Question

Given the following bond-dissociation energies, calculate the average bond enthalpy for the Ti-Cl bond. \begin{tabular}{ll} \hline & \(\Delta H(\mathbf{k J} /\) mol \()\) \\ \hline \(\mathrm{TiCl}_{4}(g) \longrightarrow \mathrm{TiCl}_{3}(g)+\mathrm{Cl}(g)\) & 335 \\ \(\mathrm{TiCl}_{3}(g) \longrightarrow \mathrm{TiCl}_{2}(g)+\mathrm{Cl}(g)\) & 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{tabular}

Short answer

The average bond enthalpy for the Ti-Cl bond is approximately \(430.25 kJ/mol\).

Step-by-step solution

Identify the number of Ti-Cl bonds broken in each reaction

We will determine the number of Ti-Cl bonds being broken in each reaction as follows: 1. TiCl4(g) → TiCl3(g) + Cl(g) - In this reaction, 1 Ti-Cl bond is being broken (4 bonds in TiCl4 to 3 bonds in TiCl3) 2. TiCl3(g) → TiCl2(g) + Cl(g) - In this reaction, 1 Ti-Cl bond is being broken (3 bonds in TiCl3 to 2 bonds in TiCl2) 3. TiCl2(g)→ TiCl(g) + Cl(g) - In this reaction, 1 Ti-Cl bond is being broken (2 bonds in TiCl2 to 1 bond in TiCl) 4. TiCl(g) → Ti(g) + Cl(g) - In this reaction, 1 Ti-Cl bond is being broken (1 bond in TiCl to 0 bonds in Ti)

Calculate the cumulative bond dissociation energies for all Ti-Cl bonds

To calculate the cumulative bond dissociation energies, we need to multiply the bond dissociation energy for each reaction by the number of Ti-Cl bonds broken in the corresponding reaction. Then we need to sum the values for each reaction to find the total energy. Total Energy = (1 x 335 kJ/mol) + (1 x 423 kJ/mol) + (1 x 444 kJ/mol) + (1 x 519 kJ/mol) Total Energy = 335 kJ/mol + 423 kJ/mol + 444 kJ/mol + 519 kJ/mol = 1721 kJ/mol

Calculate the average bond enthalpy for the Ti-Cl bond

To calculate the average bond enthalpy for the Ti-Cl bond, divide the total cumulative bond dissociation energy by the total number of Ti-Cl bonds broken in all reactions. Average Bond Enthalpy = Total Energy / Total Number of Ti-Cl Bonds Broken There are a total of 1 + 1 + 1 + 1 = 4 Ti-Cl bonds broken over the four reactions. So, Average Bond Enthalpy = 1721 kJ/mol / 4 Average Bond Enthalpy = 430.25 kJ/mol The average bond enthalpy for the Ti-Cl bond is approximately 430.25 kJ/mol.

Key concepts

Bond-Dissociation Energy

The bond-dissociation energy is a measure of the strength of a chemical bond. It represents the energy required to break a bond between two atoms in a molecule. This energy is expressed in kilojoules per mole (kJ/mol). Bond-dissociation energy is a crucial concept in understanding how strong a particular bond is.
In chemical reactions, bonds in reactants are broken to form new bonds in the products. The bond-dissociation energy helps predict the energy changes that occur during these transformations. A higher bond-dissociation energy indicates a stronger bond, requiring more energy to break. Understanding this concept is valuable in fields like chemistry and material science, where it aids in predicting reaction pathways and stability of compounds.

Ti-Cl Bond

The Ti-Cl bond is a type of chemical bond between titanium (Ti) and chlorine (Cl). These bonds are formed in compounds such as titanium tetrachloride (TiCl₄) and its lower chlorides, TiCl₃, TiCl₂, and TiCl.
In the context of the exercise, bonding is broken as you move from TiCl₄ all the way down to Ti and Cl individually. Each step involves breaking one Ti-Cl bond, demonstrating the sequential breakdown of a compound containing titanium and chlorine. This highlights the individual impact of each bond on the stability and energy requirements of the compound. Understanding the nature of the Ti-Cl bond assists in calculating energies needed for changes and predicting reaction behaviors.

Average Bond Enthalpy

The average bond enthalpy is the average amount of energy required to break one bond in a molecule in the gas phase. It's derived by averaging the bond-dissociation energies from several similar compounds or steps.
In the given exercise, calculating the average bond enthalpy for the Ti-Cl bond involves averaging the bond-dissociation energies for each distinct bond broken in the series of reactions transitioning from TiCl₄ to Ti. The overall cumulative energy calculated (1721 kJ/mol) was divided by the total number of bonds broken (four) to find the average, resulting in 430.25 kJ/mol. This average value provides an overall understanding of the energy involved in breaking the Ti-Cl bonds.

Chemical Reactions

Chemical reactions involve the rearrangement of atoms through the breaking and formation of bonds, converting reactants into products. Each reaction has an associated energy change, dominated by the bond-dissociation processes involved.
In the exercise, each step is a chemical reaction representing the breakdown of a compound with varying numbers of Ti-Cl bonds. Understanding these reactions is crucial as it showcases how energy is absorbed to overcome the bond energies during the transformation process. Knowledge of such reactions is important for studying reaction mechanics and kinetic behaviors of compounds.

Enthalpy Calculation

Enthalpy calculation is vital for understanding energy changes in a chemical system. It represents the total energy change, mainly the heat energy, involved when a reaction occurs at constant pressure.
In our exercise, different reactions break one Ti-Cl bond each, requiring a particular amount of energy stated as their bond-dissociation enthalpies. By adding these energies, we find the cumulative enthalpy change, which informs us about the total energy intake needed for these processes.
Calculating enthalpy changes helps in predicting reaction direction, feasibility, and energy efficiency in chemical processes. It forms the backbone of thermodynamics in the study of chemistry.