Problem 2
Question
Given the following reactions and their enthalpies: $$ \begin{array}{lr} \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{H}(\mathrm{g}) & \frac{\Delta H(\mathrm{~kJ} / \mathrm{mol}}{\longrightarrow}+436 \\ \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{O}(\mathrm{g}) & +495 \\\ \mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) & -242 \end{array} $$ (a) Devise a way to calculate \(\Delta H\) for the reaction $$ \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow 2 \mathrm{H}(\mathrm{g})+\mathrm{O}(\mathrm{g}) $$ (b) From this, estimate the \(\mathrm{H}-\mathrm{O}\) bond energy.
Step-by-Step Solution
Verified Answer
\( \Delta H \) for the reaction is 925.5 kJ/mol, and the estimated \( \mathrm{H-O} \) bond energy is 462.75 kJ/mol.
1Step 1: Write the Target Reaction
We need to determine the enthalpy change \( \Delta H \) for the reaction: \( \mathrm{H}_{2} \mathrm{O(g)} \longrightarrow 2 \mathrm{H(g)} + \mathrm{O(g)} \). This is our target reaction.
2Step 2: Reverse and Adjust Given Reactions
To relate given reactions to the target reaction, reverse the third reaction to: \( \mathrm{H}_{2} \mathrm{O(g)} \longrightarrow \mathrm{H}_{2}(\mathrm{g}) + \frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \), which changes \( \Delta H \) to +242 kJ/mol because the process is now endothermic instead of exothermic.
3Step 3: Combine Adjusted Reaction with Other Reactions
The target reaction can now be achieved by adding the reversed third reaction with the other two given reactions:1. \( \mathrm{H}_{2} \mathrm{O(g)} \longrightarrow \mathrm{H}_{2}(\mathrm{g}) + \frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \) with \( \Delta H = +242 \) kJ/mol.2. \( \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2\mathrm{H}(\mathrm{g}) \) with \( \Delta H = +436 \) kJ/mol.3. \( \frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{O}(\mathrm{g}) \) with \( \Delta H = \frac{1}{2} \times 495 = +247.5 \) kJ/mol.
4Step 4: Calculate Total Enthalpy Change
Sum the enthalpies of the reactions:\(+242 \text{ kJ/mol} + 436 \text{ kJ/mol} + 247.5 \text{ kJ/mol} = 925.5 \text{ kJ/mol}.\)This is the \( \Delta H \) for the target reaction \( \mathrm{H}_{2} \mathrm{O(g)} \longrightarrow 2 \mathrm{H(g)} + \mathrm{O(g)} \).
5Step 5: Estimate H-O Bond Energy
The target reaction consists of breaking 2 \(\mathrm{H-O}\) bonds. Since \( \Delta H = 925.5 \text{ kJ/mol} \) for breaking two \(\mathrm{H-O}\) bonds, the energy required to break one \( \mathrm{H-O} \) bond is \( \frac{925.5}{2} = 462.75 \text{ kJ/mol}.\)
Key Concepts
Understanding Bond EnergyChemical Reactions and Energy ChangesExploring Thermochemistry
Understanding Bond Energy
Bond energy is a fundamental concept in understanding chemical reactions. It refers to the amount of energy required to break one mole of bonds in a gaseous state. Simply put, if you want to separate atoms that are held together by chemical bonds, you need to provide energy. More energy is needed for stronger bonds. This energy is measured in kilojoules per mole (kJ/mol).
Many students find it helpful to think about this as if you are breaking something solid into pieces. The amount of force or energy you need to use depends on how strongly the parts are stuck together! In chemical terms, each type of bond between atoms has a specific bond energy value.
Bond energies play a crucial role in calculating the heat change during chemical reactions. For example, in the exercise above, the goal was to find the energy required to break the bonds in water (H-O bonds). By knowing the total energy change and the number of bonds broken, the energy per individual bond can be determined.
Many students find it helpful to think about this as if you are breaking something solid into pieces. The amount of force or energy you need to use depends on how strongly the parts are stuck together! In chemical terms, each type of bond between atoms has a specific bond energy value.
Bond energies play a crucial role in calculating the heat change during chemical reactions. For example, in the exercise above, the goal was to find the energy required to break the bonds in water (H-O bonds). By knowing the total energy change and the number of bonds broken, the energy per individual bond can be determined.
- Bond Strength: Stronger bonds have higher bond energy values.
- Bond Length: Typically, the shorter a bond, the stronger it is.
- Units: Bond energy is commonly given in kJ/mol.
Chemical Reactions and Energy Changes
Chemical reactions involve the rearrangement of atoms. This means that bonds between atoms are broken and new ones are formed. These processes either absorb or release energy. When analyzing chemical reactions, it's helpful to consider the energy profile of the reaction.
- **Exothermic Reactions**: These are reactions that release energy, usually in the form of heat. When the total energy needed to break bonds is less than the energy released when new bonds are formed, the result is a release of energy. - **Endothermic Reactions**: In contrast, endothermic reactions absorb energy. This happens when the energy cost of breaking bonds is greater than the energy released from forming new bonds.
In the problem provided, initially, energy is required to break the bonds, making it an endothermic process. Reversing the reaction and comparing the energies helps understand the nature of the energy flow during chemical reactions. It boils down to comparing the sum of bond energies of reactants and products.
- **Exothermic Reactions**: These are reactions that release energy, usually in the form of heat. When the total energy needed to break bonds is less than the energy released when new bonds are formed, the result is a release of energy. - **Endothermic Reactions**: In contrast, endothermic reactions absorb energy. This happens when the energy cost of breaking bonds is greater than the energy released from forming new bonds.
In the problem provided, initially, energy is required to break the bonds, making it an endothermic process. Reversing the reaction and comparing the energies helps understand the nature of the energy flow during chemical reactions. It boils down to comparing the sum of bond energies of reactants and products.
- Reaction Pathway: Visualize energy changes during reactions.
- Balance: Consider energy needed for breaking and forming bonds.
- Net Energy Change: Sum of energies in reactants vs. products.
Exploring Thermochemistry
Thermochemistry is the study of heat and energy in chemical reactions. It combines both chemistry and physics principles to understand how energy changes within a system. When chemical reactions occur, they can either absorb or release heat, changing the enthalpy (heat content) of a system.
The concept of enthalpy ( ) is critical in thermochemistry. It represents the total heat content of a system. The change in enthalpy ( ) during a reaction indicates whether energy is absorbed or released.
In practical terms, thermochemistry helps predict how energy efficient reactions are, which is essential for both industrial and academic purposes. For instance, calculating the ∆H (enthalpy change) for reactions, as in the exercise above, gives insight into the energy involved in breaking bonds and forming new ones. This informs us about efficiencies and feasibilities of processes.
The concept of enthalpy ( ) is critical in thermochemistry. It represents the total heat content of a system. The change in enthalpy ( ) during a reaction indicates whether energy is absorbed or released.
In practical terms, thermochemistry helps predict how energy efficient reactions are, which is essential for both industrial and academic purposes. For instance, calculating the ∆H (enthalpy change) for reactions, as in the exercise above, gives insight into the energy involved in breaking bonds and forming new ones. This informs us about efficiencies and feasibilities of processes.
- Enthalpy Changes: > 0 for endothermic reactions, < 0 for exothermic reactions.
- Importance: Helps in designing energy-efficient production processes.
- Relevance: Essential for understanding reaction kinetics and dynamics.
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