Question

What is the connection between bond order, bond length, and bond energy? Use ethane \(\left(C_{2} \mathrm{H}_{6}\right),\) 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 leads to shorter bond length and higher bond energy.

Step-by-step solution

Understand the Concepts

Bond order refers to the number of chemical bonds between a pair of atoms. Bond length is the distance between the nuclei of two bonded atoms. Bond energy is the energy required to break the bond between two atoms.

Identify Bond Orders for Molecules

Ethane \(C_2H_6\) has a single bond between carbon atoms, so its bond order is 1. Ethylene \(C_2H_4\) has a double bond between carbon atoms, so its bond order is 2. Acetylene \(C_2H_2\) has a triple bond between carbon atoms, so its bond order is 3.

Analyze Bond Lengths

As bond order increases, bond length decreases due to a stronger attraction between the bonded atoms. Ethane has the longest bond length due to the single bond, ethylene has shorter bond length with a double bond, and acetylene has the shortest bond length with a triple bond.

Examine Bond Energies

Higher bond order also leads to higher bond energies, meaning more energy is required to break the bond. Thus, ethane has the lowest bond energy with a single bond, ethylene has intermediate bond energy with a double bond, and acetylene has the highest bond energy with a triple bond.

Conclusion of Connection

The relationship between bond order, bond length, and bond energy is that as bond order increases, bond length decreases and bond energy increases. This is demonstrated by the increasing bond order from ethane to ethylene to acetylene, associated with decreasing bond lengths and increasing bond energies.

Key concepts

Bond Order

When we talk about bond order, we're essentially counting the number of bonds between two atoms. Think of bond order as the strength of a handshake: the more bonds, the stronger the connection.

- **Single bond**: This is a bond order of 1, like in ethane ( C_2H_6 ), where there's one single bond between the two carbon atoms. - **Double bond**: Found in ethylene ( C_2H_4 ), this has a bond order of 2, indicating two bonds at play. - **Triple bond**: The strongest amongst the three, acetylene ( C_2H_2 ) has a triple bond, which gives it a bond order of 3.

A higher bond order implies a stronger bond. As bond order escalates from one to three, so does the bond's robustness and overlapping electronic interaction. This is key to understanding why molecules behave differently based on their bonds.

Bond Length

Bond length refers to the distance between the nuclei of two bonded atoms. Imagine it as the space between two friends standing while holding hands. This distance changes with the nature of the bond.

- **Ethane ( C_2H_6 )**: Single bonds mean longer distances, giving ethane the longest bond length. - **Ethylene ( C_2H_4 )**: With double bonds, these molecules have shorter bond lengths as the connection is stronger. - **Acetylene ( C_2H_2 )**: Triple bonds pull the nuclei even closer, leading to the shortest bond length.

The general rule is that as bond order increases, bond length decreases. This happens because more bonds pull the atoms closer together, creating a tighter bond. So, not only is a double or triple bond stronger, but it's tighter as well.

Bond Energy

Bond energy is the amount of energy you'd need to break a bond apart. Think of this as the amount of effort needed to uncouple two connected entities. Higher bond energy means a tougher bond to break, similar to pulling apart two magnets that are strongly attracted to each other.

- **Ethane ( C_2H_6 )**: With a bond order of 1, it has the lowest bond energy as it's easier to split the single bond. - **Ethylene ( C_2H_4 )**: Here, the double bond gives it moderate bond energy; it's tougher than ethane but not as tough as acetylene. - **Acetylene ( C_2H_2 )**: Exhibiting the highest bond energy, its triple bond requires the most effort to break apart.

This illustrates that as bond order rises, so does bond energy. More bonds mean more strength, more stability, and thus more energy needed to dissociate the bond. Understanding this relationship helps explain molecular stability and reactions involving these molecules.