Question

Determine \(\Delta \mathrm{H}^{\circ}\) for the following reaction of buming ethy1 alcohol in oxygen: \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)+3 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2} \mathrm{O}(\ell)\) \(\Delta \mathrm{H}^{\circ} \mathrm{f}\) of \(\mathrm{C}_{2} \mathrm{H}_{2} \mathrm{OH}(\ell)=-65.9 \mathrm{Kcal} / \mathrm{mole}\) \(\Delta \mathrm{H}^{\circ} \mathrm{f}\) of \(\mathrm{CO}_{2}(\mathrm{~g})=-94.1 \mathrm{Kcal} / \mathrm{mole}\) \(\Delta \mathrm{H}^{\circ} \mathrm{f}\) of \(\mathrm{H}_{2} \mathrm{O}(\ell)=-68.3 \mathrm{Kcal} / \mathrm{mole}\)

Short answer

The enthalpy change (ΔH°) for the given reaction of burning ethyl alcohol in oxygen is -327.2 kcal.

Step-by-step solution

Identify the reactants and products

In the given reaction, the reactants are ethyl alcohol (C2H5OH(ℓ)) and oxygen (O2(g)), while the products are carbon dioxide (CO2(g)) and water (H2O(ℓ)).

Write out the enthalpy of formation values

We are given the ΔH°f values for each compound involved in the reaction: ΔH°f of C2H5OH(ℓ) = -65.9 kcal/mole ΔH°f of CO2(g) = -94.1 kcal/mole ΔH°f of H2O(ℓ) = -68.3 kcal/mole (Note: The ΔH°f of O2(g) is zero because it is an element in its standard state.)

Apply the stoichiometric coefficients and calculate the sums of enthalpy of formation

Multiply the ΔH°f values of the products by their stoichiometric coefficients, and add them together. Then, do the same for the reactants. Sum for products: 2 × ΔH°f of CO2(g) + 3 × ΔH°f of H2O(ℓ) = 2 × (-94.1) + 3 × (-68.3) = -188.2 - 204.9 = -393.1 kcal Sum for reactants: 1 × ΔH°f of C2H5OH(ℓ) + 3 × ΔH°f of O2(g) = 1 × (-65.9) + 3 × (0) = -65.9 kcal

Calculate ΔH° for the reaction

Subtract the sum of reactants' enthalpy of formation values from the sum of products' enthalpy of formation values: ΔH° = Σ (ΔH°f(products)) - Σ (ΔH°f(reactants)) = -393.1 - (-65.9) = -327.2 kcal The enthalpy change (ΔH°) for the given reaction of burning ethyl alcohol in oxygen is -327.2 kcal.

Key concepts

Enthalpy of Formation

Enthalpy of formation, represented as \( \Delta H_f^\circ \), is the change in enthalpy when one mole of a compound is formed from its elements under standard conditions. These conditions are typically set at 298 K temperature and 1 atm pressure, and all substances are in their standard states. Each compound has a unique \( \Delta H_f^\circ \) value, which reflects how much energy is released or absorbed during its formation.

Elements in their most stable form, like \( O_2(g) \) for oxygen, have a formation enthalpy of zero because they are already in a stable state. This is important to consider when calculating reaction enthalpies. For instance, in the exercise, \( \Delta H_f^\circ \) of \( O_2(g) \) is zero because it's an elemental state in standard conditions. By understanding the construction of molecules from elemental forms, learners can appreciate how energy transformations occur in chemical processes.

Combustion Reaction

Combustion reactions are exothermic chemical reactions that typically involve oxygen and produce heat and light. These reactions are characterized by the burning of a substance, often a hydrocarbon or organic compound, in the presence of oxygen. The general equation is \( \text{Fuel} + O_2 \rightarrow \text{Products} \), which often includes \( CO_2 \) and \( H_2O \) as products.

In the context of the exercise, ethyl alcohol \( (C_2H_5OH) \) reacts with oxygen, forming carbon dioxide and water. The combustion of organic compounds typically releases a large amount of energy, observable as the enthalpy change \( \Delta H \) is negative, indicating an exothermic reaction. Combustion reactions not only show the transfer of energy but also serve as a model to understand reactions' energy dynamics and air-fuel chemistry.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It is derived from the balanced chemical equation, which provides the mole ratio of reactants to products. Understanding stoichiometry is crucial for computing amounts involved in a reaction, allowing chemists to predict how much of each substance is consumed or generated.

Using stoichiometry in the exercise, we applied coefficients from the balanced equation to determine the overall change in enthalpy. For instance, the stoichiometric coefficient for \( CO_2 \) is 2, which scales its \( \Delta H_f^\circ \) value, reflecting the stoichiometric impact on energy changes. This fundamental concept ensures accurate predictions and optimizations in chemical processes, from laboratory experiments to industrial applications.

Chemical Energetics

Chemical energetics is the study of energy changes associated with chemical reactions. It examines how heat, work, and energy flow are affected by chemical processes. Enthalpy change \( \Delta H \) is a key component, indicating whether a reaction is endothermic (absorbing heat) or exothermic (releasing heat).

The exercise illustrates an exothermic reaction, with a negative \( \Delta H \) value, meaning energy is released as ethyl alcohol combusts. This concept helps in understanding the efficiency and viability of reactions, guiding decisions in choosing reactions for energy production or chemical synthesis.

By analyzing such changes, chemists can develop more sustainable processes, optimize reaction conditions, and better understand the fundamental principles that drive chemical reactions, empowering innovative solutions across scientific fields.