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: ∆H_vap/T_bp ≈ 88 J/(K*mol) (b) Explain why liquids tend to have the same value of ∆Hvap/Tbp.

Verified step by step guidance

1. Trouton's rule is an empirical observation that the entropy of vaporization (\( \Delta S_{vap} \)) for many liquids is approximately the same when they are at their normal boiling point.
2. The entropy of vaporization is given by the formula \( \Delta S_{vap} = \frac{\Delta H_{vap}}{T_{bp}} \), where \( \Delta H_{vap} \) is the molar heat of vaporization and \( T_{bp} \) is the boiling point in Kelvin.
3. According to Trouton's rule, \( \Delta S_{vap} \) is approximately 88 J/(K*mol) for many liquids, indicating that the change in entropy when a liquid vaporizes is similar across different substances.
4. This similarity arises because the process of vaporization involves overcoming intermolecular forces to transition from a liquid to a gas, which requires a similar amount of energy per mole for many substances.
5. The rule holds best for non-polar and non-hydrogen-bonded liquids, as these substances have similar intermolecular forces, leading to similar \( \Delta H_{vap} \) values when normalized by their boiling points.

Key Concepts

Trouton's Rule

Trouton's Rule states that the ratio of the molar heat of vaporization (∆H_vap) of a liquid to its boiling point (T_bp) in Kelvin is approximately constant for many liquids, typically around 88 J/(K·mol). This empirical observation suggests that despite differences in molecular structure, many liquids exhibit similar intermolecular forces, leading to comparable energy requirements for vaporization relative to their boiling points.

Molar Heat of Vaporization

The molar heat of vaporization (∆H_vap) is the amount of energy required to convert one mole of a liquid into vapor at its boiling point. This energy is necessary to overcome the intermolecular forces holding the liquid molecules together. A higher ∆H_vap indicates stronger intermolecular forces, while a lower value suggests weaker forces, influencing the boiling point and vaporization behavior of the liquid.

Boiling Point

The boiling point (T_bp) of a liquid is the temperature at which its vapor pressure equals the external pressure, allowing the liquid to transition into the gas phase. It is influenced by the strength of intermolecular forces; stronger forces typically result in higher boiling points. The relationship between boiling point and heat of vaporization is crucial for understanding why many liquids exhibit similar ratios of ∆H_vap/T_bp as described by Trouton's Rule.