Question

(a) Using average bond enthalpies, predict which of the following reactions will be most exothermic: (i) \(\mathrm{C}(g)+2 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)\) (ii) \(\mathrm{CO}(g)+3 \mathrm{~F}_{2} \longrightarrow \mathrm{CF}_{4}(g)+\mathrm{OF}_{2}(g)\) (iii) \(\mathrm{CO}_{2}(g)+4 \mathrm{~F}_{2} \longrightarrow \mathrm{CF}_{4}(g)+2 \mathrm{OF}_{2}(g)\) (b) Explain the trend, if any, that exists between reaction exothermicity and the extent to which the carbon atom is bonded to oxygen.

Short answer

The most exothermic reaction is Reaction (iii), with an enthalpy change of -676 kJ/mol. The reaction exothermicity decreases as the number of bonds between carbon and oxygen increases, due to the need for more energy to break the strong C=O and C-O bonds.

Step-by-step solution

Write the bond enthalpies associated with each reaction

First, we need to write down the bond enthalpies needed for each reaction: Average Bond Enthalpies (in kJ/mol): - C-F: \(488\) - C=O: \(805\) - C-O: \(360\) - F-F: \(159\) - O-F: \(190\)

Calculate reaction enthalpies using bond enthalpies

Now, we will use the given bond enthalpies to calculate the enthalpy change for each reaction: For Reaction (i): \[\Delta H_{i} = \text{Bonds broken} - \text{Bonds formed} \newline \Delta H_{i} = (\text{4 C-F bonds formed}) - (\text{0 bonds broken + 4 F-F bonds broken}) \newline \Delta H_{i} = (4 \times 488) - (4 \times 159) = \text{1316 kJ/mol}\] For Reaction (ii): \[\Delta H_{ii} = (\text{1 C=O bond broken + 3 F-F bonds broken}) - (\text{4 C-F bonds formed + 2 O-F bonds formed}) \newline \Delta H_{ii} = (805 + 3 \times 159) - (4 \times 488 + 2 \times 190) = -\text{556 kJ/mol}\] For Reaction (iii): \[\Delta H_{iii} = (\text{2 C-O bonds broken + 1 O=O bond broken + 4 F-F bonds broken}) - (4 \times \text{C-F bonds formed + 4 O-F bonds formed}) \newline \Delta H_{iii} = (2 \times 360 + 1 \times 498 + 4 \times 159) - (4 \times 488 + 4 \times 190) = -\text{676 kJ/mol}\]

Identify the most exothermic reaction

Comparing the reaction enthalpies, the most exothermic reaction is the one with the lowest (most negative) enthalpy change: Reaction (iii) is the most exothermic.

Explain the trend between reaction exothermicity and bonding to oxygen

The reaction exothermicity decreases as the number of bonds between carbon and oxygen increases. This is because breaking the strong C=O and C-O bonds consumes more energy, while forming new bonds only releases energy. The more carbon is bonded to oxygen, the higher the energy needed to break these bonds, leading to lower overall exothermic reactions.

Key concepts

Understanding Bond Enthalpy

Bond enthalpy, also known as bond energy, refers to the measure of the strength of a chemical bond. This value is crucial for predicting the heat change during chemical reactions.
It is defined as the energy required to break one mole of a bond in a molecule in the gas phase for diatomic molecules.
Average bond enthalpy values help us understand if a reaction is endothermic or exothermic.

• Bond Breaking: Bonds broken in reactants require energy input, thus it's an endothermic process.
• Bond Formation: Bonds formed in products release energy, making this an exothermic process.

By calculating the difference between the total bond energies of the broken bonds and the formed bonds, we can determine the enthalpy change of the reaction, \( \Delta H \). If more energy is released during the formation than absorbed during breaking, the reaction is exothermic. Otherwise, it's endothermic.

The Nature of Exothermic Reactions

Exothermic reactions are chemical processes that release energy, usually in the form of heat or light, to the surroundings.
This occurs when the energy required to break the initial bonds is less than the energy released when new bonds are formed.In terms of bond enthalpy:

• Reactions with a negative enthalpy change (\(\Delta H < 0\)) are exothermic.
• The greater the magnitude of the negative enthalpy, the more energy is released.

The reactions listed in the exercise indicate different degrees of exothermicity. For instance, when fewer or weaker initial bonds are broken compared to the bonds formed, as in Reaction (iii), more energy is released, indicating a more exothermic reaction.

Examining Carbon-Oxygen Bonds

Carbon-oxygen bonds, such as the double bond in carbon monoxide (C=O) or the single bond in carbon dioxide (C-O), are among the strongest types of chemical bonds.
This makes these bonds highly significant in reaction chemistry, primarily due to the energy they require for breaking.When carbon is involved in reactions where these bonds need to be severed, the \(\Delta H\) becomes significantly affected. For example:

• The C=O bond in CO has an enthalpy of about 805 kJ/mol, requiring substantial energy input if broken.
• As discussed in the Step 4 of the solution, reactions decrease in exothermicity as carbon forms more bonds with oxygen due to the increased energy needed for bond cleavage.

Thus, understanding the nature of C-O and C=O bonds helps predict the trend of exothermicity in reactions where these bonds play a crucial role.