The enthalpy of vaporization of ethanol is 38.7 kJ / mol at its boiling point (78^∘ C). Determi

step 1 Hi guys, so in problem 44, we are provided with the enthalpy of vaporization of ethanol at its b

The enthalpy of vaporization of ethanol is 38.7 kJ / mol at...

The enthalpy of vaporization of ethanol is $38.7 \mathrm{~kJ} / \mathrm{mol}$ at its boiling point $\left(78^{\circ} \mathrm{C}\right)$. Determine $\Delta S_{\text {sys }}, \Delta S_{\text {surr }}$ and $\Delta S_{\text {univ }}$ when $1.00$ mol ethanol is vaporized at $78^{\circ} \mathrm{C}$ and $1.00 \mathrm{~atm}$.

Key Concepts

Entropy Change of the Universe

The total change in entropy, which includes both the system and the surroundings, is a key indicator of the spontaneity of a process. In a reversible process, the entropy gain of the system is exactly balanced by the loss in the surroundings, resulting in zero net entropy change in the universe. This concept is central to the second law of thermodynamics.

Entropy Change of the Surroundings

For a reversible process, the heat absorbed by the system is released by the surroundings. The entropy change of the surroundings is calculated as the negative of the heat exchanged divided by the temperature, reflecting the decrease in disorder in the surroundings that balances the increase in the system.

Phase Change at Equilibrium

In a phase change process occurring at the boiling point, the system is at equilibrium between the two phases. This implies that the process can be considered reversible, which allows the use of equilibrium thermodynamic relations such as ?S = Q_rev/T to evaluate entropy changes.

Enthalpy of Vaporization

This concept refers to the amount of energy required to convert one mole of a substance from the liquid phase to the gas phase at its boiling point, under constant pressure. It is a crucial thermodynamic parameter that provides insights into the strength of intermolecular interactions in the liquid phase.

Entropy Change of the System

The entropy change for a system undergoing a phase transition at constant temperature can be calculated by dividing the heat absorbed during the process by the absolute temperature. This represents the increase in disorder as the substance transitions from a more ordered phase (liquid) to a less ordered phase (gas).

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