Complete combustion of 1 mol of acetone (C₃H₆O) liberates 1790 kJ: C₃H₆O(l) + 4 O₂(g) → 3 CO₂(g) + 3 H₂O(l) ΔH° = -1790 kJ Using this information together with the standard enthalpies of formation of O₂(g), CO₂(g), and H₂O(l) from Appendix C, calculate the standard enthalpy of formation of acetone.

Verified step by step guidance

1. Identify the given reaction and the enthalpy change: C_3H_6O(l) + 4 O_2(g) → 3 CO_2(g) + 3 H_2O(l) with ΔH° = -1790 kJ.
2. Recall that the standard enthalpy change of a reaction (ΔH°_rxn) is calculated using the formula: ΔH°_rxn = ΣΔH°_f(products) - ΣΔH°_f(reactants).
3. List the standard enthalpies of formation (ΔH°_f) for the products and reactants: ΔH°_f[CO_2(g)] = -393.5 kJ/mol, ΔH°_f[H_2O(l)] = -285.8 kJ/mol, and ΔH°_f[O_2(g)] = 0 kJ/mol (since O_2 is in its standard state).
4. Set up the equation using the enthalpy of formation values: -1790 kJ = [3(-393.5) + 3(-285.8)] - [ΔH°_f[C_3H_6O(l)] + 4(0)].
5. Solve for the standard enthalpy of formation of acetone (ΔH°_f[C_3H_6O(l)]) by rearranging the equation and performing the necessary arithmetic operations.

Key Concepts

Standard Enthalpy of Formation

The standard enthalpy of formation (ΔH°f) is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. It is a crucial concept in thermodynamics, as it allows for the calculation of the energy changes associated with chemical reactions. The values are typically tabulated and can be used to determine the enthalpy changes for reactions using Hess's law.

Hess's Law

Hess's Law states that the total enthalpy change for a chemical reaction is the same, regardless of the number of steps taken to achieve the reaction. This principle allows chemists to calculate the enthalpy change of a reaction by using known enthalpy changes of other reactions. In the context of the question, it enables the calculation of the standard enthalpy of formation of acetone by using the enthalpy of combustion and the enthalpies of formation of the products.

Combustion Reaction

A combustion reaction is a chemical reaction that typically involves a hydrocarbon reacting with oxygen to produce carbon dioxide and water, releasing energy in the form of heat. In this case, the complete combustion of acetone is represented by the given reaction, which provides the enthalpy change associated with the process. Understanding the stoichiometry of combustion reactions is essential for calculating energy changes and determining the enthalpy of formation of reactants.