dipoles if respective atoms are of the same electronegativity, leading the molecule to be nonpolar.

However, if a symmetrical molecule has atoms with different electronegativities, such as CF_2Cl_2carbon tetrachloride (CCl4), the polarity depends on the arrangement and types of atoms. CCl4, even though it has polar C-Cl bonds, is nonpolar overall because of its symmetrical tetrahedral geometry that causes the bond dipoles to cancel out. On the flip side, an asymmetrical molecule like chloroform (CHCl3) would be polar, as its geometry doesn't allow for cancelation of the dipole moments, not considered in this exercise.

Such geometric considerations are essential when interpreting the polarity of a molecule and were crucial in analyzing the molecules in the given exercise.

Dipole Moment

Dipole moment is the measure of the separation of charge in a molecule. It is the product of the charge separation and the distance between the charges. A higher dipole moment indicates a molecule where electrons are not shared equally and thus is usually more polar.

A dipole forms in a molecular bond due to the difference in electronegativity of the bonded atoms. The presence or absence of a dipole moment in a molecule is a clear sign of its polarity or nonpolarity. For example, in CF_2H_2, the presence of the highly electronegative fluorine atoms creates individual dipoles. With a tetrahedral geometry, these dipoles do not cancel each other, resulting in a molecule with an overall dipole moment and therefore, a polar molecule.

To reiterate from the exercise, the C-Cl and C-F bonds have sufficient differences in electronegativity causing individual dipole moments. But the overall molecule's polarity is determined by whether these moments cancel out each other due to molecular geometry, as seen with CCl4, or add up to a net dipole moment, as seen with CF_2Cl_2 and CF_2H_2.