Question

Given the following bond-dissociation energies, calculate the average bond enthalpy for the \(\mathrm{Ti}-\mathrm{Cl}\) bond. $$ \begin{array}{lc} \hline & \Delta H(\mathrm{~kJ} / \mathrm{mol}) \\ \hline \mathrm{TiCl}_{4}(g) \longrightarrow \mathrm{TiCl}_{3}(g)+\mathrm{Cl}(g) & 335 \\ \mathrm{TiCl}_{3}(\mathrm{~g}) \longrightarrow \mathrm{TiCl}_{2}(g)+\mathrm{Cl}(g) & 423 \\ \mathrm{TiCl}_{2}(g) \longrightarrow \mathrm{TiCl}(g)+\mathrm{Cl}(g) & 444 \\ \mathrm{TiCl}(g) \longrightarrow \mathrm{Ti}(g)+\mathrm{Cl}(g) & 519 \\ \hline \end{array} $$

Short answer

The average bond enthalpy for the \(\mathrm{Ti}-\mathrm{Cl}\) bond is \(430.25 ~\mathrm{kJ/mol}\).

Step-by-step solution

Identify the number of \(\mathrm{Ti}-\mathrm{Cl}\) bonds broken in each reaction

Observe the given reactions. In each reaction, the total number of \(\mathrm{Ti}-\mathrm{Cl}\) bonds broken are: - In reaction 1, \(\mathrm{TiCl}_{4}(g) \to \mathrm{TiCl}_{3}(g) + \mathrm{Cl}(g)\), one \(\mathrm{Ti}-\mathrm{Cl}\) bond is broken. - In reaction 2, \(\mathrm{TiCl}_{3}(g) \to \mathrm{TiCl}_{2}(g) + \mathrm{Cl}(g)\), one \(\mathrm{Ti}-\mathrm{Cl}\) bond is broken. - In reaction 3, \(\mathrm{TiCl}_{2}(g) \to \mathrm{TiCl}(g) + \mathrm{Cl}(g)\), one \(\mathrm{Ti}-\mathrm{Cl}\) bond is broken. - In reaction 4, \(\mathrm{TiCl}(g) \to \mathrm{Ti}(g) + \mathrm{Cl}(g)\), one \(\mathrm{Ti}-\mathrm{Cl}\) bond is broken.

Calculate total bond dissociation energy for \(\mathrm{Ti}-\mathrm{Cl}\) bonds

The bond dissociation energy in each reaction represents the energy needed to break the \(\mathrm{Ti}-\mathrm{Cl}\) bond. We need to sum the bond dissociation energy for all the reactions in order to obtain the total bond dissociation energy. Total Bond Dissociation Energy = \(335 + 423 + 444 + 519 = 1721 ~\mathrm{kJ/mol}\)

Calculate the average bond enthalpy for the \(\mathrm{Ti}-\mathrm{Cl}\) bond

To find the average bond enthalpy, we divide the total bond dissociation energy by the number of bonds present in the compound. In this case, \(\mathrm{TiCl}_{4}\) has 4 \(\mathrm{Ti}-\mathrm{Cl}\) bonds. Hence, the average bond enthalpy is: Average Bond Enthalpy = \(\frac{1721}{4} = 430.25 ~\mathrm{kJ/mol}\) Thus, the average bond enthalpy for the \(\mathrm{Ti}-\mathrm{Cl}\) bond is \(430.25 ~\mathrm{kJ/mol}\).

Key concepts

Bond Dissociation Energy

Bond dissociation energy is crucial in understanding the energy required to break a specific bond in a molecule. In our example involving the titanium-chlorine (\(\mathrm{Ti}-\mathrm{Cl}\)) bond, we calculate the total energy needed to break all the bonds one by one.

• It is the energy change required to dissociate one mole of bonds in a gaseous substance into gaseous atoms. In simpler terms, it measures how strong a bond is.
• The values are generally measured in kilojoules per mole (kJ/mol).

When calculating the bond dissociation energy:
You sum up the energy values for each stage where a bond is broken. In the case of \(\mathrm{Ti}-\mathrm{Cl}\) bonds, we used the given energies: 335, 423, 444, and 519 kJ/mol for each stage. Adding these values gives a total bond dissociation energy of 1721 kJ/mol.
This total value helps in determining the average bond enthalpy, providing insights into the strength and stability of the chemical bonds present in the compound.

Chemical Reactions

Chemical reactions involve the breaking and forming of chemical bonds, which is where the concept of bond dissociation energy plays a vital role. During a chemical reaction:

• Bonds in the reactants are broken while new bonds are formed in the products.
• The energy required to break bonds is absorbed, whereas the energy released in forming new bonds comes off as heat.

In the example provided:
We experience the sequence of reactions where a \(\mathrm{Ti}-\mathrm{Cl}\) bond is broken at each step, converting \(\mathrm{TiCl}_4\) into elemental \(\mathrm{Ti}\) and \(\mathrm{Cl}\). These reactions showcase how energy is utilized and released, supporting the interconnectivity between bond dissociation energy and chemical processes.
Understanding these reactions offers insight into how chemical processes can be balanced energetically, allowing predictions related to reaction outcomes and feasibility.

Thermodynamics

Thermodynamics is the study of energy changes, particularly how energy flows in systems, including chemical reactions. Analyzing the bond dissociation energy in a chemical reaction provides valuable insight into its thermodynamic properties.

• Thermodynamics helps us understand how energy is absorbed or released, determining whether a reaction is endothermic or exothermic.
• Endothermic reactions absorb heat, as evident when breaking bonds, while exothermic reactions release heat during bond formation.

In the breakdown of \(\mathrm{TiCl}_4\),
Each of the provided reactions requires energy input for bond breaking, making these reactions endothermic. The cumulative bond dissociation energies reflect the overall energy absorption needed.
By understanding these thermodynamic principles, one can predict how temperature changes may influence the reaction's rate or even its possibility, providing a broader understanding of any chemical process in question.