Question

The HF bond length is \(92 \mathrm{pm}, 16 \%\) shorter than the sum of the covalent radii of \(\mathrm{H}(37 \mathrm{pm})\) and \(\mathrm{F}(72 \mathrm{pm})\). Suggest a reason for this difference. Similar data show that the difference becomes smaller down the group, from HF to HI. Explain.

Short answer

The HF bond length is shorter due to fluorine's high electronegativity, forming a stronger bond. The difference decreases down the group because of decreasing electronegativity.

Step-by-step solution

Determine the sum of the covalent radii

Add the covalent radii of hydrogen (\text{H}) and fluorine (\text{F}). \[ \text{Covalent radius of H} = 37 \text{ pm} \]\[ \text{Covalent radius of F} = 72 \text{ pm} \]\[ \text{Sum of covalent radii} = 37 \text{ pm} + 72 \text{ pm} = 109 \text{ pm} \]

Calculate 16% of the sum of the covalent radii

Find 16% of the sum calculated in the previous step. \[ 0.16 \times 109 \text{ pm} = 17.44 \text{ pm} \]

Subtract to find the HF bond length

Subtract 16% of the sum from the sum to find the bond length of HF. \[ 109 \text{ pm} - 17.44 \text{ pm} = 91.56 \text{ pm} \] This is approximately 92 pm, which is the given bond length.

Reason for the bond length difference

The HF bond length is shorter because of the high electronegativity of fluorine. The strong attraction between the hydrogen and fluorine atoms leads to a shorter bond length.

Explain trend down the group

As we go down the group from HF to HI, the electronegativity of the halogens decreases. This weaker attraction results in a smaller difference between the bond length and the sum of covalent radii.

Key concepts

covalent radius

The covalent radius is a measure of the size of an atom within a molecule. Specifically, it is half the distance between two atoms that are bonded together.
Atoms bond to form molecules by sharing electrons, and the covalent radius gives us a way to understand how large an atom is when it is part of such a molecule.
For instance, in the case of hydrogen fluoride (HF), the covalent radius of hydrogen is 37 picometers (pm) and that of fluorine is 72 pm. By adding these values, we can estimate the bond length to be 109 pm. However, the actual HF bond length is shorter, at 92 pm.
The difference suggests that other factors, such as electronegativity, play a role.

electronegativity

Electronegativity is a measure of how strongly an atom attracts the electrons in a bond.
Fluorine is the most electronegative element, which means it has a very strong pull on the electrons in a bond.
Because fluorine strongly attracts electrons, the shared electron pair in the HF molecule is pulled closer to the fluorine atom. This causes the bond to be shorter than the sum of the covalent radii of hydrogen and fluorine.
High electronegativity leads to stronger bonds and shorter bond lengths.
This principle explains why the HF bond length is 92 pm, rather than the 109 pm expected from adding the covalent radii.

group trends in halogens

In the periodic table, elements are arranged in groups (columns) and periods (rows), with each group sharing similar chemical properties.
The halogens are found in Group 17, and they include fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and astatine (At).
One key trend down the group is a decrease in electronegativity. Fluorine, at the top of the group, is the most electronegative, while iodine, further down, has a lower electronegativity.
As we move from HF to HI, the bond length increases. This increase is because the atoms get larger (which can be seen from their increased covalent radii).
Additionally, the decrease in electronegativity means that the bond attraction is weaker, causing less shortening of the bond length.
Hence, HF has a bond length that is much shorter compared to HI, as the electronegativity of fluorine results in a stronger pull on the bonding electrons.