Question

(a) Use enthalpies of formation given in Appendix C to calculate \(\Delta H\) for the reaction \(\mathrm{Br}_{2}(g) \longrightarrow 2 \operatorname{Br}(g)\), and use this value to estimate the bond enthalpy \(D(\mathrm{Br}-\mathrm{Br})\). (b) How large is the difference between the value calculated in part (a) and the value given in Table 5.4 ?

Short answer

The bond enthalpy of \(\mathrm{Br}-\mathrm{Br}\) is estimated to be 223.76 kJ/mol using enthalpies of formation. The given value in Table 5.4 is 193 kJ/mol, resulting in a difference of 30.76 kJ/mol.

Step-by-step solution

Write down the given reaction and identify the enthalpies of formation values

The given reaction is: $$ \mathrm{Br}_{2}(g) \longrightarrow 2 \operatorname{Br}(g) $$ Let's call the enthalpy of formation of \(\mathrm{Br}_{2}(g)\) as \(\Delta H_\text{f1}\) and that of \(\operatorname{Br}(g)\) as \(\Delta H_\text{f2}\). These values can be found in Appendix C.

Find the values of enthalpies of formation in Appendix C

In Appendix C, we find the following values: - \(\Delta H_\text{f1}\) (Enthalpy of formation of \(\mathrm{Br}_{2}(g)\)) = 0 kJ/mol - \(\Delta H_\text{f2}\) (Enthalpy of formation of \(\operatorname{Br}(g)\)) = 111.88 kJ/mol

Calculate the enthalpy change for the given reaction

The enthalpy change for the reaction, \(\Delta H_\text{rxn}\), can be calculated using the following equation: $$ \Delta H_\text{rxn} = \sum \text{Products} - \sum \text{Reactants} $$ So, in our case, we have: $$ \Delta H_\text{rxn} = 2 \times \Delta H_\text{f2} - \Delta H_\text{f1} $$ Plug in the values: $$ \Delta H_\text{rxn} = 2 \times 111.88\,\text{kJ/mol} - 0 $$ $$ \Delta H_\text{rxn} = 223.76\,\text{kJ/mol} $$

Estimate the bond enthalpy of \(D(\mathrm{Br}-\mathrm{Br})\)

Since there are two Br atoms in \(\mathrm{Br}_2\), and each bond between these atoms contributes to the enthalpy change, the bond enthalpy is approximately equal to the enthalpy change of the reaction: $$ D(\mathrm{Br}-\mathrm{Br}) \approx \Delta H_\text{rxn} = 223.76\,\text{kJ/mol} $$ Now, we have found the bond enthalpy of \(\mathrm{Br}-\mathrm{Br}\) in part (a).

Compare the bond enthalpy value from part (a) with the value in Table 5.4

According to Table 5.4, the given bond enthalpy value for \(\mathrm{Br}-\mathrm{Br}\) is 193 kJ/mol. Let's calculate the difference between our calculated value and the given value: $$ \text{Difference} = |D(\mathrm{Br}-\mathrm{Br})_\text{calculated} - D(\mathrm{Br}-\mathrm{Br})_\text{Table 5.4}| $$ $$ \text{Difference} = |223.76\,\text{kJ/mol} - 193\,\text{kJ/mol}| $$ $$ \text{Difference} = 30.76\,\text{kJ/mol} $$ The difference between the calculated bond enthalpy value and the value given in Table 5.4 is 30.76 kJ/mol.

Key concepts

Enthalpy of formation

Enthalpy of formation is a fundamental concept in thermodynamics and chemistry. It refers to the heat change that occurs when one mole of a compound forms from its elements in their standard states. This value is critical because it allows scientists and students to determine the energy required to synthesize substances from simpler components. For example, in the reaction \(\mathrm{Br}_{2}(g) \longrightarrow 2 \operatorname{Br}(g)\), the enthalpy of formation shows how much energy is absorbed or released. The enthalpy of formation for \( \mathrm{Br}_2(g) \) is commonly 0 \(\text{kJ/mol}\) because it is in its most stable form, while for \( \operatorname{Br}(g) \), it is 111.88 \(\text{kJ/mol}\). Thus, using these values, we can analyze how reactions proceed and calculate reaction enthalpies.

Bond enthalpy

Bond enthalpy, also known as bond dissociation energy, represents the amount of energy required to break one mole of bonds in a chemical reaction, under standard conditions. This concept is vital in predicting reaction behavior and evaluating the stability of molecules. For diatomic molecules like \(\mathrm{Br}_{2}\), bond enthalpy is directly related to how much energy is needed to separate the molecule into individual atoms. In the case of \(\mathrm{Br}_{2}(g) \longrightarrow 2 \operatorname{Br}(g)\), the bond enthalpy is determined by the energy needed for this dissociation process. We estimated it to be approximately 223.76 \(\text{kJ/mol}\), but the lookup table value is 193 \(\text{kJ/mol}\), showcasing potential discrepancies in experimental or calculated data.

Chemical reactions

Understanding chemical reactions involves knowing both the products and reactants involved. Every reaction has a distinct energy profile, often described using enthalpy changes. During a reaction, bonds between atoms either form or break, altering the system's energy. The reaction \(\mathrm{Br}_{2}(g) \longrightarrow 2 \operatorname{Br}(g)\) exemplifies a process where a stable molecule dissociates into its atomic components. By calculating the change in enthalpy for this reaction, we get insight into the energy dynamics involved in breaking the bromine-bromine bond, an essential aspect when you're analyzing or predicting reaction courses in various chemical contexts.

Appendix C data

Appendices in chemistry textbooks, like Appendix C, provide valuable numerical data for calculations. They contain standard enthalpy of formation values, among other essential constants. These values are vital for students and professionals as they offer a reference point for calculating unknown parameters in chemical reactions. For instance, Appendix C's reporting \(\Delta H_\text{f1}\) as 0 for \(\mathrm{Br}_{2}(g)\) and \(111.88\,\text{kJ/mol}\) for \(\operatorname{Br}(g)\) allows you to accurately compute reaction enthalpies and predict bond energies. Access to consistent and legitimate data ensures that calculations align with established scientific knowledge and practices, maintaining the integrity of chemical analysis.

Calculations in chemistry

Calculations in chemistry often require integrating various pieces of data to solve complex problems. These calculations may involve determining enthalpy changes, bond enthalpies, or even reaction progress. An example calculation involves using enthalpy of formation data to predict the enthalpy change for a reaction, as in \(\mathrm{Br}_{2}(g) \longrightarrow 2 \operatorname{Br}(g)\). By performing such calculations, practitioners can estimate the energies involved in molecular transformations. Understanding how to perform these calculations is crucial for accurately predicting reaction behaviors and making informed decisions in chemical engineering, pharmaceuticals, and everyday scientific inquiry. Students learning these calculations develop key analytical skills, applying theoretical knowledge to practical scenarios.