Problem 83 - Chemistry: The Central Science in SI Units, Global Edition

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

To estimate the change in enthalpy, ΔH, for reaction (a), first identify the bonds formed and broken during the reaction: - Breaking: 1 H-H bond and 1 Br-Br bond - Forming: 2 H-Br bonds Next, use the bond enthalpy values from Table 5.4: - H-H bond: 436 kJ/mol - Br-Br bond: 193 kJ/mol - H-Br bond: 364 kJ/mol The equation for ΔH is: ΔH = (Bond enthalpies of bonds broken) - (Bond enthalpies of bonds formed) ΔH = [(1 × 436) + (1 × 193)] - (2 × 364) = 629 - 728 = -99 kJ/mol So, for reaction (a), ΔH = -99 kJ/mol.

Step 1: Identify the bonds formed and broken in the first reaction

In reaction (a), we have: - Breaking: 1 H-H bond and 1 Br-Br bond - Forming: 2 H-Br bonds

Step 2: Write the equation for ΔH in terms of bond enthalpies

Using the bond enthalpies, we can write the equation for ΔH as: ΔH = (Bond enthalpies of bonds broken) - (Bond enthalpies of bonds formed)

Step 3: Find the bond enthalpy values from Table 5.4

Look up the bond enthalpy values for the bonds involved 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 4: Calculate ΔH for the first reaction

Use the bond enthalpy values found in Table 5.4 to substitute into the ΔH equation: ΔH = [(1 × 436) + (1 × 193)] - (2 × 364) = 629 - 728 = -99 kJ/mol For reaction (a), ΔH = -99 kJ/mol

Step 5: Identify the bonds formed and broken in the second reaction

In reaction (b), repeat steps 1 through 4, taking care to use the bond information given for the specific reaction.

Key Concepts

Enthalpy Change

Enthalpy change, denoted as \(\Delta H\), is a measure of the heat absorbed or released during a chemical reaction. It is expressed in kilojoules per mole (kJ/mol) and provides insights into whether a reaction is endothermic or exothermic. An endothermic reaction absorbs heat, resulting in a positive \(\Delta H\), while an exothermic reaction releases heat, marked by a negative \(\Delta H\).

Understanding \(\Delta H\) helps predict reaction spontaneity. In a practical sense, using bond enthalpies calculated from bond energy tables allows you to estimate the \(\Delta H\) for a reaction.
To determine \(\Delta H\), calculate the total bond energies of all bonds broken and subtract the total bond energies of bonds formed.

This computation reflects the energy changes associated with bond enthalpies, guiding predictions about the heat exchange in a chemical system.

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of chemical bonds. Each reaction includes reactants that are converted into products, resulting in different molecular structures.

The uniqueness of each reaction lies in the specific types and numbers of bonds broken and made. Understanding this transformation is key to estimating its enthalpy change. For instance, in reaction (a) \(\text{H-H(g) + Br-Br(g) \rightarrow 2H-Br(g)}\), involves:

• Breaking apart an H-H bond and a Br-Br bond.
• Forming two H-Br bonds.
  
  Since bond enthalpies show varied values for each bond type, the detailed study of these reactions allows chemists to envision and calculate energy requirements or releases.
  Using bond enthalpies, you can understand the energy profiles of chemical reactions, which are fundamental in predicting how these reactions behave energetically.

Bond Formation and Breaking

The process of bond formation and breaking is central to understanding chemical reactions. When bonds are broken, that requires energy input (endothermic), whereas bond formation releases energy (exothermic). These processes are quantified using bond enthalpies, the energy needed to break one mole of a particular bond type in the gas phase.

• For a reaction, identify all bonds that will be broken and those that will be formed.
  
  
• Calculate the energy required for breaking bonds and compare it to the energy released from forming new bonds.
  
  Bond enthalpies can vary based on the molecular environment, and the sum of these energy changes gives an estimate of the total enthalpy change (\(\Delta H\)) for the chemical reaction.
  In essence, whether a reaction is endothermic or exothermic depends on the comparison between the energy absorbed to break bonds and the energy released while forming new bonds.
  This understanding demystifies why some reactions generate heat and others consume it, offering predictive power in both laboratory and industrial settings.