Entropy Calculations: Phase Changes - Online Tutor, Practice Problems & Exam Prep

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 of Liquids

Now, similar to the change in the entropy of surroundings, we now talk about the entropy of liquids and they have formulas that are used to calculate either the change in entropy or the change in entropy. Now we're going to say that the below formulas are being used during phase changes and the phase changes that we care about are vaporization and fusion. It's because these two phase changes deal with liquid in some way.

In vaporization, we're talking about going from a liquid to a gas, an infusion, which is another name for melting. We're going from a solid to a liquid. In both phase changes, a liquid is involved. Now here we're going to say that these formulas, they connect entropy and entropy together. In the first one, we're going to say that the change in the entropy of vaporization equals the change in the enthalpy of vaporization divided by our boiling point of the liquid.

Here we're going to say that the change in entropy of our fusion equals the change in enthalpy of fusion divided by the melting point temperature. So here change in ΔSₖvape and ΔSₖfusion. They are typically units of Joules per Kelvin, and entropy of vaporization and enthalpy of fusion are typically in units of joules or kilojoules. And as always when we talk about temperature, even in this case a boiling point temperature and melting point temperature, it has to be in units of Kelvin.

So just remember that these formulas are wave connecting entropy and enthalpy together, whether they deal with vaporization or with fusion.

Entropy Calculations: Phase Changes Example

You were told that methanol has a normal melting point of 64.7°C and an entropy of fusion of 9.36 joules per Kelvin. Determine its enthalpy of fusion. All right, so we're talking about fusion. We know that the original formula that connects entropy of fusion and entropy of fusion is

ΔS fusion = ΔH fusion R melting point temperature

We need to isolate this variable here, so multiply both sides by temperature. So now we're going to say that the enthalpy of fusion equals the change in the entropy of fusion times my melting point temperature. Here we plug in 9.36 Joules per Kelvin. Because the entropy of fusion uses Kelvin, that is an indication we need to convert temperature into Kelvin, so add 273.15 to these degrees Celsius.

When we do that, we get 337.15 Kelvin, which is what we plug here. Kelvin's cancel out and we get 3155.724 Joules. So we can say this is our answer, SO3156 joules, or if we decide to convert it into kilojoules, 3.156 kilojoules. So either one could represent our entropy of fusion.

And here we're talking about this per mole. So if you wanted to, you could say joules per mole or kilojoules. Same difference. Here we're assuming we're dealing with a mole of a substance, so here this will be our enthalpies of fusion.

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

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.