Calculate the entropy change for the vaporization of liquid...

Calculate the entropy change for the vaporization of liquid methane and liquid hexane using the following data. Compare the molar volume of gaseous methane at $112 \mathrm{~K}$ with that of gaseous hexane at $342 \mathrm{~K}$. How do the differences in molar volume affect the values of $\Delta S_{v p}$ for these liquids?

Key Concepts

Entropy Change for Vaporization

This concept refers to the change in entropy when a substance transforms from the liquid phase to the gaseous phase. During vaporization, the substance experiences a marked increase in disorder because gas molecules have more freedom to move and occupy a larger volume than liquid molecules. The entropy change is often approximated by the latent heat of vaporization divided by the boiling temperature, although actual values also depend on other factors such as molecular interactions and volume differences.

Molar Volume of a Gas

Molar volume is defined as the volume occupied by one mole of a substance in the gaseous state. According to the ideal gas law, the molar volume is directly influenced by temperature and pressure. A larger molar volume implies that the gas occupies a greater space, increasing the number of accessible microstates and, consequently, the entropy. This is particularly significant when comparing gases at different temperatures or compositions.

Ideal Gas Law

The ideal gas law (PV = nRT) relates the pressure, volume, temperature, and number of moles of an ideal gas. It provides a useful approximation for understanding how changes in temperature and pressure impact the molar volume of a gas. This concept is crucial when comparing the molar volumes of different gases, as it allows for predictions on how the volume – and therefore the entropy – will change under varying thermodynamic conditions.

Temperature Effects on Vaporization

Temperature plays a significant role in phase transitions by influencing both the magnitude of the latent heat of vaporization and the molar volume of the vapor. Higher temperatures not only provide the energy required to overcome intermolecular attractions in the liquid but also result in a larger molar volume in the gas phase, thus leading to greater entropy changes. This effect must be considered when comparing the vaporization properties of different substances at different temperatures.

Relationship Between Molar Volume and ?Svap

The increase in entropy upon vaporization, ?Svap, is strongly related to the change in volume from the liquid to the gas phase. A larger molar volume in the gas corresponds to a larger increase in the number of accessible microstates. As a result, substances that vaporize into gases with significantly larger molar volumes will exhibit higher entropy changes during vaporization. Differences in the molar volumes of gases at their respective vaporization temperatures explain why ?Svap values vary for different liquids.

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