Question

Experiments show that it takes \(1656 \mathrm{~kJ} / \mathrm{mol}\) to break all the bonds in methane \(\left(\mathrm{CH}_{4}\right)\) and \(4006 \mathrm{~kJ} / \mathrm{mol}\) to break all the bonds in propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right) .\) Based on these data, calculate the average bond enthalpy of the \(\mathrm{C}-\mathrm{C}\) bond.

Short answer

The average C-C bond enthalpy is \(347 \mathrm{~kJ/mol}\).

Step-by-step solution

Identify the Bonds in Methane

Methane (\(\mathrm{CH}_4\)) consists of one carbon atom bonded to four hydrogen atoms. Therefore, it has four C-H bonds.

Identify the Bonds in Propane

Propane (\(\mathrm{C}_3\mathrm{H}_8\)) consists of three carbon atoms and eight hydrogen atoms. It contains two C-C bonds and eight C-H bonds.

Calculate Enthalpy for C-H Bonds in Methane

Since breaking all bonds in methane requires \(1656 \mathrm{~kJ/mol}\) and there are four \(\mathrm{C-H}\) bonds in methane, the average bond enthalpy for a single \(\mathrm{C-H}\) bond is \(\frac{1656}{4} = 414 \mathrm{~kJ/mol}\).

Calculate Total C-H Bond Enthalpy in Propane

With eight C-H bonds in propane and each having an enthalpy of \(414 \mathrm{~kJ/mol}\), the total enthalpy for breaking all C-H bonds is \(8 \times 414 = 3312 \mathrm{~kJ/mol}\).

Determine C-C Bond Enthalpy in Propane

Breaking all bonds in propane requires \(4006 \mathrm{~kJ/mol}\). Subtract the total C-H bond enthalpy from this to find the total C-C bond enthalpy: \(4006 - 3312 = 694 \mathrm{~kJ/mol}\).

Calculate Average C-C Bond Enthalpy

Since propane involves two C-C bonds, the average enthalpy for a single C-C bond is \(\frac{694}{2} = 347 \mathrm{~kJ/mol}\).

Key concepts

Methane

Methane, represented as \( \mathrm{CH}_4 \), is a simple hydrocarbon consisting of one carbon atom surrounded by four hydrogen atoms. It is a key component of natural gas and is commonly used as a fuel. The structure of methane is a tetrahedral shape, where each hydrogen atom is equidistant from the carbon atom, allowing for maximum stability. This common molecule serves as a great example for learning about bond enthalpies because its structure is straightforward and involves only carbon-hydrogen (C-H) bonds.
Understanding methane's structure and how energy is involved in breaking and forming its bonds is essential in chemistry. It provides insight into the concept of bond enthalpy, a measure of bond strength in a chemical bond.

Propane

Propane, represented as \( \mathrm{C}_3\mathrm{H}_8 \), consists of three carbon atoms and eight hydrogen atoms. It is often used as a fuel source for heating and in vehicles. Structurally, propane has a backbone of three carbon atoms connected in a chain, with the hydrogen atoms surrounding them. This molecule combines both C-H bonds and carbon-carbon (C-C) bonds.
In chemistry, examining propane provides a real-world example of how different types of bonds contribute to the overall energy needed to break them. By studying propane, students can see the cumulative effect of multiple bonds of different types, yielding a more comprehensive understanding of bond energy in slightly more complex molecules.

C-H Bond Enthalpy

The C-H bond enthalpy is the energy required to break a carbon-hydrogen bond in a molecule. In the case of methane, which only contains C-H bonds, it requires \(1656 \mathrm{~kJ/mol}\) to break all four bonds. Thus, the average bond enthalpy of a single C-H bond can be computed as \( \frac{1656}{4} = 414 \mathrm{~kJ/mol} \).
This value shows you the energy associated with the stability of the C-H bond. Since these bonds are common in organic molecules, understanding their bond enthalpies helps in calculating reaction energetics and is crucial for predicting reaction behaviors in organic chemistry.

C-C Bond Enthalpy

C-C bond enthalpy refers to the energy needed to break a carbon-carbon bond. In propane, there are both C-C and C-H bonds. While the C-H bonds in propane are similar in energy to those in methane, the presence of C-C bonds adds additional considerations.
Breaking all bonds in propane requires \(4006 \mathrm{~kJ/mol}\). Subtracting the calculated total energy for the C-H bonds \(3312 \mathrm{~kJ/mol}\), the remaining energy is due to the C-C bonds, equalling \(694 \mathrm{~kJ/mol}\). With two C-C bonds in propane, this means each C-C bond has an average energy of \( \frac{694}{2} = 347 \mathrm{~kJ/mol} \). This information is crucial for understanding internal energy distributions within carbon chains.

Bond Energy Calculations

Bond energy calculations involve determining the total energy required to break all the bonds in a molecule, often with the goal of finding average bond enthalpies for specific types of bonds. These calculations are based on the assumption that the enthalpy change in breaking and forming bonds is a reliable measure of bond strength.

• Start by identifying all the bonds in a molecule.
• Determine the total energy needed to break the molecule down to individual atoms.
• Divide this energy by the number of each type of bond to find the average bond enthalpy.

These calculations are pivotal when predicting the energy required for a reaction or when designing molecules with specific energetic properties. They allow chemists to construct a clearer picture of molecular stability and reactivity.