The molar heat of vaporization of ethanol is 39.3 kJ/mol and the boiling point of ethanol is \(78.3^{\circ} \mathrm{C}\). Calculate \(\Delta S\) for the vaporization of 0.50 mol ethanol.

Entropy, symbolized by \( \Delta S \), is a fundamental concept in both thermodynamics and physical chemistry, reflecting the disorder or randomness in a system. The calculation of entropy change involves understanding how energy exchange, particularly heat exchange, affects the disorder within a system.

When heat is added to a substance, like evaporating ethanol, its particles begin to move more rapidly and the overall disorder of the system increases, leading to a positive entropy change. To calculate this change, we use the equation \( \Delta S = \frac{\Delta H}{T} \), where \( \Delta H \) is the heat of vaporization, and \( T \) is the temperature in Kelvin at which the process occurs. It is vital to ensure the units for \( \Delta H \) (in joules or kilojoules) and \( T \) (in Kelvin) are consistent to avoid errors in calculations.

Additionally, when dealing with multiples of a substance, such as 0.50 mol of ethanol in the given exercise, the calculated entropy change must be adjusted for the amount of substance to reflect the total change for that specific quantity.

Why Convert Boiling Point to Kelvin?

Boiling point conversion from Celsius to Kelvin is an essential step in many thermodynamic calculations because Kelvin is the SI unit for temperature. It allows us to have a standard reference point since Kelvin starts at absolute zero, which is the theoretical point where particles have the minimum thermal motion.

The conversion formula is simple but unintuitive for many, given by \( T(K) = T(\degree C) + 273.15 \). In our exercise, the boiling point of ethanol is first converted from Celsius to Kelvin to correctly use it in the entropy change formula. This step is a crucial example where understanding unit conversion ensures accuracy in chemistry calculations.

Thermodynamics is the branch of physical science concerned with heat and its relation to other forms of energy and work. It defines macroscopic variables (such as temperature, entropy, and energy) that characterize materials and radiation, and explains how they are related and by what laws they change with time.

Thermodynamics and Phase Changes

The principles of thermodynamics are crucial when analyzing phase changes, like vaporization. Vaporization, where a liquid becomes a gas, involves significant changes in energy and entropy. The molar heat of vaporization (\( \Delta H_{vap} \) or \( \Delta H_{vap} \)) is the amount of energy needed to transform one mole of a substance from liquid to gas at constant temperature and pressure. This heat is absorbed from the surroundings, highlighting the importance of understanding energy exchange in thermodynamics.

Physical chemistry combines principles of physics and chemistry to study the physical properties of molecules, the forces that act upon them, and their reactions. Within physical chemistry, the concepts of enthalpy and entropy are indispensable in understanding the energetics and spontaneity of chemical processes, such as the vaporization of ethanol.

The study of the enthalpy change, including the molar heat of vaporization, helps us to comprehend how entities absorb or release heat during a phase change. By exploring these principles, students can not only solve textbook problems efficiently but also gain deeper insight into the nature of chemical reactions and the laws governing them.