Entropy Calculations: Phase Changes: Videos & Practice Problems

Understanding the thermodynamic concepts of entropy change during phase transitions is crucial in chemistry. Entropy, a measure of disorder or randomness, changes when substances undergo vaporization or fusion. Vaporization, the transition from liquid to gas, and fusion, also known as melting, from solid to liquid, both involve liquids and are accompanied by changes in entropy. The change in entropy of vaporization (ΔS_vap) is calculated using the heat of vaporization (ΔH_vap) divided by the boiling point temperature in Kelvin. Similarly, the change in entropy of fusion (ΔS_fus) is determined by dividing the heat of fusion (ΔH_fus) by the melting point temperature in Kelvin. These calculations are essential for predicting how substances will behave under different thermal conditions and are expressed in units of joules per Kelvin for entropy and joules or kilojoules for enthalpy. Understanding these relationships helps grasp the energy dynamics during phase changes.

$\Delta S_{\mathrm{vap}}=\frac{\Delta H_{\mathrm{vap}}}{T}$ $\Delta S_{\mathrm{fus}}=\frac{\Delta H_{\mathrm{fus}}}{T}$

Entropy in Phase Changes

In thermodynamics, understanding the relationship between entropy and enthalpy during phase changes is crucial, particularly for liquids. The two primary phase changes involving liquids are vaporization and fusion. Vaporization refers to the transition from a liquid to a gas, while fusion, also known as melting, describes the change from a solid to a liquid. Both processes are significant as they involve the liquid state.

The formulas that connect entropy (ΔS) and enthalpy (ΔH) during these phase changes are essential for calculations. For vaporization, the change in entropy can be expressed as:

$$\Delta S_{\text{vaporization}} = \frac{\Delta H_{\text{vaporization}}}{T_{\text{boiling}}}$$

In this equation, ΔS_vaporization represents the change in entropy during vaporization, ΔH_vaporization is the change in enthalpy of vaporization, and T_boiling is the boiling point temperature, which must be measured in Kelvin.

Similarly, for fusion, the relationship is given by:

$$\Delta S_{\text{fusion}} = \frac{\Delta H_{\text{fusion}}}{T_{\text{melting}}}$$

Here, ΔS_fusion denotes the change in entropy during fusion, ΔH_fusion is the change in enthalpy of fusion, and T_melting is the melting point temperature, also expressed in Kelvin.

Typically, the units for the change in entropy are joules per Kelvin (J/K), while the enthalpy values are measured in joules (J) or kilojoules (kJ). These formulas effectively illustrate how entropy and enthalpy are interconnected during the phase transitions of liquids, providing a foundational understanding of thermodynamic processes.

Entropy in Phase Changes Example

Methanol has a normal melting point of 64.7 degrees Celsius, which is crucial for calculating its enthalpy of fusion. The relationship between the enthalpy of fusion (\( \Delta H_{\text{fusion}} \)) and the entropy of fusion (\( \Delta S_{\text{fusion}} \)) is given by the formula:

\( \Delta S_{\text{fusion}} = \frac{\Delta H_{\text{fusion}}}{T} \)

To isolate the enthalpy of fusion, we rearrange the equation:

\( \Delta H_{\text{fusion}} = \Delta S_{\text{fusion}} \times T \)

Here, \( \Delta S_{\text{fusion}} \) is provided as 9.36 joules per Kelvin. Since the melting point must be in Kelvin for the calculation, we convert the temperature from Celsius to Kelvin by adding 273.15:

\( T = 64.7 + 273.15 = 337.15 \, \text{K} \)

Now, substituting the values into the equation gives:

\( \Delta H_{\text{fusion}} = 9.36 \, \text{J/K} \times 337.15 \, \text{K} \)

Calculating this results in:

\( \Delta H_{\text{fusion}} = 3155.724 \, \text{J} \)

This can also be expressed in kilojoules:

\( \Delta H_{\text{fusion}} = 3.156 \, \text{kJ} \)

It is important to note that this value represents the enthalpy of fusion per mole of methanol, which can be stated as either joules per mole or kilojoules per mole, depending on the preferred unit of measurement.

Calculate entropy of vaporization of 8.4 g of acetic acid (CH₃COOH) with a boiling point of 118 °C, ∆H_vap = 23.7 kJ/mol.

• A. 201 J/K
• B. 60.3 J/K
• C. 28.1 J/K
• D. 8.48 J/K

Answer: (D)

Here’s what students ask on this topic:

During which phase change does the entropy of a sample of H₂O increase?

Entropy is a measure of the disorder or randomness in a system. For a sample of H₂O (water), the entropy increases during phase changes that involve a transition from a more ordered to a less ordered state. Specifically, the entropy of H₂O increases during the following phase changes:

1. Melting: When ice (solid H₂O) melts to form liquid water, the structured lattice of ice breaks down, and the molecules can move more freely, increasing the entropy.
2. Vaporization: When liquid water boils and turns into water vapor (gas), the molecules spread out even more and move more randomly, leading to a significant increase in entropy.
3. Sublimation: This is a direct change from solid to gas, bypassing the liquid phase, as seen with dry ice. For H₂O, this occurs under certain conditions, such as when ice evaporates directly into water vapor without melting first. This also results in an increase in entropy due to the greater freedom of movement for the molecules in the gas phase.

In each of these transitions, the energy input (usually in the form of heat) disrupts the existing molecular order, allowing for a greater range of molecular motion and configurations, hence increasing the entropy.

Which of the following phase changes would you predict to have the largest positive change in entropy?

When considering phase changes and their impact on entropy, which is a measure of disorder or randomness, the change from a solid to a gas (sublimation) typically has the largest positive change in entropy. This is because in the solid phase, particles are arranged in a highly ordered structure and have limited freedom of movement. As they change to the gas phase, the particles are much more dispersed and have a significantly greater degree of freedom to move and occupy space. This dispersal represents a substantial increase in randomness and disorder, hence a large positive change in entropy. Sublimation, therefore, is the phase change you would predict to have the largest positive change in entropy compared to other phase changes like melting, freezing, vaporization, condensation, or deposition.

How do you calculate the entropy of a phase change?

To calculate the entropy change (ΔS) for a phase change, you use the formula:

$\mathrm{\Delta S}=\frac{q}{T}$

where q_rev is the heat that is absorbed or released during the reversible phase change, and T is the temperature at which the phase change occurs, measured in Kelvin.

For a phase change, the process is typically isothermal (occurs at constant temperature), such as melting or boiling. You need to know the amount of heat involved in the phase change, which is the enthalpy change (ΔH) for the process. For example, if you're calculating the entropy change for melting ice, you would use the enthalpy of fusion for water.

Here's a step-by-step process:

1. Determine the enthalpy change (ΔH) for the phase change. This value is usually given per mole or per unit mass.
2. Ensure that the temperature (T) is in Kelvin.
3. Use the formula $\mathrm{\Delta S}=\frac{\mathrm{\Delta H}}{T}$ to find the entropy change.

Remember that the heat is absorbed (endothermic process) for melting and vaporization, and it is released (exothermic process) for freezing and condensation. This will determine the sign of ΔS.