Question

The energy of the \(\mathrm{C}-\mathrm{C}\) bond is \(347 \mathrm{~kJ} / \mathrm{mol},\) and that of the \(\mathrm{Cl}-\mathrm{Cl}\) bond is \(243 \mathrm{~kJ} / \mathrm{mol} .\) Which of the following values might you expect for the \(\mathrm{C}-\mathrm{Cl}\) bond energy? Explain. (a) \(590 \mathrm{~kJ} / \mathrm{mol}\) (sum of the values given) (b) \(104 \mathrm{~kJ} / \mathrm{mol}\) (difference of the values given) (c) \(295 \mathrm{~kJ} / \mathrm{mol}\) (average of the values given) (d) \(339 \mathrm{~kJ} / \mathrm{mol}\) (greater than the average of the values given)

Short answer

The expected \( \text{C-Cl} \) bond energy is \(295 \text{ kJ/mol}\), option (c).

Step-by-step solution

Understand the Problem

Given the bond energies for \(\text{C-C}\) and \(\text{Cl-Cl}\) bonds, we need to estimate the bond energy for \(\text{C-Cl}\). We are given four options: \(590 \text{ kJ/mol}\), \(104 \text{ kJ/mol}\), \(295 \text{ kJ/mol}\), and \(339 \text{ kJ/mol}\).

Calculate the Average Bond Energy

To find a reasonable estimate, calculate the average of the given bond energies. The formula is: \[ \text{Average} = \frac{\text{Energy of C-C bond} + \text{Energy of Cl-Cl bond}}{2} = \frac{347 + 243}{2} = 295 \text{ kJ/mol} \] This is option (c).

Evaluate Given Options

Review the given options: \ (a) \(590 \text{ kJ/mol}\): Adding the bond energies exceeds typical bond energy ranges. \ (b) \(104 \text{ kJ/mol}\): The difference is typically not indicative of bond energy estimation. \ (c) \(295 \text{ kJ/mol}\): The calculated average, fits within typical bond energy ranges. \ (d) \(339 \text{ kJ/mol}\): Slightly greater than the average, suggesting some variation from average, but within a reasonable range.

Choose the Most Logical Value

Comparing the options, \(295 \text{ kJ/mol}\) is the most logical choice. It is backed by calculation and fits within typical bond energy ranges.

Key concepts

chemical bond energy

Chemical bond energy refers to the amount of energy required to break one mole of bonds in a substance. It helps us understand the strength of a chemical bond. Different chemical bonds have different energies. This energy can be measured in kilojoules per mole (kJ/mol). Having a strong grasp on bond energies aids in predicting the stability and reactivity of molecules.
For instance, the energy needed to break a carbon-carbon (C-C) bond is typically higher than that needed to break a chlorine-chlorine (Cl-Cl) bond.
By analyzing bond energies, chemists can decipher why certain reactions occur and how much energy is required for these reactions.

bond energy calculation

Calculating bond energy is fundamental in chemistry. It's essentially the average value of the energies of bonds when broken and formed under specific conditions. To compute this, you often have to consider the energies provided for different bonds.
For example, if you know the bond energies of C-C and Cl-Cl, you can estimate the bond energy of a C-Cl bond. The formula used for average bond energy is:
\[ \text{Average bond energy} = \frac{\text{Energy of C-C bond} + \text{Energy of Cl-Cl bond}}{2} \]
Using the data of C-C (347 kJ/mol) and Cl-Cl (243 kJ/mol), the calculation would be
\[ \frac{347 + 243}{2} = 295 \text{ kJ/mol} \]
Thus, the estimated bond energy for C-Cl can be logically derived.

average bond energy

The concept of average bond energy is crucial for estimating the bond energies of new bonds, not directly given. It simplifies the predictions about stability and reactivity.
In our initial problem, we needed to estimate the bond energy of a C-Cl bond using the known values of C-C and Cl-Cl bonds. The average bond energy is determined by taking the average of these known energies:
\[ \text{Average bond energy} = \frac{347\text{ }\text{kJ/mol} + 243\text{ }\text{kJ/mol}}{2} = 295 \text{kJ/mol} \]
This makes option (c) the most logical choice. It aligns with the intuitive understanding that the bond energy of C-Cl should be somewhere between that of C-C and Cl-Cl.

chemical bonds

Chemical bonds are the forces holding atoms together in molecules. They form due to the attraction between opposite charges, which could be between electrons and protons. Different types of chemical bonds include ionic, covalent, and metallic bonds.
Covalent bonds, like those in our example between carbon and chlorine, involve the sharing of electrons between atoms. Studying bond energies helps in comparing how strong these bonds are relative to one another.
Breaking these bonds requires a specific amount of energy, known as bond energy. By understanding bond energies, chemists can predict the energy changes in chemical reactions and the stability of compounds.