Most liquids follow Trouton's rule, which states that the...

Most liquids follow Trouton's rule, which states that the molar entropy of vaporization lies in the range of $88 \pm 5 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$. The normal boiling points and enthalpies of vaporization of several organic liquids are as follows: (a) Calculate $\Delta S_{\text {vap }}$ for each of the liquids. Do all the liquids obey Trouton's rule? (b) With reference to intermolecular forces (Section 11.2), can you explain any exceptions to the rule? (c) Would you expect water to obey Trouton's rule? By using data in Appendix $\mathrm{B}$, check the accuracy of your conclusion. (d) Chlorobenzene $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}\right)$ boils at $131.8^{\circ} \mathrm{C}$. Use Trouton's rule to estimate $\Delta H_{\text {van }}$ for this substance.

Most liquids follow Trouton's rule, which states that the molar entropy of vaporization lies in the range of $88 \pm 5 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$. The normal boiling points and enthalpies of vaporization of several organic liquids are as follows:
(a) Calculate $\Delta S_{\text {vap }}$ for each of the liquids. Do all the liquids obey Trouton's rule?
(b) With reference to intermolecular forces (Section 11.2), can you explain any exceptions to the rule? (c) Would you expect water to obey Trouton's rule? By using data in Appendix $\mathrm{B}$, check the accuracy of your conclusion. (d) Chlorobenzene $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}\right)$ boils at $131.8^{\circ} \mathrm{C}$. Use Trouton's rule to estimate $\Delta H_{\text {van }}$ for this substance.

Key Concepts

Intermolecular Forces

Intermolecular forces encompass the attractions between molecules, such as London dispersion forces, dipole-dipole interactions, and hydrogen bonding. They play a critical role in determining a liquid's physical properties, including its boiling point and the extent of entropy change upon vaporization. Variations in these forces lead to deviations from general empirical rules like Trouton’s rule.

Normal Boiling Point

The normal boiling point is defined as the temperature at which the vapor pressure of a liquid equals atmospheric pressure (1 atm), allowing it to boil. It serves as a reference temperature for calculating thermodynamic properties like enthalpy and entropy of vaporization and is crucial for comparing substances under standardized conditions.

Hydrogen Bonding

Hydrogen bonding is a specific type of strong dipole-dipole interaction occurring when hydrogen is covalently bound to highly electronegative atoms like oxygen or nitrogen. This bonding significantly influences a liquid’s thermodynamic properties by raising its boiling point and reducing the molar entropy of vaporization, often resulting in deviations from the typical value predicted by Trouton’s rule.

Molar Entropy of Vaporization

The molar entropy of vaporization represents the change in entropy per mole when a substance vaporizes at its boiling point. It is calculated from the relationship ?S_vap = ?H_vap/T_b, where ?H_vap is the molar enthalpy of vaporization and T_b is the normal boiling point in Kelvin. This concept is key in assessing the degree of disorder change between the liquid and gas phases.

Trouton's Rule

Trouton’s rule is an empirical observation stating that the molar entropy of vaporization for many liquids at their normal boiling point is approximately constant, typically around 88 J/(mol·K) with a moderate variation. It implies that the disorder increase when a liquid transforms into a vapor is similar for many substances, provided that the liquid’s intermolecular forces and molecular structure do not lead to anomalies.

Enthalpy of Vaporization

The enthalpy of vaporization is the amount of energy required to convert one mole of a liquid into a gas at its boiling point under constant pressure. It directly relates to the strength of intermolecular attractions; stronger attractions require more energy to overcome. It is also used in conjunction with Trouton's rule to estimate the entropy change during vaporization.

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