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.

검증된 단계별 안내

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.

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.

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).

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.

Rearrange the equation to isolate \(\Delta\) H_f^\(\circ\) for 2,3,4-trimethylpentane and solve for its value.

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주요 개념

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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.