Problem 85 - General Chemistry: Principles and Modern Applications

Question

Without referring to tables in the text, indicate which of the following bonds you would expect to have the greatest bond length, and give your reasons. (a) \(\mathrm{O}_{2}\); (b) \(\mathrm{N}_{2} ;\) (c) \(\mathrm{Br}_{2} ;\) (d) \(\mathrm{BrCl}\).

Step-by-Step Solution

Answer

Among \(\mathrm{O}_{2}\), \(\mathrm{N}_{2}\), \(\mathrm{Br}_{2}\) and \(\mathrm{BrCl}\), the \(\mathrm{BrCl}\) bond is expected to have the greatest length. This is due to it being composed of larger atoms (compared to O and N) and it being a single bond (longer than double or triple bonds).

Step 1: Understand Elements' Properties

To start with, recognize the periodic table properties of the elements involved. Oxygen (O) and Nitrogen (N) are Period 2 elements, while Bromine (Br) and Chlorine (Cl) are Period 4 and 3 elements respectively. This means Bromine and Chlorine are larger than Oxygen and Nitrogen.

Step 2: Determine Bond Types

Next, identify the type of bond present in the given molecules. In \(\mathrm{O}_{2}\) and \(\mathrm{N}_{2}\), they are double and triple bonds respectively while in \(\mathrm{Br}_{2}\) and \(\mathrm{BrCl}\), they are single bonds. Single bonds are generally longer than double and triple bonds.

Step 3: Compare Bond lengths

Now compare the bond lengths based on the above information. Given that single bonds are typically longer and Period 4/3 elements are larger, it can be expected that \(\mathrm{BrCl}\) and \(\mathrm{Br}_{2}\) will have greater bond lengths than \(\mathrm{O}_{2}\) and \(\mathrm{N}_{2}\). Between \(\mathrm{BrCl}\) and \(\mathrm{Br}_{2}\), \(\mathrm{BrCl}\) is likely to have a slightly longer bond because mixing different elements often increases bond length.

Key Concepts

Periodic Table

The periodic table is a systematic way of organizing all known chemical elements. Each row is called a "period," and each column is known as a "group."
This arrangement helps in predicting the properties of elements based on their positions. Elements are placed in order of increasing atomic number, which is the number of protons in an atom's nucleus. This organization means elements in the same group often have similar chemical properties.

• Elements in higher periods tend to be larger in size as they have more electron shells.
• Period 2 includes smaller elements with fewer electron shells, such as Oxygen (O) and Nitrogen (N).
• Period 3 and 4 elements, such as Bromine (Br) and Chlorine (Cl), are larger due to additional electron shells.

Understanding this layout is crucial because it allows us to predict the size of atoms, which influences the bond length they form when combined with other elements.

Single Bonds

Single bonds occur when two atoms share one pair of electrons. This bond type is generally formed between larger atoms.
Because only one pair of electrons is shared, single bonds are typically the longest of the bond types.Take Bromine (Br) for example, which forms a single bond in \( \text{Br}_2 \). Bromine, being a larger atom from Period 4, results in longer bond lengths due to less electron density between the bonded atoms compared to double or triple bonds. Additionally, single bonds allow for free rotation around the bond axis, which can also affect molecule shape and reactivity. In general, when considering bond lengths in a series of molecules, single bonds will tend to be longer than double or triple bonds, making them significant in determining the physical properties of substances.

Double Bonds

Double bonds are characterized by the sharing of two pairs of electrons between atoms. This type of bond is shorter and stronger than single bonds.
For example, the oxygen molecule \( \text{O}_2 \) consists of a double bond between the two oxygen atoms. Because two pairs of electrons are shared, there is greater electron density between the nuclei of bonded atoms, drawing them closer together and thus creating a shorter bond length compared to single bonds.Double bonds also restrict rotation around the bond axis, which adds to the stability and rigidity of a molecule's structure. Double bonds can influence the chemical reactivity, affecting how molecules interact with each other in reactions. The presence or absence of a double bond can significantly impact a molecule's chemical behavior and physical properties.

Triple Bonds

Triple bonds involve three pairs of shared electrons between two atoms. These bonds are even shorter and stronger than double bonds, due to the high electron density between the atoms.
This significant electron density pulls the bonded atoms closer together, resulting in a bond that is both short and strong.An extraordinary example of a molecule with a triple bond is nitrogen gas \( \text{N}_2 \). This is one of the strongest known bonds, contributing to nitrogen's low reactivity under standard conditions.The characteristics of triple bonds, such as >- Increased bond strength- Restricted rotationmake them crucial in understanding the properties of molecules where such bonds are present. Like double bonds, they significantly affect the shape and stability of molecules, making them an essential topic for study in chemistry. These features demonstrate the relationship between electron sharing and bond strength, providing insight into molecular stability.