Entropy - Online Tutor, Practice Problems & Exam Prep

• Entropy measures disorder in a system
• Thermodynamics relates to heat energy and reaction favorability
• Spontaneous reactions cause entropy to increase
• Factors that increase entropy include molecular degrees of freedom, complexity and mass
• Standard molar entropy varies based on phase, complexity, and mass
• Physical changes can increase or decrease entropy through temperature and pressure
• Chemical changes' entropy change is determined by the number of moles of products
• An increase in the moles of products leads to an increase in entropy
• A decrease in the moles of products leads to a decrease in entropy
• Entropy change is a measure of the increase or decrease in disorder due to physical or chemical changes

Understanding Entropy

In this video we're going to take a look at entropy, which uses the variable S. Now it is the measure of disorder. This order could also be called randomness or chaos that exists within a system, surroundings and universe. When we say system, we're just talking about a chemical reaction or an object of focus. The surroundings is everything else. Together they form our universe.

Now energy is dispersed between or because our system is not able to convert all energy into usable energy. With this idea we have thermodynamics. Thermodynamics describes a relationship between heat energy and reaction favorability. Now recall the first law of thermodynamics. Energy cannot be created or destroyed, nor destroyed, but it is transformed.

So how does this relate to everyday life? Well, you might be seeing talks of energy transitions about EVs, solar power and all this stuff. So let's take a look at this image. Let's imagine that this represents a battery, and that battery is solar powered. So we have the sun here that's beaming its energy and the battery is absorbing it. This is transforming the energy. It's converting it from solar energy to electrical energy. So now our battery is more charged up.

But here's the thing. Things like this are not 100% efficient. Some of the energy will not be absorbed by the battery and it's going to be lost. So this energy is lost as entropy, as randomness. And this is a natural process. Energy is not created nor destroyed, but not 100% of it is transformed or transferred cleanly. Some of it is lost as entropy.

Now here the second law of thermodynamics deals directly with entropy. It states that the entropy of the universe is always increasing. Remember, entropy is chaos or disorder. We say that the entropy of the universe is always increasing. This kind of calls back to the whole Big Bang Theory. The end. The universe is ever expanding from a center, so the universe is moving outwards. More disorder, more chaos. Planets die, Suns, supernovas, all this stuff is a natural process of the universe.

Now here we're going to say all spontaneous reactions involve an increase in the entropy of the universe. So we know that a spontaneous reaction will always 'cause our S variable entropy to go up, right? So keep this in mind when we talk about the variable of entropy.

Entropy Example

Here the second law of normal dynamics leads us to conclude what? Here the total energy of the universe is constant? No, the second law of thermodynamics doesn't talk about the total energy of the universe.

The disorder of the universe is increasing with the passage of time. This is what the second law of thermodynamics discusses, that the entropy of my universe changing my energy of my or entropy of my universe is ever increasing. So it's going up, which is what this is saying.

Here the total energy of the universe is increasing with time. No, not energy entropy. The total entropy of the universe is decreasing with time. No, that's saying the exact opposite of the second law of thermodynamics.

So out of my options, option B is the correct answer.

Factors Affecting Entropy

Now here we're going to say that there are three main factors that can increase my entropy. The first one is my molecular degrees of freedom. This is just the ways in which a molecule is free to move. Here we say the more ways a molecule can move, then the more entropic it is.

Next, the number of arrangements and this deals with molecular complexity and mass. When we say molecular complexity, it's just the number of atoms in a substance. So for example, let's say it gave us Chapter 4, which is methane versus ethane, which is chapter three, Chapter 3. This has five total atoms in IT1 carbon and four hydrogens. And this one here has 8 total atoms in it, 6 hydrogens, 2 carbons. That thing is more complex, therefore it's more entropic. More atom just means, more arrangements, more ways they can move, more ways they can position themselves.

Now connected also to this is Massachusetts. The greater the mass, the greater the complexity, the more entropic it can be as well. Finally, we can look at the number of moles of substances. More moles, more possibilities, more chaos, more disorder, an increase in entropy. So keep in mind these three different factors and how they can themselves increase our entropy overall.

Standard Molar Entropy

Now, standard mobile entropy represented by S0 is the entropy possessed by 1 mole of a substance at standard conditions. And remember, standard conditions means we're at 25°C and one atmosphere. Now here's something important to note. Different phases of a substance can exist simultaneously at standard conditions. For example, water. We know that water exists in its liquid phase predominantly between 0°C and 100°C. Here we're at standard conditions of temperature, which is 25°C. Even at that temperature, if you were looking at some liquid water, there would be some water vapor involved. Even in the room that you're standing in, there's water vapor all around us.

