Problem 77 - Chemistry: The Central Science in SI Units, Global Edition

Question

A new compound is made that has a \(\mathrm{C}-\mathrm{O}\) bond length of \(120 \mathrm{pm}\). Is this bond likely to be a single, double, or triple C-O bond?

Step-by-Step Solution

Answer

The given bond length of the C-O bond in the new compound is \(120 \: pm\). Comparing it with the approximate bond lengths of single, double, and triple C-O bonds (\(143 \: pm\), \(123 \: pm\), and \(113 \: pm\) respectively), we find that the bond length is closest to the double C-O bond length with a difference of only \(3 \: pm\). Therefore, it is most likely that the new compound contains a double C-O bond.

Step 1: Identify the bond lengths of single, double, and triple C-O bonds

To determine the type of bond present in the new compound, we need to know the typical bond lengths of single, double, and triple C-O bonds. Here are the approximate bond lengths for each type of bond: - Single C-O bond: \(143 \: pm\) - Double C-O bond: \(123 \: pm\) - Triple C-O bond: \(113 \: pm\)

Step 2: Compare the given bond length with the known bond lengths

The given bond length for the new compound is \(120 \: pm\). We will compare this value with the bond lengths of the single, double, and triple C-O bonds: - For the single C-O bond: \(|120 - 143| = 23 \: pm\) - For the double C-O bond: \(|120 - 123| = 3 \: pm\) - For the triple C-O bond: \(|120 - 113| = 7 \: pm\)

Step 3: Determine the most likely bond type

To determine the most likely C-O bond in the new compound, we will look at the smallest difference between the given bond length and the known bond lengths for single, double, and triple bonds. In this case, the smallest difference is between the given bond length and the known bond length for a double C-O bond (\(3 \: pm\)). Therefore, it is most likely that the new compound contains a double C-O bond.

Key Concepts

Single Bond

In chemistry, a single bond is the simplest type of covalent bond, where one pair of electrons is shared between two atoms. In the context of carbon-oxygen (C-O) bonds, a single bond typically has a bond length around 143 picometers (pm). A single bond between carbon and oxygen implies a relatively loose connection, allowing for more rotational freedom than multiple bonds. This bond length results in a stable connection, though not as strong as double or triple bonds, due to fewer shared electrons. Understanding the bond lengths can help in identifying the nature of the molecular bond present in a compound.

• Characterized by the sharing of one electron pair between two atoms.
• Typically longer and weaker compared to double and triple bonds.
• In C-O bonds, the bond length is approximately 143 pm.

Double Bond

Double bonds form when two pairs of electrons are shared between two atoms. In the case of C-O bonds, a double bond typically has a bond length of around 123 picometers (pm). This is shorter than a single bond, indicating a stronger connection due to increased electron sharing. Double bonds restrict the rotation around the bond axis, resulting in a planar structure which directly influences the geometry and reactivity of the molecule. The given bond length in our problem is 120 pm, very close to the typical double bond length, suggesting the presence of a C-O double bond.

• Involves the sharing of two pairs of electrons.
• Shorter and stronger than a single bond, with restricted rotation.
• C-O bond length is close to 123 pm, suggesting a stronger interaction.

Triple Bond

A triple bond involves the sharing of three pairs of electrons between two atoms, making it the strongest type of covalent bond among single, double, and triple bonds. For a C-O bond, a triple bond typically exhibits a bond length of about 113 picometers (pm), which is the shortest of the three types. This short distance reflects a very strong attraction as the electrons are held more tightly between the carbon and oxygen atoms. Triple bonds feature even higher electron density, resulting in a linear bond geometry due to the maximum overlap of the involved atomic orbitals. Although very strong, the bond length in this exercise (120 pm) does not quite match the expected value for a triple bond, thus ruling this possibility out.

• Characterized by three shared pairs of electrons.
• The shortest and strongest bond type, providing high stability.
• C-O bond length is around 113 pm, much shorter than double or single bonds.