Entropy - Online Tutor, Practice Problems & Exam Prep

Entropy, a measure of disorder, is crucial in thermodynamics, linking energy transformations in biological systems. Living organisms, as open systems, exchange energy and mass, allowing local entropy to decrease while universal entropy increases. The Gibbs Free Energy Equation, ${\mathrm{\Delta G}}^{=}\Delta H-T\Delta S$, connects changes in entropy (ΔS), enthalpy (ΔH), and free energy (G), emphasizing that higher universal entropy correlates with stability and lower energy states. Understanding these concepts is essential for grasping biochemical reactions and energy dynamics.

Entropy, Thermodynamics & System vs. Surroundings

In this video, we're going to begin our discussion on entropy. So you guys have learned in your previous courses that entropy is a measure of randomness, and we'll talk more about entropy in our next video. But before we get there, we need to first brush up on some concepts that are going to help us better understand entropy. Entropy is a property of thermodynamics, and the laws of thermodynamics describe the flows and changes of heat, energy, and matter in reactions and in living things. In our example below, we'll see that we have the sun here, which is the source of energy for the vast majority of living organisms on Earth, and the sun provides the solar energy that can be absorbed by plants and photosynthetic organisms. Then, the photosynthetic organisms convert the solar energy into chemical energy, and then animals can eat plants to obtain the chemical energy and convert it into mechanical energy or kinetic energy for their movements. Also, notice that with each transfer of energy here, there is also a loss of energy in the form of heat. We'll talk more about this when we talk about the second laws of thermodynamics in our later videos.

Another important thing is that thermodynamics requires a distinction between the system and the surroundings. The system refers to the local portion of the universe that we are focused on, whereas the surroundings refer to the rest of the universe. Living things are systems that are referred to as biological systems, and they are a specific type of system known as an open system. Open systems exchange mass and energy with the surroundings, making them open systems. Let's take a look at our example. Down below on the left here, we have a living system, which is a cell, and then we have the system boundary or our biological system boundary, which is the plasma membrane. Notice that the cell is an open system, which means that it can take in mass and also export mass with the surroundings, and it can also import and export energy.

Now, our system could be a biological system like an entire cell, or it could be a specific chemical reaction. Here we have a reaction that occurs within most cells where glucose is converted into glucose-6-phosphate. The main difference is that we have a hydroxyl group here, whereas over here, we have a phosphate group. It is catalyzed by an enzyme, and there are also ions such as magnesium, which is an essential ion of life, and then we have ATP or energy that's required for this reaction. So, you can have a specific system be a chemical reaction, and we'll see a lot of this as we move forward in our biochemistry course. In our next video, we're going to use these concepts to help us better understand entropy. So I'll see you guys in that video.

Understanding Entropy

So we've already said that entropy is a measure of randomness or disorder. And the greater the disorder is, the greater the entropy will be. So they go hand in hand. And let's take a look at an example. What you'll see is that we have these 2 billiard tables and the one that's on the left, notice that the billiard balls are very nicely organized. They're highly ordered and so that creates a state of low entropy. Whereas on the right billiard table, the billiard balls are scattered everywhere and they're no longer a single unit. You can see they're all over the table and very disorganized, exhibiting a state of high entropy. This creates a state of high entropy, and the reactions of the universe moving towards increased entropy tend to confuse students because students know that cells are able to take a bunch of amino acids and link those amino acids together to create a single protein that's highly ordered and lowers the entropy. So cells are able to essentially lower entropy. So how is it that the universe is increasing entropy? Here's the thing. Recall that cells are biological systems, as we said in our previous video that systems are a local portion of the universe that we specifically focused on. The deal is that the local entropy is able to decrease as long as it's accompanied by an increase in universal entropy. So, yes, cells are able to decrease the local entropy, they're able to lower entropy, but they have to be accompanied, these reactions have to be accompanied by another reaction that ultimately ends up increasing the overall universal entropy. And we'll talk more about this in our later videos. But in this video, I want you guys to know that high universal entropy is associated with more stability, as well as lowered energy of a system.

Let's take a look at this example below and at this graph. Notice that the graph has free energy of the system on the y-axis, as well as the reaction coordinate on the x-axis or the time that passes as the reaction progresses. For this particular reaction, we have reactants that have higher free energy than the products. Recall that this reaction looks somewhat like this. What I want you guys to know is that the free energy of the reactants for this particular reaction is high. Here we have high energy, and for the products down low, we have low energy. High energy of a system is associated with being unstable. It is unstable. It's also more ordered, associated with being more ordered, and that is associated with having lower entropy. Conversely, being stable is associated with having more disorder and that is associated with high universal entropy. That's what we said earlier, that high universal entropy, over here on the right, is associated with more stability, being more stable, as well as having lower energy. You can see that the lower energy here corresponds with all of these things. We'll discuss and distinguish a lot more about this when we talk about the second law of thermodynamics in some of our later videos. But in our next video, we're going to talk about how entropy is incorporated into the Gibbs free energy equation. I'll see you guys in that video.

