Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium

Problem 78d

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Chapter 18, Problem 78d

For the vaporization of benzene, ∆H_vap = 30.7 kJ/mol and ∆S_vap = 87.0 J/(K*mol). Does benzene boil at 70 °C and 1 atm pressure? Calculate the normal boiling point of benzene.

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Convert the given temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.

Use the Gibbs free energy equation for phase changes: \( \Delta G = \Delta H - T \Delta S \).

Substitute the given values into the equation: \( \Delta H_{vap} = 30.7 \text{ kJ/mol} \) and \( \Delta S_{vap} = 87.0 \text{ J/(K*mol)} \). Remember to convert \( \Delta H_{vap} \) to J/mol to match the units of \( \Delta S_{vap} \).

Calculate \( \Delta G \) at 70 °C (converted to Kelvin) to determine if it is zero, which indicates boiling at that temperature.

To find the normal boiling point, set \( \Delta G = 0 \) and solve for \( T \) using the equation \( T = \frac{\Delta H_{vap}}{\Delta S_{vap}} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the spontaneity of a process at constant temperature and pressure. The change in Gibbs Free Energy (∆G) is calculated using the equation ∆G = ∆H - T∆S, where ∆H is the change in enthalpy, T is the temperature in Kelvin, and ∆S is the change in entropy. A process is spontaneous when ∆G is negative, which is crucial for determining boiling points.

Boiling Point

The boiling point of a substance is the temperature at which its vapor pressure equals the external pressure surrounding the liquid. At this point, the liquid can transition to a gas phase. For a substance to boil at a given temperature, the Gibbs Free Energy change must be zero (∆G = 0), indicating equilibrium between the liquid and vapor phases.

Phase Changes and Thermodynamics

Phase changes, such as vaporization, involve energy changes that can be quantified using enthalpy (∆H) and entropy (∆S). The relationship between these quantities helps determine the conditions under which a substance will change phases. For vaporization, the enthalpy change represents the energy required to convert a mole of liquid to gas, while the entropy change reflects the increase in disorder associated with this transition.

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Related Practice

Textbook Question

Phosphorus pentachloride forms from phosphorus trichloride and chlorine:

(a) Use data in Appendix B to calculate ∆S_sys, ∆S_surr, and ∆S_total for this reaction. Is the reaction spontaneous under standard-state conditions at 25 °C?

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Textbook Question

Phosphorus pentachloride forms from phosphorus trichloride and chlorine: PCl₃(g) + Cl₂(g) → PCl₅(g) (b) Estimate the temperature at which the reaction will become nonspontaneous.

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Textbook Question

For the vaporization of benzene, ∆H_vap = 30.7 kJ/mol and ∆S_vap = 87.0 J/(K*mol). Calculate ∆S_surr and ∆S_total at: (a) 70 °C

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Textbook Question

For the melting point of sodium chloride, ΔHfusion = 28.16 kJ/mol and ΔSfusion = 26.22 J/(K·mol). Does NaCl melt at 1100 K? Calculate the melting point of NaCl.

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Textbook Question

The entropy change for a certain nonspontaneous reaction at 50 °C is 104 J/K. (a) Is the reaction endothermic or exothermic? (b) What is the minimum value of ∆H (in kJ) for the reaction?