We may not see it, but it exists, and because of that we can find standard molar entropies of liquid water and gaseous water within our books. Now, solid water, though, the temperature is too high for it to exist under these standard conditions, so you won't find a standard molar entropy for solid water. Now here, if we're comparing standard mode entropies, we first have to look at the states of matter that are involved. If we're going from solid to liquid to gas, we see that the molecules are more and more spread out. As we transition from solid, liquid to gas, then becoming more spread out means they're more random in their orientation and arrangements, and therefore they're more chaotic. This would mean that we're increasing our standard molar entropies here.

If they're in the same phase, like you're comparing 2 solids, or comparing 2 liquids, or comparing 2 gases, then we look at what happens when the states of matter are the same. The first thing we do is we look at complexity. We're going to say the greater the complexity, the greater the standard molar entropy. For example, let's say we're looking at oxygen, the gaseous phase, and sulfur in the gaseous phase. Since they're both in the same phase, we then look at their complexity. Here O2 is made-up of two atoms of oxygen. An S8 is made-up of eight atoms of sulfur. S8 has more atoms involved, therefore it's more chaotic and therefore it's standard molar entropy would be higher.

But let's say that the two substances that I'm comparing are in the same phase. They have the same complexity. The last thing we look at is Massachusetts. The greater the mass, the greater the standard molar entropy. So for example, let's say we're looking at Br2 and iTunes, and let's say they both were in the same phase. They're both in the same phase. So next we look at it is our complexity. They both are composed of two atoms. Br2 is composed of two atoms of bromine. I2 is composed of two atoms of iodine, so the tiebreaker would look at their mass. If you look at their molar masses, you would see that I2 weighs more than Br2, and because of that I2 would be more chaotic and therefore a higher standard molar entropy.

All right, so just remember we can compare the standard mode entropies of different substances by first looking at the phases that they're in. Gases have the most entropy, followed by liquids, then solids. If they're tied, then look at the complexities, so the number of atoms composed within that substance. If they're still tied, use the mass as the final tiebreaker.

Entropy Example

Here it says select a substance with greatest molar entropy. So remember when comparing the entropies of different substances, the first thing we look at is their phase. So gases have the most entropy, then liquids, then solids. If we take a look at our options here, we have 3 gases. They would have the greatest entropy. So that means A is out, B is out, and D is out.

The next thing we look at to break the tie is their complexity. Basically, the more atoms comprising the substance, the greater its entropy. Ammonia has four atoms involved because it has one nitrogen and three hydrogens. Carbon dioxide only has three atoms since it's one carbon and two oxygens. And sulfur trioxide has four atoms because it's one sulfur and three oxygens. So E is out.

Now we see that ammonia and sulfur trioxide have the same complexity. So the last thing we look at to break the tie is their mass. The greater the mass of the substance, the greater the entropy here. If we compare the masses of ammonia versus sulfur trioxide, sulfur trioxide weighs more. Therefore it's going to have the higher molar entropy. So here the answer is option F.

Entropy and Physical Changes

So here in this video we're going to take a look at physical changes and how they can affect the overall change in our entropy. Will it increase our entropy or decrease our entropy? So here we're going to say that entropy change, which is ΔS, is a measure of the increase or decrease in disorder due to physical or chemical changes. Now we're going to say an increase in the entropy change is due to an increase in molecular degrees of freedom. So the more movement a substance has, the greater the change in entropy can be.

Now here we're going to say the greater the degree of freedom, which is molecular motion, this is going to cause the greater the change in entropy. So here, let's take a look at change in entropy when it comes to physical changes. All right, so here we have our three major states of matter: solid, liquid, and gas. We can say that our entropy increasing means ΔS goes up. So how can we play around with temperature and pressure to cause this change?

Well, we want more motion, more molecular motion, and we should know that at higher temperatures, molecules absorb the external energy and use it to move themselves even more. So increasing our temperature can lead to an increase in our entropy, our change in entropy. What about pressure? Well, if we have our substances within a container with a movable piston, if we push down on that piston, we're increasing the pressure inside of the container. This would cause molecules to come closer and closer together. They're going to become less disordered, because disorder means you're out and about moving anywhere you want. Increasing the pressure stops that.

So if we want to increase entropy, we want to decrease our pressure, giving the molecules more space, more freedom of movement. Now here, how do we decrease the change in entropy? By doing the exact opposite. If we want to decrease entropy, we force molecules closer together, become more organized. This would happen at higher pressures. And then how do we force molecules to come closer together? We decrease the temperature, so decreasing the temperature would force them to come closer and closer together.

Think of gaseous water. Lower the temperature enough, it will condense down into a liquid. Liquids have way less freedom of motion than gases, right? So keep in mind these changes that we can do in terms of temperature and pressure and how they can affect our entropy change.

