Problem 112 - Chemistry The Central Science In Si Units

Question

The hydrocarbons cyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{12}(I), \Delta H_{i}^{\circ}=-156\right.\) \(\mathrm{kJ} / \mathrm{mol}\) ) and 1 -hexene \(\left.\left(\mathrm{C}_{6} \mathrm{H}_{12}(I), \Delta H_{f}^{\circ}=-74 \mathrm{k}\right] / \mathrm{mol}\right)\) have the same empirical formula. (a) Calculate the standard enthalpy change for the transformation of cyclohexane to 1-hexene. (b) Which has greater enthalpy, cyclohexane or 1 -hexene? (c) Without doing a further calculation and knowing the answer to (b), do you expect cyclohexane of 1-hexene to have the larger combustion enthalpy?

Step-by-Step Solution

Answer

(a) +82 kJ/mol; (b) 1-hexene has greater enthalpy; (c) Cyclohexane has a larger combustion enthalpy.

Step 1: Write Down Given Information

We are given the standard enthalpies of formation for cyclohexane, \(\Delta H_{i}^{\circ} = -156\, \text{kJ/mol}\), and for 1-hexene, \(\Delta H_{f}^{\circ} = -74\, \text{kJ/mol}\). Both have the same molecular formula \(\mathrm{C}_{6}\mathrm{H}_{12}\).

Step 2: Calculate Enthalpy Change for Conversion

The standard enthalpy change for the conversion from cyclohexane to 1-hexene is given by the equation \[ \Delta H_{\text{reaction}} = \Delta H_{f}^{\circ}(\text{products}) - \Delta H_{f}^{\circ}(\text{reactants}). \] Here, the product is 1-hexene, and the reactant is cyclohexane. Therefore, \[ \Delta H_{\text{reaction}} = (-74\, \text{kJ/mol}) - (-156\, \text{kJ/mol}) = +82\, \text{kJ/mol}. \]

Step 3: Compare Enthalpies of Cyclohexane and 1-Hexene

Since the enthalpy change for conversion from cyclohexane to 1-hexene is positive, \(+82\, \text{kJ/mol}\), 1-hexene has greater enthalpy than cyclohexane.

Step 4: Predict Combustion Enthalpies

Without further calculations, knowing that 1-hexene has greater enthalpy than cyclohexane, one would expect cyclohexane to have a larger (more negative) combustion enthalpy. This is because combustion enthalpy is greater for compounds with initially lower enthalpy values.

Key Concepts

Standard Enthalpies of Formation

The concept of standard enthalpies of formation is crucial when analyzing chemical reactions. It refers to the heat change that occurs when one mole of a compound is formed from its elements in their standard states. This value is usually expressed as \(\Delta H_f^\circ\), and it is typically measured in kilojoules per mole (kJ/mol). These values are essential because they allow us to predict how much energy is absorbed or released during a reaction. In our example, cyclohexane has a standard enthalpy of formation \(\Delta H_f^\circ = -156\, \text{kJ/mol}\), and 1-hexene has \(\Delta H_f^\circ = -74\, \text{kJ/mol}\). These values signify that both compounds release energy when they form from their elements. By comparing these enthalpy values, we can understand the energy relationships in the conversion of cyclohexane to 1-hexene.

Hydrocarbons

Hydrocarbons are organic compounds composed entirely of hydrogen and carbon atoms. They serve as fundamental building blocks in organic chemistry. Common forms of hydrocarbons include alkanes, alkenes, and alkynes, each classified based on the types of bonds present between carbon atoms.- **Alkanes**: Single bonds between carbon atoms, e.g., cyclohexane.- **Alkenes**: One or more double bonds between carbon atoms, e.g., 1-hexene.- **Alkynes**: At least one triple bond between carbon atoms.Cyclohexane and 1-hexene are important hydrocarbons with the same molecular formula \(\mathrm{C}_{6}\mathrm{H}_{12}\). Cyclohexane is an alkane with no double bonds, while 1-hexene is an alkene with a single double bond. The presence of a double bond in 1-hexene increases its energy content compared to cyclohexane.

Combustion Enthalpy

Combustion enthalpy refers to the amount of heat released when a substance undergoes complete combustion with oxygen. It is an essential concept for understanding energy release during processes like burning fuels.Generally, substances with lower initial enthalpy values tend to have more negative combustion enthalpies, meaning they release more energy. In the case of cyclohexane and 1-hexene, knowing that cyclohexane has a lower initial enthalpy \((-156 \, \text{kJ/mol})\) compared to 1-hexene \((-74 \, \text{kJ/mol})\), we can reasonably expect cyclohexane to possess a larger (more negative) combustion enthalpy. This higher negative value indicates it releases more energy upon combustion, making it a more potent fuel source.

Conversion Reaction

A conversion reaction involves the transformation of one chemical compound into another, often with significant changes in their energy states. The enthalpy change of a conversion reaction can be calculated by subtracting the enthalpy of formation of the reactants from the products. For example, to convert cyclohexane to 1-hexene, we take the difference between their standard enthalpies of formation:\[ \Delta H_{\text{reaction}} = \Delta H_f^\circ(\text{1-hexene}) - \Delta H_f^\circ(\text{cyclohexane}) \]By plugging in the values: \[ \Delta H_{\text{reaction}} = (-74 \, \text{kJ/mol}) - (-156 \, \text{kJ/mol}) = +82 \, \text{kJ/mol} \]This positive enthalpy change indicates that the conversion from cyclohexane to 1-hexene requires energy input, making it an endothermic process. Understanding conversion reactions helps in predicting reaction behavior and potential energy requirements or releases.