Ethanol boils at \(78.4^{\circ} \mathrm{C}\) and the enthalpy of vaporisation of ethanol is \(42.4 \mathrm{~kJ} \mathrm{~mol}^{-1}\). Calculate the entropy of vaporisation of ethanol.

Enthalpy of vaporization, often denoted as \( \Delta H_{vap} \) or simply \( \Delta H \), is a crucial concept in thermodynamics, specifically within the context of phase changes. It refers to the amount of heat energy required to convert a substance from its liquid phase to its gaseous phase at a constant pressure. This energy is needed to overcome intermolecular forces within the liquid, allowing the molecules to disperse and move freely in the vapor phase.

Understanding \( \Delta H_{vap} \) is essential because it reflects the strength of the intermolecular forces in a liquid; the larger the value, the stronger the forces that must be overcome. \( \Delta H_{vap} \) is commonly expressed in units of kilojoules per mole (kJ/mol), and its precise value depends on the substance in question as well as the temperature at which vaporization takes place.\
We see its practical application in the calculation of entropy of vaporization, as illustrated in the problem about ethanol. The value, in this case, provides the necessary data to solve for the entropy change when ethanol transitions from liquid to gas.

Temperature conversion between Celsius (°C) and Kelvin (K) scales is a straightforward but essential procedure in thermodynamics and physical chemistry calculations. Scientists use the Kelvin scale because it is an absolute temperature scale, starting at absolute zero, where all molecular motion stops. \( 0 K \) is equivalent to -273.15°C.

To convert Celsius to Kelvin, the formula \( K = °C + 273.15 \) is used. This is particularly important when dealing with thermodynamic equations, as they require temperature in Kelvin to ensure consistency and accuracy. In the context of the exercise provided, the boiling temperature of ethanol must be converted from Celsius to Kelvin before you can calculate the entropy of vaporization. Failing to convert units correctly can lead to significant errors in calculations and conclusions.

Physical chemistry thermodynamics is a fundamental field that deals with the laws governing energy transformations and the properties of matter. One of the core concepts is the idea of entropy, denoted as \( S \), which is a measure of the disorder or randomness in a system. Entropy change, especially during phase transitions like vaporization, is an intrinsic part of understanding thermodynamic processes.

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. As substances vaporize, there is an increase in entropy because the vapor phase has greater disorder than the liquid phase.

In practical terms, when solving for the entropy of vaporization (\( \Delta S_{vap} \)), the relevant formula \( \Delta S_{vap} = \frac{\Delta H_{vap}}{T} \) is applied, where \( \Delta H_{vap} \) is the enthalpy of vaporization and \( T \) is the temperature in Kelvin. This relationship reveals not only the amount of disorder introduced during vaporization but also how energy disperses in a system undergoing a phase change.