Question

Which of the following is less? (a) the sum of the \(\mathrm{H}\) and \(\mathrm{Br}\) atomic radii, or the bond length in \(\mathrm{H}-\mathrm{Br}\) (b) the sum of the \(S\) and \(O\) atomic radii, or the bond length in \(S=O\)

Short answer

(a) Bond length; (b) Bond length.

Step-by-step solution

Identify Given Data

We need to determine the values of the atomic radii and the bond lengths. The atomic radius of hydrogen (H) is approximately 53 pm (picometers), and bromine (Br) is approximately 94 pm. The H-Br bond length is approximately 141 pm. The atomic radius of sulfur (S) is 88 pm, and oxygen (O) is 66 pm. The S=O bond length is approximately 142 pm.

Compare Atomic Radii and Bond Length for H and Br

For part (a), calculate the sum of the atomic radii of H and Br, which is 53 pm + 94 pm = 147 pm. Compare this to the H-Br bond length of 141 pm.

Compare Atomic Radii and Bond Length for S and O

For part (b), calculate the sum of the atomic radii of S and O, which is 88 pm + 66 pm = 154 pm. Compare this to the S=O bond length of 142 pm.

Determine the Smaller Quantity

For (a), since the bond length 141 pm is less than the sum of atomic radii 147 pm, the bond length is less. For (b), since the bond length 142 pm is less than the sum of atomic radii 154 pm, the bond length is less.

Key concepts

Atomic Radius

The atomic radius represents the distance from the nucleus of an atom to the boundary of its surrounding cloud of electrons. It's a measure of an atom's size and plays a crucial role in determining how atoms bond together.

When atoms form compounds, their atomic radii influence the resulting bond lengths. For example, knowing the radii helps us understand molecular interactions and predict how atoms will connect in a molecule.

• Hydrogen has a relatively small atomic radius of about 53 pm because it only has one electron shell.
• Bromine, with more electron shells, has a larger radius of 94 pm, reflecting its position further right in the periodic table.
• Sulfur and oxygen, both in the same column of the periodic table, exhibit atomic radii of 88 pm and 66 pm respectively, due to sulfur having an additional shell compared to oxygen.

Bond Length

Bond length is the average distance between the nuclei of two bonded atoms. It depends on the atomic radii of the bonding atoms as well as their electronegativities and bond types.

In general, a bond's length is shorter when the bond is stronger. For instance, as seen in hydrogen bromide (H-Br) and sulfur dioxide (SO), bond lengths are smaller than the sum of atomic radii because atoms often overlap each other's electron clouds to form a stable bond.

• The bond length of an H-Br molecule is approximately 141 pm, slightly shorter than the combined atomic radii of H and Br, which total to 147 pm.
• Similarly, the S=O bond length in sulfur dioxide stands at 142 pm, while the atomic radii of S and O add up to 154 pm.

Molecular Structure

Molecular structure refers to the arrangement of atoms within a molecule. This arrangement is key to both the properties and behavior of the molecule.

Understanding the molecular structure provides insight into how molecules like hydrogen bromide and sulfur dioxide interact with other compounds. Their structures are influenced by the types of bonds they form, which are determined by atomic radius, bond length, and the number of electrons involved in bonding.

• Molecules such as H-Br exhibit a straightforward structure, where hydrogen and bromine share a single covalent bond.
• By contrast, sulfur dioxide has a bent molecular shape due to the presence of a double bond between sulfur and oxygen, and its overall trigonal planar electron geometry.

Hydrogen Bromide

Hydrogen bromide (H-Br) forms when hydrogen and bromine atoms bond covalently. The nature of this molecule highlights the importance of atomic radius and bond length.

The H-Br bond is a single covalent bond. Differences in atomic radius and overlaps in electron clouds help stabilise the atoms' structure, resulting in a bond length slightly shorter than the sum of individual atomic radii.

• The interaction between hydrogen's comparatively small radius and bromine's larger radius results in a polar covalent bond, where electrons are unevenly distributed towards the more electronegative bromine.
• This polarness gives hydrogen bromide distinct molecular properties such as reactivity and boiling point characteristics.

Sulfur Dioxide

Sulfur dioxide (SO₂) is a compound where sulfur and oxygen atoms are bonded with double bonds, making a distinctive structure reflective of overlapping orbitals.

In sulfur dioxide, one sulfur atom is double-bonded to two oxygen atoms, resulting in a bent shape. These bonds are shorter than if sulfur and oxygen were only single bonded.

• The SO₂ molecule’s bond length of about 142 pm is shorter than the sum of sulfur and oxygen atomic radii, reflecting the bond's double nature.
• This specific bonding gives SO₂ unique chemical characteristics such as its acidic nature and role as a common pollutant in the atmosphere.