Entropy (Simplified): Study with Video Lessons, Practice Problems & Examples

Entropy (S) measures disorder and randomness in the universe, with the second law of thermodynamics stating that the entropy of the universe is always increasing. Spontaneous reactions lead to an increase in entropy (ΔS). Physical changes, like transitioning from solid to gas, result in positive ΔS, while chemical changes, such as breaking bonds or increasing moles of gas, also increase entropy. Conversely, forming bonds or decreasing gas moles leads to negative ΔS. Understanding these changes is crucial for grasping concepts in thermodynamics and chemical reactions.

Entropy (Simplified) Concept 1

Entropy, which is represented by the symbol S, is the measure of disorder, which is connected to the randomness of molecules or chaos in general in the universe. It is related to systems, surroundings, and the universe. Now we're going to say connected to entropy is the second law of thermodynamics. It states that the entropy of the universe is always increasing. So chaos and disorder are always increasing in the universe. Stars die, planets break apart. It's just a normal progression of the universe. Nothing lasts forever. We're going to say connected to this also is the idea of spontaneity. So the second law says that in the universe, all entropy is always increasing. Well, all spontaneous reactions involve an increase in entropy of the universe. Right? So basically, this is connecting to spontaneity.

Entropy (Simplified) Example 1

So here, the second law of thermodynamics leads us to conclude, the total energy of the universe is constant. Well, nowhere did it talk about the energy of the universe. It's talking about the randomness or chaos of the universe. The disorder of the universe is increasing with the passage of time. That is true. It says entropy is increasing, so over time, it's going to get more and more chaotic. Universes don't last forever. Planets and stars die. This is the natural progression of the universe. The total energy of the universe is increasing with time. Again, we don't know anything about energy, that's not what the second law is related to, so both options c and d are out. So here the answer would have to be option b.

Entropy (Simplified) Concept 2

So we can say we can determine the sign of the entropy change, which is Δs, in a system by examining physical and chemical changes. Now we're going to say that our entropy change, which is Δs, is a measure of increase or decrease in order due to chemical or physical changes. So here, let's take a look at entropy and physical changes first. We're going to say in this first image, we're transitioning from our solid to liquid to gas. We're heading in a direction where the space between the molecules is increasing. And if you think about it, which is more chaotic? A solid object is sitting there on a table or a container filled with gases that are bouncing everywhere. We'd say that gases have the most entropy. So as we're heading from solids towards the gases, we're gonna say that our entropy is increasing. That means that our Δs value is going to be positive. There's a positive change in entropy. We're going to say that this move from solid to gas is usually accompanied by an increase in our temperature. Think about it. Increasing temperature on a solid would cause it to melt, increasing it further will cause that liquid to vaporize into gases. Now let's think about the opposite direction. If we were to decrease the temperature, molecules would come closer and closer together, our gases would condense down into liquid, and if we lower the temperature even more, they would freeze into a solid. As we head from gas to solid, we expect a decrease in entropy, so a negative change in entropy. Alright. So now that's physical changes.

Let's look at chemical changes. Here we can say that we can have entropy increasing, so positive Δs if we are breaking bonds. Right? Remember, chaos, chaotic, disorder. The more things we can break apart, the more chaotic things become. Breaking bonds is a chaotic action. We can also say, if we look at this chemical reaction, we have calcium carbonate solid, it breaks apart into calcium oxide and carbon dioxide gas. It's an increase in chaos because we are breaking bonds, but it's also an increase in chaos because we just increased the moles of gas. So there's an increase in moles of gas. Remember, gases have the most entropy. Their molecules are further spread apart, bouncing everywhere. Now entropy decreasing, so a negative change in Δs is if we did the opposite, if we're forming bonds or if we decreased the number of moles of gas. Here we have 1 mole of nitrogen gas plus 3 moles of hydrogen gas for a total of 4 moles of gas. They combine together to give me 2 moles of gas here. So not only am I forming bonds, but I've decreased the number of moles that I have. You don't have to have both happen, but as long as one of these is happening that tells us if there's an increase or decrease in entropy. If you're breaking bonds, it's an increase in entropy. If you're decreasing the number of moles of gas, it's a decrease in entropy. Both don't need to happen for this to be an increase. Alright. So keep in mind the different physical and chemical changes and how they can affect the increasing or decreasing of entropy.

