Problem 70 - Chemistry: The Central Science

Question

(a) Use bond enthalpies to estimate the enthalpy change for the reaction of hydrogen with ethene: $$\mathrm{H}_{2}(g)+\mathrm{C}_{2} \mathrm{H}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)$$ (b) Calculate the standard enthalpy change for this reaction, using heats of formation. Why does this value differ from that calculated in (a)?

Step-by-Step Solution

Answer

The enthalpy change using bond enthalpies is estimated to be \(-682\:kJ/mol\), indicating an exothermic reaction. However, when using standard heats of formation, the enthalpy change is calculated to be \(-136.4\:kJ/mol\). The difference between these values is due to bond enthalpies being average values, while heats of formation are specific to the molecule and provide a more accurate estimation.

Step 1: Determine bond enthalpies of reactants and products

We will break down the given reaction into its bond enthalpies. We need to find the bond enthalpies of the reactants and products. The values are as follows: - H-H bond in H2(g): \(436\:kJ/mol\) - C-H bond in C2H4(g): \(413\:kJ/mol\) - C=C bond in C2H4(g): \(612\:kJ/mol\) - C-H bond in C2H6(g): \(413\:kJ/mol\) - C-C bond in C2H6(g): \(347\:kJ/mol\)

Step 2: Calculate the enthalpy change using bond enthalpies

We will now use the bond enthalpies to estimate the enthalpy change of the reaction: ΔH = [(bond enthalpies of products) - (bond enthalpies of reactants)] ΔH = [(6 × C-H bond in C2H6(g) + 1 × C-C bond in C2H6(g)) - (1 × H-H bond in H2(g) + 4 × C-H bond in C2H4(g) + 1 × C=C bond in C2H4(g))] = [\(6 \times 413 + 1 \times 347 \) - (436 + 4 \times 413 + 612)] = [2820 - 3502] ΔH = \(-682\:kJ/mol\)

Step 3: Interpret the result

The estimated enthalpy change of the reaction, using bond enthalpies, is -682 kJ/mol. This means that the reaction is exothermic, releasing energy into the surroundings. (b) Calculate the standard enthalpy change using heats of formation

Step 1: Determine standard heats of formation

We need to find the standard heats of formation (ΔH°f) of the reactants and products involved in the reaction: - H2(g): \(0\:kJ/mol\) - C2H4(g): \(+52.4\:kJ/mol\) - C2H6(g): \(-84.0\:kJ/mol\)

Step 2: Calculate the standard enthalpy change using heats of formation

We will now use the standard heats of formation to estimate the enthalpy change of the reaction: ΔH° = [(heats of formation of products) - (heats of formation of reactants)] ΔH° = [(1 × ΔH°f of C2H6(g)) - (1 × ΔH°f of H2(g) + 1 × ΔH°f of C2H4(g))] = [(-84.0) - (0 + 52.4)] ΔH° = \(-136.4\:kJ/mol\)

Step 3: Interpret the result and explain the difference

The standard enthalpy change of the reaction, using heats of formation, is -136.4 kJ/mol. This result is also exothermic but has a lower magnitude compared to the bond enthalpy estimation. The difference between the two methods is because bond enthalpy values are average values for a specific bond type. Bond enthalpies do not account for the precise molecular environment in which the bond exists. On the other hand, heats of formation are specific to the molecule and provide a more accurate estimation of the enthalpy change.

Key Concepts

Bond Enthalpies

When dealing with chemical reactions, especially in gas-phase reactions like the one combining hydrogen and ethene to form ethane, bond enthalpies can offer a useful way to estimate the reaction's enthalpy change. Bond enthalpy, also known as bond dissociation energy, refers to the energy required to break one mole of a particular type of bond in a molecule. This value is typically measured in kilojoules per mole (kJ/mol). In our exercise, we use bond enthalpies to discern how much energy is absorbed or released during the breaking and forming of bonds as the reaction proceeds from reactants to products.

Since each molecule can have different bonds, we need to calculate the total energy for both the reactants and the products:

• Breaking bonds: Energy is required to break chemical bonds in the reactants.
• Forming bonds: Energy is released when new bonds form in the products.

By using bond enthalpy values, you can estimate the energy change (∆H) of a reaction by subtracting the total energy of the bonds formed from the total energy of the bonds broken. Using these values for the given reaction yields a negative result, indicating an exothermic process where energy is released to the surroundings.

Standard Enthalpy of Formation

The standard enthalpy of formation provides a more precise way of calculating a chemical reaction's energy change. This approach considers the standard states of reactants and products at 1 atm pressure and 25°C. The data are curated for specific elements and compounds. The standard enthalpy of formation, ΔH°f, refers to the change in enthalpy when one mole of a compound is formed from its constituent elements in their standard states.

Applying this concept involves finding the difference between the heats of formation of products and reactants:

• Standard Heat of Formation for products: the enthalpy change when the product is formed from its elements.
• Standard Heat of Formation for reactants: the enthalpy change when each reactant is formed from its elements.

This calculation is straightforward and typically provides a more accurate measure of the energy changes in reactions compared to using bond enthalpies. This method considers the energies specifically assigned to the molecular structure in question, offering a reliable estimation for enthalpy changes. It accounts for the environment of the molecules better than bond enthalpies, which is why results can differ between the two methods.

Exothermic Reaction

In chemical thermodynamics, an exothermic reaction is one that releases energy into the surroundings, typically in the form of heat. This occurs because the energy needed to break old bonds in the reactants is less than the energy released when new bonds are formed in the products.

As seen in our exercise, both methods — using bond enthalpies and standard enthalpies of formation — conclude that the reaction is exothermic. The negative ∆H calculated indicates that the overall process releases energy, confirming the exothermic nature.

Understanding whether a reaction is exothermic or not has practical applications:

• It informs us about the feasibility and spontaneity of reactions under certain conditions.
• It helps in designing industrial processes, where heat management is crucial.
• Energy release informs safety considerations, as exothermic reactions can sometimes lead to conditions like runaway reactions.

In essence, knowing whether a reaction is exothermic is a cornerstone for both academic studies and practical applications in chemical engineering and environmental sciences.