Entropy Example

Predict how the entropy of the system is affected in the following process. Alright, so for the first one, we have methane gas at 125℃ and it's transitioning to methane gas at 200℃. So the phase of method is still staying the same, but our temperature is increasing. Increasing our temperature would mean that our methane molecules can absorb that extra thermal energy, using it to propel themselves even more, becoming more chaotic, increasing their degrees of freedom. So here increasing temperature would cause an increase. It might change in entropy.

Alright. Next we have here potassium chlorate solid, and it's in a 7 liter container. And then we have potassium chlorate liquid in a three liter container, all right. So changing the volume of the container is a way of affecting the pressure in the container. Remember, there's an inverse relationship between pressure and volume. So our volume is going down from 3 liters to 7 liters, which would mean pressure is going up. But that's kind of a trick question here. Why? Because whether we're looking at what we're starting with and what we're ending, we're dealing with solids and liquids.

Solids and liquids are not going to be as affected by changes in pressure, at least not something as small as going from A7 litre container to a three liter container. So what you should really be looking at is the phase change we're going from solid potassium chlorate to liquid potassium chlorate. Liquids have more degrees of freedom. Their molecules are able to move around more. So because of this change in our phase, there's going to be an increase in the change in entropy. So again, entropy change is going up because we're going from a solid, which has less degrees of freedom, less entropy, to a liquid which has more degrees of freedom, more movement, more entropy.

Alright, So in both choices, the changing entropy is increasing.

Entropy and Chemical Changes

Now when looking at chemical changes, in order to determine the change in entropy, we're going to look at it very simplistically. We're going to say entropy change of chemical reactions are determined by the number of moles of products. So here we take a look in the first image, we're talking about increasing our entropy. So that means the change in entropy is going up.

If we look at our example, we have one mole of reactant and then if we look at the number of products, we have two moles of reactant of product. The number of moles of product has gone up, so there's an increase in moles of product. More product being made means there's more chaos, more disorder, therefore a higher change in entropy.

How about decreasing entropy? Well, here decreasing entropy will mean we're going down in terms of changing entropy. Here we have initially 1 mole of nitrogen gas, 3 moles of hydrogen gas or 4 total moles. When we transition over to the product side, we only have two moles of product, so we have less moles at the end, which means there's less chaos, less disorder and therefore less entropy.

So if there's a decrease in the moles of product, usually that means that there's going to be a decrease in the change in entropy. So just look at it simplistically as that is my number of moles going up when I transition to products or is it going down? This will determine the overall change in our entropy. So look at this in this simplistic type of way.

Entropy Example

Which one of the following reactions produces a decrease in the entropy of the system? So for A, we're starting out with one mole of solid potassium chloride. It dissolves to produce 2 moles of products. So the number of moles of product has gone up. Therefore, this should be an increase in my change in entropy of my system. So this is not the answer.

For the next one, we're going from three moles of reactants to just two moles of product. The number of moles of products has decreased, so we've decreased the number of moles going towards the product side. So this would be a decrease in the entropy of my system.

Now let's look at the other options. Here we're going from 1 mole of reactant to three moles of product. So the number of moles of product is going up. Therefore, this will be an increase in entropy.

Then finding the last one, what do we have here? We have 7 moles total of reactants and over here we have 12 moles of products. So the number of moles has increased as we transition towards the product side, which will cause an increase in my entropy of the system. So out of all the choices, option B represents the one where there's a decrease in the entropy of my system.

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

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)

Identify sign of entropy changes for the following processes.

1) freezing water to form ice

2) ideal gas allowed to expand in a closed container at constant T

3) mixing of two gases into one container

4) NH₂ (g) (1atm) → NH₂ (g) (3 atm)

5) gas mixture transferred from larger to smaller container

• A. 1) −∆S, 2) +∆S, 3) +∆S, 4) −∆S, 5) −∆S
• B. 1) −∆S, 2) −∆S, 3) +∆S, 4) +∆S, 5) −∆S
• C. 1) +∆S, 2) −∆S, 3) +∆S, 4) −∆S, 5) +∆S
• D. 1) +∆S, 2) +∆S, 3) −∆S, 4) +∆S, 5) −∆S

Select correct statement(s) below:

a) gaseous CO₂ has higher entropy in 2 L container compared to in 5 L container

b) N₂O (g) contains higher standard molar entropy then HI (g)

c) NaHCO₃ (aq) + HC₂H₃O₂ (aq) → NaC₂H₃O₂ (aq) + H₂O (l) + CO₂ (g) has a negative ∆S

d) evaporation of water at 100 °C involves greater ∆S than evaporation at 112 °C

• A. gaseous CO₂ has higher entropy in 2 L container compared to in 5 L container
• B. N₂O (g) contains higher standard molar entropy then HI (g)
• C. NaHCO₃ (aq) + HC₂H₃O₂ (aq) → NaC₂H₃O₂ (aq) + H₂O (l) + CO₂ (g) has a negative ∆S
• D. evaporation of water at 100 °C involves greater ∆S than evaporation at 112 °C