Question

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

Short answer

The enthalpy change for the reaction of hydrogen with ethene using bond enthalpies is -958 kJ/mol, while using standard enthalpy of formations, it is -137 kJ/mol. The difference in values is because bond enthalpies provide an estimate using average values from various molecules, while heats of formation are specific values for a particular substance, giving more accurate results.

Step-by-step solution

Write the reaction and identify the bonds involved

The given reaction is: \[\mathrm{H}_{2}(g)+\mathrm{C}_{2} \mathrm{H}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)\] We need to identify the bonds involved in this reaction and their respective enthalpies. The bonds involved are: 1. H-H bond in hydrogen molecule 2. C=C bond in ethene 3. C-H bond in ethene 4. C-C bond in ethane 5. C-H bond in ethane +

Calculate the enthalpy change using bond enthalpies

To calculate the enthalpy change, we need to find the difference in bond enthalpies of the bonds broken and the bonds formed. The enthalpy change, ΔH, can be calculated as: ΔH = Σ (Bond enthalpies of bonds broken) - Σ (Bond enthalpies of bonds formed) Using standard bond enthalpies, we have: - H-H bond: 436 kJ/mol - C=C bond: 612 kJ/mol - C-H bond in ethene: 413 kJ/mol (2 C-H bonds in ethene) - C-C bond in ethane: 348 kJ/mol - C-H bond in ethane: 414 kJ/mol (6 C-H bonds in ethane) Now, let's apply the formula to find the enthalpy change: ΔH = [(1 × 436) + (1 × 612) + (2 × 413)] - [(1 × 348) + (6 × 414)] ΔH = (436 + 612 + 826) - (348 + 2484) ΔH = 1874 - 2832 ΔH = -958 kJ/mol The enthalpy change for the reaction calculated using bond enthalpies is -958 kJ/mol. #PART B: Using Standard Enthalpy of Formation# +

Write the reaction and find the heats of formation

The given reaction is: \[\mathrm{H}_{2}(g)+\mathrm{C}_{2} \mathrm{H}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)\] We need to find the heats of formations for all the substances involved in this reaction. The standard heats of formation (ΔHf°) values are as follows: - H2(g): 0 kJ/mol (element in its standard state) - C2H4(g): +52.3 kJ/mol - C2H6(g): -84.7 kJ/mol +

Calculate the standard enthalpy change using heats of formation

To find the standard enthalpy change for the reaction, use the following formula: ΔH° = Σ (ΔHf° of products) - Σ (ΔHf° of reactants) Now, let's apply the formula: ΔH° = [(1 × -84.7)] - [(1 × 0) + (1 × 52.3)] ΔH° = -84.7 - 52.3 ΔH° = -137 kJ/mol The standard enthalpy change for the reaction calculated using heats of formation is -137 kJ/mol. #Comparing the results and discussing the difference# The enthalpy change calculated using bond enthalpies is -958 kJ/mol, while using standard enthalpy of formations we get -137 kJ/mol. The values are different because in reality, bond enthalpies are average values obtained from a variety of molecules, while heats of formation are specific values for a particular substance. Hence, using bond enthalpies can provide an estimate, and not an exact value, of the enthalpy change for the reaction. In contrast, standard heats of formation offer more specific and accurate values for the enthalpy changes.

Key concepts

Bond Enthalpies

In the context of chemical reactions, bond enthalpies refer to the energy required to break a bond in a molecule into its constituent atoms. These energies are a vital part of calculating the enthalpy change (ΔH) for reactions. Bond enthalpies are particularly useful as they give us an estimate of the energy changes during a reaction.

The calculation is straightforward: sum the bond enthalpies of all the bonds broken in the reactants and subtract from that the sum of the bond enthalpies of all the bonds formed in the products. However, it's important to keep in mind that these values are average bond energies, often derived from a range of compounds, and so they provide a good approximation rather than an exact value. In educational materials, we ensure that students understand that the bond enthalpy values may lead to slight inaccuracies compared to experimentally obtained enthalpy changes.

Standard Enthalpy of Formation

The standard enthalpy of formation, denoted as ΔHf°, measures the heat change that occurs when one mole of a compound is formed from its elements in their standard states. These values are essential to chemists as they enable the calculation of the heat absorbed or released during a reaction under standard conditions (typically 298 K and 1 atm pressure).

When looking at a chemical equation, the standard enthalpy change for the reaction can be calculated by summing up the standard enthalpies of formation of the products and subtracting those of the reactants. The standard enthalpy of formation of any element in its most stable form is zero because there is no change involved in forming an element from itself.

Heat of Formation

The term 'heat of formation' is often used interchangeably with 'standard enthalpy of formation'. It represents the energy change associated with the formation of a substance from its constituent elements under standard conditions. This value is crucial for understanding chemical reaction energetics because it allows us to predict whether a reaction will release heat (exothermic) or absorb heat (endothermic).

It is crucial for students to appreciate the practical significance of the heat of formation, as it is used to calculate the energy content of fuels, food, and other substances. By using these standardized values, one can anticipate the energy required for chemical processes and the potential energy available for work.

Chemical Reaction Energetics

Chemical reaction energetics describe the energy changes that occur during chemical reactions. They encompass the concepts of bond enthalpies and standard enthalpy of formation to determine whether a reaction is endothermic (absorbs heat) or exothermic (releases heat).

Diving deeper into chemical energetics, terms such as 'enthalpy', 'entropy', and 'Gibbs free energy' become important. Entropy measures disorder within a system, and Gibbs free energy combines enthalpy and entropy to predict whether a reaction will proceed spontaneously. Understanding the basics of these concepts is foundational for students as they explore the driving forces behind chemical reactions and learn to predict the direction and conditions under which reactions will occur.