Entropy (Simplified) Example 2

Which one of the following processes produces a decrease in the entropy of the system? Boiling water to form steam. Here, remember boiling means we're breaking bonds as we transition from a liquid to a gas. Breaking bonds causes an increase in entropy. Melting ice to form water, here the same situation happens, we're breaking bonds. In this case, we're going from solid to liquid, so that's going to be an increase in entropy. Mixing of 2 gases into 1 container, we had 1 container with gases, and now we've increased it by adding even more. More gases, more fun, more chaos. So this is going to increase entropy as well. Freezing water to form ice. So, we're going from liquid to solid, so we're forming bonds, which is a decrease in entropy. So this would be our answer. Now let's look at e just to make sure that e is not an answer as well. The dissolution of solid potassium chloride in water, so dissolution means we're dissolving and we're breaking it down. So it's going from KCl into its ions, so you're breaking the connections, so that's breaking bonds, so that's an increase in entropy. So here only option D would be a decrease in entropy of the system.

Predict how the entropy of the substance is affected in the following processes:

CH₄ (g, 125°C)   →   CH₄ (g, 200°C)

• A. increases
• B. decreases
• C. remains the same

PRACTICE: Which reaction is most likely to have a positive ∆S of system?

a) SiO₂ (s) + 3 C (s) → SiC (s) + 2 CO (g)

b) 6 CO₂ (g) + 6 H₂O (g) → C₆H₁₂O₆ (s) + 6 O₂ (g)

c) CO (g) + Cl₂ (g) → COCl₂ (g)

d) 3 NO₂ (g) + H₂O (l) → 2 HNO₃ (l) + NO (g)

• A. SiO₂ (s) + 3 C (s) → SiC (s) + 2 CO (g)
• B. 6 CO₂ (g) + 6 H₂O (g) → C₆H₁₂O₆ (s) + 6 O₂ (g)
• C. CO (g) + Cl₂ (g) → COCl₂ (g)
• D. 3 NO₂ (g) + H₂O (l) → 2 HNO₃ (l) + NO (g)

Which of the following processes shows a decrease in entropy of the system?

• A. NaClO₃(s) → Na⁺(aq) + ClO₃^–(aq)
• B. CH₃OH(l) → CO(g) + 2 H₂(g)
• C. H₂O(l) → H₂O(g)
• D. 2 NO(g) + O₂(g) → 2 NO₂(g)
• E. COCl₂(g) → CO(g) + Cl₂(g)

Here’s what students ask on this topic:

What is entropy and how is it related to the second law of thermodynamics?

Entropy (S) is a measure of disorder or randomness in a system. It quantifies the amount of chaos or unpredictability among the molecules in a system. The second law of thermodynamics states that the entropy of the universe is always increasing. This means that natural processes tend to move towards a state of greater disorder or randomness. For example, stars die and planets break apart over time, contributing to the overall increase in entropy. This law also implies that all spontaneous reactions result in an increase in the entropy of the universe.

How does entropy change during physical transitions like melting or vaporization?

During physical transitions such as melting (solid to liquid) or vaporization (liquid to gas), entropy increases. This is because the molecules in a solid are closely packed and orderly, while in a liquid, they are more spread out and less ordered. In a gas, the molecules are even more dispersed and chaotic. Therefore, as a substance transitions from solid to liquid to gas, the disorder or randomness increases, leading to a positive change in entropy (ΔS > 0). Conversely, when a gas condenses to a liquid or a liquid freezes to a solid, entropy decreases (ΔS < 0).

What is the significance of entropy in spontaneous reactions?

Entropy plays a crucial role in determining the spontaneity of a reaction. According to the second law of thermodynamics, for a reaction to be spontaneous, the total entropy of the universe must increase. This means that spontaneous reactions are those that result in a positive change in entropy (ΔS > 0). For example, breaking chemical bonds or increasing the number of gas molecules in a reaction increases entropy, making the reaction more likely to occur spontaneously. Understanding entropy helps predict whether a reaction will proceed without external intervention.

How do chemical changes affect entropy?

Chemical changes can either increase or decrease entropy. Breaking chemical bonds increases entropy because it leads to more disorder and chaos. For instance, when calcium carbonate (CaCO₃) breaks down into calcium oxide (CaO) and carbon dioxide (CO₂), the number of gas molecules increases, leading to a positive change in entropy (ΔS > 0). Conversely, forming chemical bonds or decreasing the number of gas molecules reduces entropy. For example, when nitrogen gas (N₂) and hydrogen gas (H₂) combine to form ammonia (NH₃), the number of gas molecules decreases, resulting in a negative change in entropy (ΔS < 0).

What is the relationship between temperature and entropy?

Temperature and entropy are directly related. As temperature increases, the kinetic energy of molecules also increases, leading to greater molecular motion and disorder. For example, heating a solid causes it to melt into a liquid, and further heating turns the liquid into a gas. Each of these transitions involves an increase in entropy (ΔS > 0) because the molecules become more dispersed and chaotic. Conversely, lowering the temperature reduces molecular motion, causing gases to condense into liquids and liquids to freeze into solids, thereby decreasing entropy (ΔS < 0).