Gasoline is composed primarily of hydrocarbons, including many with eight carbon atoms, called octanes. One of the cleanest–burning octanes is a compound called 2,3,4- trimethylpentane, which has the following structural formula: The complete combustion of one mole of this compound to CO₂(g) and H₂O(g) leads to ΔH° = -5064.9 kJ. (b) By using the information in this problem and data in Table 5.3, calculate H°f for 2,3,4-trimethylpentane.

Verified step by step guidance

1. Identify the balanced chemical equation for the complete combustion of 2,3,4-trimethylpentane: C_8H_{18} + \frac{25}{2}O_2 \rightarrow 8CO_2 + 9H_2O.
2. Use the standard enthalpy of formation (\Delta H_f^\circ) values from Table 5.3 for CO_2(g) and H_2O(g) to calculate the total \Delta H_f^\circ for the products.
3. Recall that the standard enthalpy change of the reaction (\Delta H_{rxn}^\circ) is given by: \Delta H_{rxn}^\circ = \sum \Delta H_f^\circ (products) - \sum \Delta H_f^\circ (reactants).
4. Substitute the known \Delta H_{rxn}^\circ value (-5064.9 kJ) and the calculated \Delta H_f^\circ for the products into the equation to solve for \Delta H_f^\circ of 2,3,4-trimethylpentane.
5. Rearrange the equation to isolate \Delta H_f^\circ for 2,3,4-trimethylpentane and solve for its value.

Key Concepts

Combustion Reactions

Combustion reactions involve the reaction of a substance with oxygen, producing heat and light. In organic chemistry, complete combustion of hydrocarbons results in carbon dioxide (CO2) and water (H2O) as products. Understanding the stoichiometry of these reactions is essential for calculating energy changes, such as enthalpy changes (ΔH), which indicate the heat released or absorbed during the reaction.

Enthalpy of Formation (H°f)

The enthalpy of formation (H°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, allowing chemists to calculate the energy changes associated with chemical reactions. By using Hess's law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for individual steps, one can derive the H°f for compounds from known enthalpy values.

Hess's Law

Hess's Law states that the total enthalpy change for a chemical reaction is the same, regardless of the pathway taken, as long as the initial and final conditions are the same. This principle allows for the calculation of enthalpy changes by combining known enthalpy values from related reactions. In the context of the question, Hess's Law can be applied to determine the enthalpy of formation for 2,3,4-trimethylpentane by using the enthalpy change from its combustion and the enthalpies of formation of the products.