Question

What is the connection between bond order, bond length, and bond energy? Use ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\), ethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right),\) and acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) as examples.

Short answer

Higher bond order results in shorter bond length and higher bond energy.

Step-by-step solution

Understand Bond Order

Bond order refers to the number of chemical bonds between a pair of atoms. For ethane (\(\mathrm{C}_2\mathrm{H}_6\)), the bond order is 1 because there is a single bond between the carbon atoms. For ethylene (\(\mathrm{C}_2\mathrm{H}_4\)), the bond order is 2 due to the presence of a double bond. In acetylene (\(\mathrm{C}_2\mathrm{H}_2\)), the bond order is 3, as there is a triple bond.

Analyze Bond Length

Bond length is the distance between the nuclei of two bonded atoms. Generally, the higher the bond order, the shorter the bond length. Therefore, ethane with a single bond has the longest bond length between the carbon atoms, ethylene with a double bond has a shorter bond length, and acetylene with a triple bond has the shortest bond length among the three.

Evaluate Bond Energy

Bond energy is the energy required to break one mole of bonds in gaseous molecules. As bond order increases, bond energy usually increases because more energy is required to break multiple bonds than a single bond. Thus, ethane has the lowest bond energy, ethylene has a moderate bond energy, and acetylene has the highest bond energy.

Connect Bond Order, Length, and Energy

The connection is clear: As bond order increases, bond length decreases, and bond energy increases. Therefore, acetylene with the highest bond order has the shortest bond length and the highest bond energy, while ethane, with the lowest bond order, has the longest bond length and the lowest bond energy.

Key concepts

Bond Length

Bond length is a fundamental concept in understanding how atoms within a molecule are held together. It refers to the distance between the nuclei of two bonded atoms. This distance can vary widely among different compounds. In general, for similar elements, a higher bond order correlates with a shorter bond length. This happens because more shared electrons create a stronger attraction between the two atoms, pulling them closer together.

Using ethane ( C_2H_6), ethylene ( C_2H_4), and acetylene ( C_2H_2) as examples, we observe the following:

• In ethane, carbon atoms are connected by a single bond. This gives it the longest bond length among the three.
• Ethylene, with its double bond, has a shorter bond length than that in ethane.
• Acetylene, containing a triple bond, has the shortest bond length. This is due to the stronger pull of three pairs of shared electrons.

Thus, understanding bond length helps chemists predict the strength and stability of a molecule, playing a pivotal role in chemical reactions.

Bond Energy

Bond energy measures the strength of a chemical bond. It quantifies the amount of energy needed to break one mole of bonds between two atoms in a gaseous state. Simply put, higher bond energy means a stronger bond. Generally, the greater the bond order, the higher the bond energy. This occurs because more energy is needed to break bonds with multiple shared electron pairs.

In comparing ethane, ethylene, and acetylene:

• Ethane's single bond requires the least energy to break, reflecting its lower bond energy.
• Ethylene's double bond demands more energy, indicating moderate bond energy.
• Acetylene's triple bond withstands chemical disruption the best, having the highest bond energy.

This understanding of bond energy is crucial not only for predicting molecular stability but also for envisioning how resources might be synthesized or broken down in industrial or natural processes.

Chemical Bonds

Chemical bonds are the glues that hold atoms together, forming everything from the air we breathe to complex biological structures. Different types of chemical bonds include covalent, ionic, and metallic bonds, each with unique characteristics and properties.

Focusing on covalent bonds observed in molecules like ethane, ethylene, and acetylene:

• Covalent bonds involve the sharing of electrons between atoms. The number of shared electron pairs determines the bond order.
• In ethane ( C_2H_6), each carbon atom shares a single pair of electrons.
• Ethylene ( C_2H_4) involves double bonds, sharing two pairs of electrons between carbon atoms.
• Acetylene ( C_2H_2) features triple bonds, with three pairs of shared electrons, resulting in a particularly strong and stable connection.

Understanding the nature and strength of these bonds is essential for manipulating chemical structures in various fields, including organic chemistry, materials science, and biochemistry.