Problem 54 - Chemistry and Chemical Reactivity

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.

Step-by-Step Solution

Answer

Higher bond order means shorter bond length and higher bond energy. Acetylene has the shortest bond length and highest energy, while ethane has the longest bond length and lowest energy.

Step 1: Define Bond Order

Bond order refers to the number of chemical bonds between a pair of atoms. For covalent bonds, a higher bond order indicates a stronger bond.

Step 2: Discuss Bond Order of Examples

- For ethane (C_2H_6), the bond between the two carbon atoms is a single bond, which gives it a bond order of 1. - For ethylene (C_2H_4), the bond between the two carbon atoms is a double bond, leading to a bond order of 2. - For acetylene (C_2H_2), the bond between the two carbon atoms is a triple bond, resulting in a bond order of 3.

Step 3: Define Bond Length

Bond length is the average distance between the nuclei of two bonded atoms. Generally, as bond order increases, bond length decreases.

Step 4: Discuss Bond Length for Examples

- In ethane (C_2H_6), the C-C single bond has the longest bond length. - In ethylene (C_2H_4), the C=C double bond is shorter compared to ethane's C-C single bond. - In acetylene (C_2H_2), the C≡C triple bond is the shortest among the three.

Step 5: Define Bond Energy

Bond energy is the measure of bond strength in a chemical bond. Higher bond order usually corresponds to higher bond energy.

Step 6: Discuss Bond Energy for Examples

- The C-C single bond in ethane (C_2H_6) has the lowest bond energy. - The C=C double bond in ethylene (C_2H_4) has a higher bond energy than in ethane, due to the double bond. - The C≡C triple bond in acetylene (C_2H_2) has the highest bond energy among the three, due to the triple bond.

Key Concepts

Bond Length

Bond length is a fundamental concept in chemistry that represents the distance between the nuclei of two bonded atoms. Understanding bond length helps us gauge the strength and stability of the bond. In general, the more bonds there are between two atoms, the closer they are drawn toward each other, resulting in a shorter bond length.

Let's look at some examples:

• In **ethane (C₂H₆)**, there is a single bond between the two carbon atoms. This single bond makes ethane's bond length the longest among the three molecules.
• In **ethylene (C₂H₄)**, the bond between the carbon atoms is a double bond. Double bonds bring the atoms closer together than single bonds, so ethylene has a shorter bond length compared to ethane.
• In **acetylene (C₂H₂)**, we find a triple bond between the carbon atoms. Triples bonds are the strongest and draw the atoms closest, resulting in acetylene having the shortest bond length among the three.

This demonstrates the direct relationship between bond order and bond length: as bond order increases, bond length typically decreases.

Bond Energy

Bond energy is a crucial measure in chemistry that indicates the strength of a chemical bond. It tells us how much energy is required to break one mole of the bond in a gaseous molecule. Generally, bonds involving multiple pairs of electrons are stronger and thus have higher bond energies.

The examples you'll often see include:

• **Ethane (C₂H₆)** with its single C-C bond has the lowest bond energy. This is because single bonds are the weakest when compared to double or triple bonds.
• **Ethylene (C₂H₄)**, which features a C=C double bond, has a higher bond energy than ethane. This is due to the additional shared electron pair in the double bond, making it more robust.
• Lastly, **acetylene (C₂H₂)** with a C≡C triple bond possesses the highest bond energy among the three. The presence of three shared electron pairs makes the bond extremely strong and thus more energy-intensive to break.

The pattern is clear: as bond order and strength increase, so does the bond energy.

Covalent Bonds

Covalent bonds form when two atoms share one or more pairs of electrons. This sharing allows each atom to achieve a more stable electron configuration, often resembling a noble gas setup. Covalent bonds can be single, double, or triple bonds.

Within this category of bonds, the examples of ethane, ethylene, and acetylene provide an excellent view of covalent bonding:

• **Single bonds** like those in ethane involve one pair of shared electrons, offering the basic level of bond stability.
• **Double bonds** such as those found in ethylene involve two pairs of shared electrons, enhancing bond strength and reducing bond length compared to single bonds.
• **Triple bonds** as seen in acetylene involve three pairs of shared electrons, resulting in the highest strength and shortest bond length among the covalent interactions discussed here.

Covalent bonds are pivotal for the structure and function of countless organic molecules. The balance of bond order, bond length, and bond energy in these structures influences their chemical properties and reactions.