Problem 73 - Chemistry: The Central Science

Question

Complete combustion of 1 mol of acetone \(\left(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}\right)\) liberates \(1790 \mathrm{~kJ}\) : $$ \begin{aligned} \mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}(l)+4 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+3 & \mathrm{H}_{2} \mathrm{O}(l) \\ & \Delta H^{\circ}=-1790 \mathrm{~kJ} \end{aligned} $$ Using this information together with data from Appendix \(C\), calculate the enthalpy of formation of acetone.

Step-by-Step Solution

Answer

The enthalpy of formation of acetone is calculated using Hess's Law and the given information: the enthalpy change for the complete combustion of 1 mole of acetone and the enthalpy changes of formation for carbon dioxide and water. Following the steps and substituting the known values into the Hess's Law equation, the enthalpy of formation of acetone is found to be \( -247.9 \, kJ/mol \).

Step 1: Identify given data and needed formula

Notice that the enthalpy change for the complete combustion of 1 mole of acetone (\(-1790 \, kJ\)) is given. The chemical reaction is given as \[ \mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}(l)+4 \mathrm{O}_{2}(g)\longrightarrow 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l) \] It is known that \( \Delta H_{\text{formation}}\) for carbon dioxide and water, are -393.5 \,kJ/mol and -285.8 \,kJ/mol respectively. Required calculation: the enthalpy of formation of acetone. Hess's Law will be used for this calculation, as it states that the total enthalpy change of a chemical reaction is the sum of the enthalpy changes of the individual steps.

Step 2: Apply Hess's Law

Hess's Law can be applied in the form of the equation: \[ \Delta H_{\text{reaction}} = \sum n\Delta H_{\text{formation products}} - \sum m\Delta H_{\text{formation reactants}} \] where \( \Delta H_{\text{reaction}} \) is the enthalpy change for the reaction (which is -1790 kJ in this case), \( \Delta H_{\text{formation products}} \) and \( \Delta H_{\text{formation reactants}} \) are the enthalpy changes of formation for the products and reactants respectively, and \( n \) and \( m \) are the stoichiometric coefficients in the balanced chemical equation. The enthalpy changes of formation for the products (carbon dioxide and water) are given as -393.5 kJ/mol and -285.8 kJ/mol respectively. And we are asked to find the enthalpy of formation for the reactant (acetone)

Step 3: Substitute the known quantities into the equation

Substituting the known values into the equation for Hess's law gives: \[ -1790\, kJ = [(3 mol \cdot -393.5\, kJ/mol) + (3 mol \cdot-285.8\, kJ/mol)] - [1 mol \cdot \Delta H_f(\text{acetone})] \]

Step 4: Solve for the unknown

Solving for \( \Delta H_f(\text{acetone}) \) gives: \[ -1790\, kJ = [-1180.5\, kJ + -857.4 \, kJ] - [1 mol \cdot \Delta H_f(\text{acetone})] \] \[ -1790\, kJ = -2037.9\, kJ - \Delta H_f(\text{acetone}) \] Bringing \( \Delta H_f(\text{acetone}) \) to the other side and adding the values: \[ \Delta H_f(\text{acetone}) = -2037.9\, kJ + 1790\, kJ \] You get: \[ \Delta H_f(\text{acetone}) = -247.9 \, kJ \] So the enthalpy of formation of acetone is \( -247.9 \, kJ/mol \)

Key Concepts

Hess's Law

Hess's Law is a fundamental concept in chemical thermodynamics that provides a path-independent means to calculate the change in enthalpy (heat change) of a chemical reaction. Essentially, it states that the total enthalpy change for a chemical reaction is the same, regardless of the number of steps taken to perform the reaction.
Hess's Law is particularly useful when the direct determination of heat change during a reaction is difficult. By breaking down a complex reaction into multiple simpler steps, whose enthalpies are known, one can sum up these individual changes to determine the overall enthalpy change.

Applying Hess's Law

To effectively apply Hess's Law in calculations, it is essential to use known enthalpies of formation or combustion. The law acts as a balancing scale, where the sum of enthalpies on the reactant side is set equal to the sum on the product side, taking into account the stoichiometry of the balanced chemical reaction. Conveniently, we can manipulate this balance to solve for the unknown enthalpy of a component in the reaction, as long as all other enthalpy values are known.

Complete Combustion

Complete combustion refers to a chemical process in which a fuel reacts with an excess of oxygen to produce carbon dioxide, water, and energy, typically in the form of heat. It's characterized by the efficient use of fuel, resulting in minimal leftover reactants and the absence of byproducts like carbon monoxide or soot, which are often produced in incomplete combustion.

Characteristics of Complete Combustion

• A sufficient supply of oxygen is available.
• Complete conversion of reactants into products.
• Higher energy output compared to incomplete combustion.

When discussing the complete combustion of a substance like acetone in a homework problem, it's implicit that there's enough oxygen present for the reaction to go to completion. This assumption allows for the calculation of precise enthalpy changes associated with the combustion process, making it easier to apply concepts like Hess's Law.

Chemical Thermodynamics

Chemical thermodynamics is the branch of science that deals with the study of energy changes accompanying chemical and physical processes. It’s an extensive field that combines principles from both chemistry and physics to predict the direction of spontaneous processes, understand the energy aspects of reactions, and calculate the quantities such as the enthalpy, entropy, and Gibbs free energy.
Key concepts include the first law of thermodynamics (conservation of energy), the second law (entropy), and the third law (absolute zero entropy). Chemical thermodynamics provides the theoretical foundation for making crucial decisions in fields such as the design of chemical processes, evaluation of reaction feasibility, and understanding of energy exchange.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It reflects the conservation of mass and the fixed proportions in which chemicals react. Stoichiometry hinges on the balanced chemical equation, which provides the ratio in which compounds combine and react, usually represented by coefficients indicating the number of moles in the reaction.

Importance of Stoichiometry

Stoichiometry is vital for quantitative predictions in chemistry. Without it, scientists and engineers would not be able to:

• Calculate the amount of reactants needed to produce a desired amount of product.
• Determine the yield from a reaction based on available reactants.
• Scale up reactions from a laboratory to an industrial scale.

In the context of calculating enthalpy changes and applying Hess's Law, stoichiometry enables us to use the balanced chemical equation to relate the change in enthalpy of the reaction to the enthalpy of formation of each individual substance involved in that reaction.