Question

Chloroform \(\left(\mathrm{CHCl}_{3}\right)\) has a normal boiling point of \(61^{\circ} \mathrm{C}\) and an enthalpy of vaporization of \(29.24 \mathrm{~kJ} / \mathrm{mol}\). What are its values of \(\Delta G_{\text {vap }}\) and \(\Delta S_{\text {vap }}\) at \(61^{\circ} \mathrm{C} ?\)

Short answer

\( \Delta G_{\text{vap}} = 0 \), \( \Delta S_{\text{vap}} \approx 87.47 \, \mathrm{J/mol} \cdot K \) at \( 61^{\circ} \mathrm{C} \).

Step-by-step solution

Identify Given Data

Here, we have the normal boiling point of chloroform, which is \( T = 61^{\circ} \mathrm{C} \) or \( T = 61 + 273.15 = 334.15 \ K \). The enthalpy of vaporization \( \Delta H_{\text{vap}} = 29.24 \, \mathrm{kJ/mol} \) or \( 29240 \, \mathrm{J/mol} \).

Apply Gibbs Free Energy Equation

At the boiling point, the Gibbs free energy change for vaporization \( \Delta G_{\text{vap}} \) is zero because the system is at equilibrium. So, \( \Delta G_{\text{vap}} = 0 \) at \( 61^{\circ} \mathrm{C} \).

Calculate Entropy of Vaporization

Using the relationship \( \Delta G = \Delta H - T \Delta S \), and since \( \Delta G = 0 \), we have: \[ 0 = \Delta H - T \Delta S \] Rearranging, we get: \[ \Delta S = \frac{\Delta H}{T} \] Substituting the given values: \( \Delta S = \frac{29240}{334.15} \approx 87.47 \, \mathrm{J/mol} \cdot K \).

Key concepts

Gibbs Free Energy

Gibbs Free Energy is a thermodynamic quantity that signifies the maximum reversible work that can be performed by a thermodynamic system at a constant temperature and pressure. It's a pivotal concept in predicting the direction of chemical reactions and phase changes, such as vaporization. The change in Gibbs Free Energy (\(\Delta G\)) tells us whether a process occurs spontaneously.
In the context of vaporization, \(\Delta G_{\text{vap}}\) indicates whether a liquid will spontaneously turn into a vapor at a given temperature and pressure. For chloroform, at its normal boiling point of \(61^{\circ} \mathrm{C}\), we find that \(\Delta G_{\text{vap}} = 0\). This means that the liquid and vapor phases of chloroform are in equilibrium at this temperature, indicating that the vaporization process is neither spontaneous nor non-spontaneous. It simply occurs without any net energy being absorbed or released.
Understanding \(\Delta G_{\text{vap}}\) helps students grasp why certain elements and compounds transition between different states under various conditions.

Entropy of Vaporization

Entropy, a measure of disorder or randomness in a system, plays a crucial role in phase transitions. The Entropy of Vaporization (\(\Delta S_{\text{vap}}\)) reflects the change in entropy when a liquid transforms into a vapor. This value provides insight into how much the molecular disorder increases during vaporization.

• In the exercise, we calculated \(\Delta S_{\text{vap}}\) for chloroform at its boiling point using the formula: \(\Delta S = \frac{\Delta H}{T}\).
• This formula stems from the Gibbs Free Energy equation rearranged at equilibrium, where \(\Delta G = 0\).
• By substituting the given enthalpy of vaporization and temperature, we found \(\Delta S_{\text{vap}} \approx 87.47 \, \mathrm{J/mol} \cdot K\).

This positive value indicates an increase in disorder, as expected when a substance moves from a more ordered liquid state to a less ordered gaseous state. Understanding \(\Delta S_{\text{vap}}\) can help students appreciate the concept of entropy and how it applies to real-world chemical processes.

Enthalpy of Vaporization

The Enthalpy of Vaporization (\(\Delta H_{\text{vap}}\)) quantifies the heat required to vaporize one mole of a liquid at a constant pressure. It reflects the energy needed to overcome intermolecular forces within a liquid, enabling the molecules to escape into the gaseous state.

• For chloroform, \(\Delta H_{\text{vap}}\) is \(29.24 \, \mathrm{kJ/mol}\), which indicates a moderate amount of energy is necessary for its vaporization.
• This value can vary widely depending on the nature of the liquid, which is influenced by factors like hydrogen bonding, molecular size, and polarity.
• Understanding \(\Delta H_{\text{vap}}\) is crucial for predicting boiling points and the energy input required to induce vaporization in practical applications such as distillation.

By grasping how \(\Delta H_{\text{vap}}\) transforms energy within a system during phase changes, students can better understand fundamental thermodynamic principles that govern chemical reactions and industrial processes.