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Chapter 5: Problem 112

The hydrocarbons cyclohexane $\left(\mathrm{C}_{6} \mathrm{H}_{12}(l), \Delta H_{f}^{\circ}=-156\right.$ \(\mathrm{kJ} / \mathrm{mol}\) ) and 1-hexene $\left(\mathrm{C}_{6} \mathrm{H}_{12}(l), \Delta H_{f}^{\circ}=-74 \mathrm{~kJ} / \mathrm{mol}\right)$ 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 or 1-hexene to have the larger combustion enthalpy?

Short Answer

Expert verified
(a) The standard enthalpy change for the transformation of cyclohexane to 1-hexene is 82 kJ/mol. (b) Cyclohexane has a greater enthalpy. (c) We can expect cyclohexane to have the larger combustion enthalpy compared to 1-hexene.

Step by step solution

01

Calculate the standard enthalpy change for the transformation

In order to calculate the standard enthalpy change for the transformation of cyclohexane to 1-hexene, use the standard enthalpy of formation values: \(\Delta H_{f}^{\circ}(\mathrm{C}_{6} \mathrm{H}_{12}(l))\) \[ \Delta H_{transformation} = \Delta H_f^{\circ} (1\text{-hexene}) - \Delta H_f^{\circ} (\text{cyclohexane}) \] Plug in the given values: \[ \Delta H_{transformation} = (-74 \,\mathrm{kJ/mol}) - (-156\, \mathrm{kJ/mol}) \]
02

Solve for the enthalpy change

Add the values to get the enthalpy change of the transformation: \[ \Delta H_{transformation} = 82\, \mathrm{kJ/mol} \] (a) The standard enthalpy change for the transformation of cyclohexane to 1-hexene is 82 kJ/mol.
03

Compare enthalpies

Compare the standard enthalpy of formation values provided in the exercise. We have: \[ \Delta H_f^{\circ} (\text{cyclohexane}) = -156\, \mathrm{kJ/mol} \] \[ \Delta H_f^{\circ} (1\text{-hexene}) = -74\, \mathrm{kJ/mol} \] A more negative enthalpy of formation indicates a more stable compound. (b) Since the enthalpy of formation of cyclohexane is more negative than that of 1-hexene, cyclohexane has a greater enthalpy.
04

Predict combustion enthalpy

Knowing that cyclohexane has greater enthalpy (more stable) and without calculating the actual combustion enthalpies, we can expect a more stable compound to release more energy upon combustion. (c) Therefore, we can expect cyclohexane to have the larger combustion enthalpy compared to 1-hexene.

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Most popular questions from this chapter

The heat of combustion of ethanol, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l),\( is -1367 \)\mathrm{kJ} / \mathrm{mol}$. A bottle of stout (dark beer) contains up to \(6.0 \%\) ethanol by mass. Assuming the density of the beer to be \(1.0 \mathrm{~g} / \mathrm{mL},\) what is the caloric content due to the alcohol (ethanol) in a bottle of beer \((500 \mathrm{~mL})\) ?

The gas-phase reaction shown, between \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\), was run in an apparatus designed to maintain a constant pressure. (a) Write a balanced chemical equation for the reaction depicted and predict whether \(w\) is positive, negative, or zero. (b) Using data from Appendix C, determine \(\Delta H\) for the formation of one mole of the product. [Sections 5.3 and 5.7\(]\)

(a) Use enthalpies of formation given in Appendix C to calculate \(\Delta H\) for the reaction \(\mathrm{Br}_{2}(g) \longrightarrow 2 \operatorname{Br}(g)\), and use this value to estimate the bond enthalpy \(D(\mathrm{Br}-\mathrm{Br})\). (b) How large is the difference between the value calculated in part (a) and the value given in Table 5.4 ?

Calculate \(\Delta E\) and determine whether the process is endothermic or exothermic for the following cases: \((\mathbf{a}) q=0.763 \mathrm{~kJ}\) and \(w=-840 \mathrm{~J}\). (b) A system releases \(66.1 \mathrm{~kJ}\) of heat to its surroundings while the surroundings do \(44.0 \mathrm{~kJ}\) of work on the system.

(a) What is the electrostatic potential energy (in joules) between an electron and a proton that are separated by \(230 \mathrm{pm}\) ? (b) What is the change in potential energy if the distance separating the electron and proton is increased to \(1.0 \mathrm{nm}\) ? (c) Does the potential energy of the two particles increase or decrease when the distance is increased to \(1.0 \mathrm{nm}\) ?
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