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

Problem 78d

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.

Verified step by step guidance

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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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?