Entropy & Gibbs Free Energy Equation

So here's an equation I know you guys have definitely seen in your previous chemistry courses, and that's the Gibbs Free Energy Equation, which expresses the link between changes in entropy, enthalpy, and free energy. Changes here are shown by a Greek symbol that's known as delta, shown as a triangle, and recall that it just means the final values minus the initial values. The Gibbs free energy equation is shown here, and on the far right, we have delta s, and recall delta s is the change in entropy of the system. So in this block, we'll just put entropy. Recall that entropy is a measure of disorder or randomness. Now, T here represents temperature, but specifically, this is temperature in units of Kelvin. This tends to trip up some students because practice problems will give you guys the temperature in Celsius, and you have to be able to convert it into Kelvin. So, here let's put that Kelvin is equal to the degrees that are given to you in Celsius plus 273.15. This is an equation that you guys should be able to know to make sure your units of temperature are always in Kelvin. Now, delta H here represents the enthalpy of the system. It represents the enthalpy. So, enthalpy here is the total energy of the system. This includes the energy within every chemical bond within every molecule or compound that's part of the system. So in this block, we can put enthalpy. Now, our last, I guess, variable over here is the Gibbs free energy, represented by the energy available to do work. So here we can put free energy. This is only a small subset of the total energy that is actually available to perform work. By work in a reaction, we really mean changing the components, changing the concentrations of components within the system. Again, we'll talk a lot more about this equation in our later videos. But for now, this is a good summary, and I'll see you guys in the practice problem videos.

ΔH-T·ΔS=ΔG K=°C+273.15

When solid ice water melts to liquid water, how does that affect its entropy?

• A. Entropy decreases.
• B. Entropy increases.
• C. Entropy stays the same.
• D. Impossible to tell. Needs more information.

How does the entropy change with the following reaction?

• A. Entropy decreases.
• B. Entropy increases.
• C. Entropy stays the same.
• D. Impossible to tell. Needs more information.

Consider a reaction at 100˚C with ΔG = 15 KJ and ΔH = 40 KJ. Calculate the system's change in entropy.

• A. 139.13 kJ/K
• B. -13.3 kJ/K
• C. 0.15 kJ/K
• D. 0.07 kJ/K

Here’s what students ask on this topic:

What is entropy in thermodynamics?

Entropy in thermodynamics is a measure of disorder or randomness within a system. It is a fundamental concept that helps describe the flow and transformation of energy and matter. In thermodynamic processes, entropy tends to increase, leading to greater disorder. This principle is encapsulated in the Second Law of Thermodynamics, which states that the total entropy of an isolated system can never decrease over time. Entropy is crucial for understanding energy dynamics in biological systems, where local decreases in entropy (e.g., protein synthesis) are offset by increases in universal entropy.

How does the Gibbs Free Energy Equation relate to entropy?

The Gibbs Free Energy Equation, given by $\mathrm{\Delta G}=\mathrm{\Delta H}-T\mathrm{\Delta S}$, links changes in entropy (ΔS), enthalpy (ΔH), and free energy (ΔG). In this equation, ΔG represents the change in free energy, ΔH is the change in enthalpy (total energy), and TΔS is the product of temperature (in Kelvin) and the change in entropy. This equation helps determine whether a reaction is spontaneous. A negative ΔG indicates a spontaneous reaction, often associated with an increase in entropy (ΔS) and a decrease in free energy.

Why is high entropy associated with stability?

High entropy is associated with stability because it corresponds to a state of greater disorder and lower energy. In thermodynamic terms, systems naturally progress towards states of higher entropy, which are more probable and stable. For example, a disordered arrangement of molecules has more possible configurations than an ordered one, making it more stable. This principle is crucial in understanding biochemical reactions, where the increase in universal entropy ensures the stability and feasibility of processes within living organisms.

What is the significance of entropy in biological systems?

In biological systems, entropy plays a vital role in energy transformations and metabolic processes. Living organisms are open systems that exchange energy and matter with their surroundings. While local entropy within a cell can decrease (e.g., during the synthesis of complex molecules), this is accompanied by an increase in universal entropy. This balance is essential for maintaining life processes. Understanding entropy helps explain how cells manage energy efficiently and how biochemical reactions are driven by changes in entropy and free energy.

How do cells decrease local entropy while increasing universal entropy?

Cells decrease local entropy by organizing molecules into complex structures, such as proteins and nucleic acids. This process requires energy, often derived from ATP hydrolysis, which increases the entropy of the surroundings. For example, when ATP is hydrolyzed to ADP and inorganic phosphate, the released energy drives the synthesis of ordered biomolecules, decreasing local entropy. However, the overall entropy of the universe increases due to the energy released as heat and the increased disorder of the hydrolysis products. This balance ensures that the Second Law of Thermodynamics is upheld.