Problem 83 - Chemistry The Central Science

Question

Use bond enthalpies in Table 5.4 to estimate \(\Delta H\) for each of the following reactions: (a) \(\mathrm{H}-\mathrm{H}(g)+\mathrm{Br}-\mathrm{Br}(g) \longrightarrow 2 \mathrm{H}-\mathrm{Br}(g)\) (b)

Step-by-Step Solution

Answer

The change in enthalpy for reaction (a) can be estimated using bond enthalpies from Table 5.4 and the formula \(\Delta H = (\text{sum of enthalpies of broken bonds}) - (\text{sum of enthalpies of formed bonds})\). Using the bond enthalpies for H-H (436 kJ/mol), Br-Br (193 kJ/mol), and H-Br (364 kJ/mol) bonds, the calculated \(\Delta H\) for the reaction is: \[\Delta H = [(1 \times 436) + (1 \times 193)] - (2 \times 364) = 629 - 728 = -99\, kJ/mol\] Thus, the change in enthalpy for reaction (a) is -99 kJ/mol.

Step 1: Identify bond enthalpies from Table 5.4

Look up the bond enthalpies for all participating bonds in the reaction from Table 5.4: - H-H bond: 436 kJ/mol - Br-Br bond: 193 kJ/mol - H-Br bond: 364 kJ/mol

Step 2: Calculate ∆H for the reaction

Use the bond enthalpies to estimate the change in enthalpy (∆H) for the reaction: \[\Delta H = (\text{sum of enthalpies of broken bonds}) - (\text{sum of enthalpies of formed bonds})\] For reaction (a): \[\Delta H = [(1 \times 436) + (1 \times 193)] - (2 \times 364)\]

Step 3: Evaluate the expression

Now evaluate the expression to determine the change in enthalpy (∆H). \[\Delta H = (436 + 193) - (2 \times 364) = 629 - 728\] \[\Delta H = -99\, kJ/mol\] The change in enthalpy for reaction (a) is estimated to be -99 kJ/mol.

Key Concepts

Enthalpy Change Estimation

Understanding the enthalpy change in chemical reactions is crucial for predicting whether a reaction will release or absorb energy. To estimate the enthalpy change, denoted as \(\Delta H\), we apply a concept known as bond enthalpy, which is the energy required to break a mole of a bond in a substance at a constant pressure.
Enthalpy change can be estimated by considering the bond enthalpies of reactants and products in a chemical reaction. The process involves two main steps: calculating total energy for breaking all bonds in reactants (which is an endothermic process) and then, subtracting the energy released upon formation of new bonds in the products (which is an exothermic process).

Key Factors in Estimation

• Accuracy of bond enthalpies: The more precise the bond enthalpy values, the more accurate the estimation of \(\Delta H\).
• Nature of the bonds: Different types of bonds have different bond enthalpies. For instance, a double bond generally has a higher bond enthalpy than a single bond.
• The physical state of substances: As bond enthalpy values may vary with the state of the substance, it is important to use values for the same physical states as the substances in your reaction.

Through these calculations, one can determine if the reaction is exothermic (with \(\Delta H < 0\)) releasing energy, or endothermic (with \(\Delta H > 0\)), absorbing energy.

Chemical Bonds Energy

The energy associated with chemical bonds is a fundamental aspect of thermochemistry. Bond energy, or bond enthalpy, is indicative of the strength of a chemical bond. A high bond enthalpy means that a large amount of energy is required to break the bond, implying a strong bond.
In a chemical process, breaking old bonds requires energy absorption, while the formation of new bonds releases energy. The energy of the bonds directly affects the reactivity and stability of molecules.

Application in Reactions

When solving problems involving chemical reactions, such as the given textbook exercise, it is essential to know the bond enthalpies of the specific bonds involved in the reaction. The table of bond enthalpies, like Table 5.4 referred to in the exercise, is often used as a reference for these values. The overall understanding of bond energy helps predict the reaction outcomes and explain the energy transfers that occur during chemical reactions.

Thermochemistry Reactions

Thermochemistry is the study of the heat involved during chemical reactions. It is a branch of thermodynamics that focusses on heat transfer in chemical processes. Thermochemistry reactions provide valuable insight into the energetics of reactions which is critical when considering the feasibility and direction of a reaction.
One of the primary considerations in thermochemistry is whether a reaction is endothermic, absorbing heat, or exothermic, emitting heat. Understanding these concepts helps in predicting the environmental conditions under which a reaction will occur, as well as its impact on the surroundings.

Real-world Applications

• Industrial Process Design: Knowledge of thermochemical reactions aids in optimizing reactions by controlling temperatures, pressures, and concentrations.
• Energy Production: In designing fuels and energy sources, thermochemistry helps in maximizing energy output while minimizing waste and unwanted byproducts.
• Environmental Impact: Thermochemistry plays a key role in assessing the heat and energy transfer during chemical processes, which is vital for environmental protection and sustainability.

In the context of the exercise, calculating the enthalpy change (\(\Delta H\)) using bond enthalpies is a practical application of thermochemistry. This calculation provides a quick estimation of the heat exchange that might occur if the reaction were to take place under standard conditions.