The Concept of Entropy Explained
HSC Chemistry Syllabus
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Analyse the differences between entropy and enthalpy
- Use modelling to illustrate entropy changes in reactions
- Predict entropy changes from balanced chemical reactions to classify as increasing or decreasing entropy
- Explain reaction spontaneity using terminology, including
Entropy and Gibbs Free Energy
This video will discuss the concept of Entropy and also explain how the combination of entropy and enthalpy values can be utilised along with the Gibbs Free Energy equation to predict the spontaneity of a reaction.
What is Entropy?
In scientific terms, entropy (represented as S) is a measure of the randomness or disorder of a system. The more ways the particles and energy in a system can be arranged, the higher its entropy.
Chemical processes (including reactions) and systems can exhibit changes in entropy (`\Delta S`). When entropy increases, the system becomes more disordered. Conversely, a decrease in entropy signifies a more ordered state.
The Second Law of Thermodynamics is a key principle related to entropy. It states that for any process, the total entropy of the universe (the system plus its surroundings) must increase. In simpler terms, things naturally tend to move towards a state of greater disorder.
$$\Delta S_{\text{universe}} = \Delta S_{\text{system}} + \Delta S_{\text{surrounding}} > 0$$
It is important to understand that the second law of thermodynamics does not mean the entropy of every single part must increase. This means a system can become more ordered (decrease its entropy) as long as it causes an even greater increase in disorder (entropy) in its surroundings.
Think about what a refrigerator does.
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The System is the inside of your fridge. It takes in disordered, warmer air and food and makes them cold and more ordered. The water molecules in a melting ice cream will slow down and eventually freeze into an ordered crystal structure. So, the entropy inside the fridge (the system) decreases (`\Delta S_{text{system}} < 0`).
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The Surrounding is the kitchen where the fridge is located. To cool the inside, the refrigerator's motor and coils on the back release heat into the room. This heat makes the air molecules in your kitchen move faster and more randomly and disordered. The entropy of the surroundings (the kitchen) increases significantly (`\Delta S_{text{surrounding}} > 0`).
The key is that the increase in the entropy of the kitchen is greater than the decrease in the entropy inside the fridge. When you add it all up, the net entropy of the universe has increased, and the Second Law is perfectly satisfied.
Difference Between Enthalpy (∆H) and Entropy (∆S)
Enthalpy and entropy are both thermodynamic quantities which describe the physical properties of a system. The principal distinction between enthalpy and entropy is that enthalpy quantifies the total heat content of a system, whereas entropy quantifies the degree of its molecular disorder or randomness
Enthalpy is a thermodynamic property representing the total heat energy of a system. It comprises the system's internal energy plus the product of its pressure and volume. In chemical reactions, the focus is on the change in enthalpy (ΔH), which corresponds to the heat exchanged with the surroundings at constant pressure.
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A negative ΔH characterises an exothermic process, wherein the system releases heat.
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A positive ΔH characterises an endothermic process, wherein the system absorbs heat.
In essence, enthalpy is a measure of the heat exchanged during a process. This is discussed separately here.
Entropy and States of Matter
Consider the states of matter:
- Solids: Particles are in fixed positions and can only vibrate. This is a highly ordered state with low entropy.
- Liquids: Particles can move past each other, leading to more possible arrangements and higher entropy than solids.
- Gases: Particles move randomly and fill their entire container. This is the most disordered state with the highest entropy.
Examples:
Consider the melting of a solid into a liquid. This process increases entropy, indicating a move towards greater disorder.
Chemical reactions that result in an increase in the number of particles, a change from a solid or liquid to a gas, or the dissolving of a solid in a liquid generally lead to an increase in entropy (a positive ΔS).
The decomposition of calcium carbonate into solid calcium oxide and carbon dioxide gas increases entropy as a solid turns into a gas.
Molecular Complexity and Entropy
For chemical substances in the same state of matter, the one with the greater molecular complexity will have higher entropy.
The main reason is that more complex molecules have more ways to move and store energy. Entropy is fundamentally about the number of possible arrangements or "microstates" a system can have. The more ways a molecule can bend, stretch, and rotate, the more microstates are available, and thus, the higher its entropy.
The more atoms a molecule has, the more of these rotational and vibrational "modes" it has. This dramatic increase in the number of ways the molecule can arrange its energy leads to a higher overall entropy.
Methane vs. Ethane:
Both methane and ethane are gases at 298 K and atmospheric pressure:
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Methane (`CH_4`) has a standard molar entropy of approximately 186 J/mol·K.
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Ethane (`C_2H_6`) is a larger, more complex molecule with more atoms and more bonds. It has a higher standard molar entropy of about 230 J/mol·K.
Entropy and Reaction Favourability
In chemistry, reactions 'prefer' to move towards greater disorder, akin to how it's easier to make a room messy than to tidy it up. We describe this tendency using the term "favourability"
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Positive `\Delta S`: Indicates a reaction moving towards disordered, deemed to be favourable.
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Negative `\Delta S`: Suggests a move towards order, considered to be less favourable or unfavourable.
The Tidy Room Analogy
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The Low Entropy State (Tidy): Your room is perfectly tidy. The books are stacked vertically on the shelf, clothes are folded in the drawer, the bed is made, and there is nothing on the floor. For the room to be considered "tidy," every single item must be in its specific, designated place. There is only one way (or very few ways) for the room to be in this highly ordered state.
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The High Entropy State (Messy): Now, think about your room after a busy week. Clothes are on the chair, books are on the bed, and a cup is on your desk. For the room to be considered "messy," items just have to be not in their designated place. The shirt can be on the floor, on the chair, or under the bed—all of these count as "messy." There are a nearly infinite number of ways for the room to be messy.
Over time, as you live in your room, you interact with it. You take things out, you put them down.
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Because there are countless "messy" places to put your textbook down and only one "tidy" place for it on the shelf, it is statistically far more probable that it will end up in a messy location.
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The room doesn't have a desire for chaos. It simply trends towards the most probable state. Since there are vastly more arrangements that count as "messy" than "tidy," the room will inevitably become messy without a continuous, deliberate effort to keep it clean.
This analogy helps us understand why a system will always tend towards its state of highest entropy (the most probable arrangement), which is why rooms get messy on their own (entropically favourable), but tidying them requires a deliberate input of your energy (entropically unfavourable).
Gibbs Free Energy
So, if nature favours disorder, does that mean all reactions that increase entropy are spontaneous? Not necessarily. This is where Gibbs free energy (G) comes in. It's a thermodynamic potential that can be used to predict whether a chemical reaction will occur spontaneously under constant temperature and pressure.
This is explained separately here.
Practice Questions
Example 1
Calculate the standard change in entropy when 50.00 mL of water evaporates to form steam.
Example 2
Calculate the standard molar change in entropy for the complete combustion of octane (C8H18).