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Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium
Chapter 18, Problem 126a

Trouton's rule says that the ratio of the molar heat of vaporization of a liquid to its normal boiling point (in kelvin) is approximately the same for all liquids: ∆Hvap/Tbp ≈ 88 J/(K*mol) (a) Check the reliability of Trouton's rule for the liquids listed in the following table.

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Trouton's rule states that the ratio of the molar heat of vaporization (\( \Delta H_{\text{vap}} \)) to the normal boiling point in Kelvin (\( T_{\text{bp}} \)) is approximately 88 J/(K*mol) for many liquids.
Collect the molar heat of vaporization (\( \Delta H_{\text{vap}} \)) and the normal boiling point (\( T_{\text{bp}} \)) in Kelvin for each liquid from the provided table.
For each liquid, calculate the ratio \( \frac{\Delta H_{\text{vap}}}{T_{\text{bp}}} \) using the values obtained from the table.
Compare the calculated ratio for each liquid to the value of 88 J/(K*mol) as predicted by Trouton's rule.
Determine if the calculated ratios are close to 88 J/(K*mol) and discuss any deviations, considering factors such as molecular complexity or hydrogen bonding that might affect the reliability of Trouton's rule.>

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Key Concepts

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

Trouton's Rule

Trouton's Rule states that the ratio of the molar heat of vaporization (∆H<sub>vap</sub>) of a liquid to its boiling point (T<sub>bp</sub> in Kelvin) is approximately constant for many liquids, typically around 88 J/(K·mol). This empirical rule helps predict the vaporization behavior of liquids and is particularly useful in thermodynamics and physical chemistry.
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Molar Heat of Vaporization

The molar heat of vaporization is the amount of energy required to convert one mole of a liquid into vapor at its boiling point, under constant pressure. It is a crucial thermodynamic property that reflects the strength of intermolecular forces in a liquid; higher values indicate stronger forces and greater energy needed for vaporization.
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Normal Boiling Point

The normal boiling point of a liquid is the temperature at which its vapor pressure equals the atmospheric pressure (1 atm). It is a key characteristic of a substance, influencing its phase transitions and is essential for applying Trouton's Rule, as the boiling point must be expressed in Kelvin for accurate calculations.
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Related Practice
Textbook Question

Use the data in Appendix B to calculate the equilibrium pressure of CO2 in a closed 1 L vessel that contains each of the following samples:

(a) 15 g of MgCO3 and 1.0 g of MgO at 25 °C

(b) 15 g of MgCO3 and 1.0 g of MgO at 280 °C .

Assume that ∆H° and ∆S° are independent of temperature.

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Textbook Question

Consider the Haber synthesis of gaseous NH3 (∆H°f = -46.1 kJ/mol; ∆G°f = -16.5 kJ/mol: (d) What are the equilibrium constants Kp and Kc for the reaction at 350 K? Assume that ∆H° and ∆S° are independent of temperature.

489
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Textbook Question
Is it possible for a reaction to be nonspontaneous yet exo-thermic? Explain.
242
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Textbook Question

Trouton's rule says that the ratio of the molar heat of vaporization of a liquid to its normal boiling point (in kelvin) is approximately the same for all liquids: ∆Hvap/Tbp ≈ 88 J/(K*mol) (b) Explain why liquids tend to have the same value of ∆Hvap/Tbp.

808
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Textbook Question
The normal boiling point of bromine is 58.8 °C, and the standard entropies of the liquid and vapor are S°[Br2(l) = 152.2 J/(K*mol); S°[Br2(g) = 245.4 J/(K*mol). At what temperature does bromine have a vapor pressure of 227 mmHg?
1899
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Textbook Question
Tell whether reactions with the following values of ΔH and ΔS are spontaneous or nonspontaneous and whether they are exothermic or endothermic. (a) ΔH = - 48 kJ; ΔS = + 135 J>K at 400 K (b) ΔH = - 48 kJ; ΔS = - 135 J>K at 400 K (c) ΔH = + 48 kJ; ΔS = + 135 J>K at 400 K (d) ΔH = + 48 kJ; ΔS = - 135 J>K at 400 K
520
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