Question

Given that the electronegativities of \(\mathrm{H}, \mathrm{Cl}, \mathrm{Br}\), and 1 are, respectively, \(4.0,3.0,2.8\), and \(2.5\), account for the fact that the dipole moment decreases in the sequence \(\mathrm{HF}, \mathrm{HCl}, \mathrm{HBr}\), and HI, even though bond length and the number of electrons increase.

Short answer

In the sequence of hydrogen halides (HF, HCl, HBr, and HI), the dipole moment decreases because the electronegativity difference between the atoms decreases, resulting in a decrease in polarity. Although bond length and the number of electrons increase in the sequence, those factors are not enough to compensate for the decrease in electronegativity difference, causing the dipole moment to decrease.

Step-by-step solution

Understand the concept of dipole moment

Dipole moment is a vector quantity that represents the separation of charge in a molecule. It is affected by three main factors: 1. Electronegativity difference between the atoms in the bond. 2. Bond length (distance between atoms in the bond). 3. The number of electrons involved in the bond. The dipole moment of a molecule can be calculated using the formula: Dipole Moment µ = Bond Length d × Charge Q

Analyze the effect of electronegativity difference on dipole moment

Electronegativity is the ability of an atom to attract the shared pair of electrons in a covalent bond. When two atoms have a significant difference in electronegativity, the more electronegative atom attracts the electron pair towards itself, creating a polar bond. In the given sequences of hydrogen halides (HF, HCl, HBr, and HI), the electronegativities are as follows: H: 4.0, F: 4.0, Cl: 3.0, Br: 2.8, and I: 2.5 Comparing the electronegativities, we can see that the difference in electronegativity decreases in the sequence HF, HCl, HBr, and HI. This results in a decrease in the polarity of the bond.

Evaluate the effect of bond length and the number of electrons on dipole moment

As bond length increases, the distance between the atoms gets longer, and the charge separation of the molecule becomes larger. However, in the case of hydrogen halides, the bond length and the number of electrons increase in the sequence HF, HCl, HBr, and HI. But as we have discussed earlier, the electronegativity difference between atoms decreases in the sequence. This means the polarity of the bonds is decreasing even though bond length and number of electrons increase.

Bringing together the factors affecting the dipole moment

To explain the decrease in the dipole moment for the sequence HF, HCl, HBr, and HI, we need to consider the combination of factors we discussed earlier. 1. The electronegativity difference is decreasing in the sequence, which reduces the polarity of the bond and hence, the dipole moment. 2. The bond length and the number of electrons are increasing, but they are not enough to compensate for the decrease in the electronegativity difference. Thus, even though bond length and the number of electrons increase in the given sequence, the decrease in electronegativity difference has a greater influence on the dipole moment, causing it to decrease in the sequence HF, HCl, HBr, and HI.

Key concepts

Electronegativity

Electronegativity refers to the ability of an atom in a molecule to attract shared electrons towards itself. It is a key factor in determining chemical polarity. Atoms with higher electronegativities are more efficient at pulling electron pairs closer. This causes an unequal sharing of electrons in covalent bonds.

In the context of hydrogen halides, the difference in electronegativity between hydrogen and the halogen atoms plays a crucial role in the overall dipole moment. For instance, in molecules like HF, HCl, HBr, and HI:

• Fluorine, with an electronegativity of 4.0, strongly attracts electrons, creating a high polarity and thus, a significant dipole moment.
• As we progress through the sequence to HI, the electronegativity of the halogens decreases (Cl: 3.0, Br: 2.8, I: 2.5), leading to a reduction in bond polarity and a consequent decrease in dipole moment.

The decreasing electronegativity difference is a primary cause of the declining dipole moments observed among these molecules.

Bond Length

Bond length is the distance between the nuclei of two bonded atoms. It is one of the components in the equation used to calculate the dipole moment. Intuitively, a longer bond could lead to a greater dipole moment due to increased charge separation.

However, in hydrogen halides, as bond length increases from HF to HI:

• The bond between hydrogen and fluorine is the shortest, while the bond between hydrogen and iodine is the longest.
• Despite this increase in bond length, the decrease in electronegativity across the series dominates the trend, reducing the dipole moment.

In summary, while longer bonds can enhance dipole moments, in hydrogen halides, it is not enough to overcome the diminishing electronegativity differences.

Hydrogen Halides

Hydrogen halides (HF, HCl, HBr, and HI) are molecules consisting of hydrogen bonded to a halogen. These compounds are excellent examples to illustrate concepts like electronegativity and dipole moment.

• They vary in electronegativity, bond length, and dipole moment, making them rich for comparison.
• Each molecule exhibits unique characteristics based on the respective halogen's properties.

Studying hydrogen halides helps in understanding how these physical properties interplay to affect molecular behavior. For instance, as you move from HF to HI, you observe a clear shift—decreased electronegativity leads to decreased molecular polarity and dipole moments.

Chemical Polarity

Chemical polarity refers to the distribution of electrical charge around atoms, molecules, or chemical groups. It significantly influences molecular dipole moments. Polar molecules have regions of positive and negative charge due to differences in electronegativity among its atoms.

In hydrogen halides, you witness varying degrees of chemical polarity. With fluorine being the most electronegative, HF is highly polar, resulting in the highest dipole moment among the series. Conversely:

• HCl, HBr, and HI exhibit progressively smaller differences in electronegativity, reducing polarity.
• Decreased polarity corresponds to decreasing dipole moments as seen from HF to HI.

Thus, the trend in the hydrogen halides sequence is a perfect demonstration of how molecular composition affects polarity and dipole moment.