If you’ve ever taken a chemistry class, you know that it’s really more math than anything else. There are so many equations that you need to know in order to understand chemical processes. One of these involves how to calculate Delta S.
Delta S has to do with entropy, which is just a scientific word for disorder. It may seem a little strange that someone can measure or calculate disorder, but they actually can. In order to calculate it, however, they need to know a few other variables.
You may or may not be a science buff, but either way, you’ll almost certainly find some value in learning a little bit more about thermodynamics. It does, in fact, apply to your life, including how to calculate Delta S.
A Little Background on Thermodynamics
According to NASA, thermodynamics is “the study of the effects of work, heat, and energy on a system.” In other words, all the stuff that moves around and happens in the world? That’s a result of energy being used to make it move around and happen. Thermodynamics is the study of that process.
If you want to learn all about how to calculate Delta S, you can take a thermodynamics course. But most people probably don’t have the time, energy, or money to do that. However, if you want to have a better understanding of what Delta S is and how to calculate it, you will need to know a little bit about thermodynamics in general.
There are three laws of thermodynamics, and how to calculate Delta S is a big part of the second one.
The three laws of thermodynamics
Before we tell you about the three laws of thermodynamics, we should mention what they refer to. When scientists refer to these laws, they’re talking about a system and its surroundings. The surroundings are basically just everything that isn’t part of the system.
The system is separated from the surroundings by some sort of a boundary. This can be the wall of the container, for example, if the system is all of the molecules that are in the container. Closed systems are systems where matter is not able to pass between the system and surroundings (like a sealed jar of peanut butter), while open systems allow for this exchange of matter (like the ocean or the atmosphere).
The first law of thermodynamics is the law of conservation of energy. It states that energy can’t be created or destroyed within a system. It can only be transferred or converted from one form of energy to another.
There are two processes that can lead to a system experiencing a change in internal energy. These would be heat and work. The system could do work on the surroundings, or heat could flow into the system from the surroundings.
In either of these cases, energy isn’t being created or destroyed. It’s just being transferred and transformed between the system and surroundings.
According to the second law of thermodynamics, the entropy of any isolated system is always going to be increasing. It’s a spontaneous process. Isolated systems are always going to be heading toward thermal equilibrium, which equals the maximum entropy that a system can have.
According to this law, while energy is being transformed or transferred, the natural tendency is for it to be wasted. Any isolated system will have a natural tendency to degenerate into a more disordered state.
Spontaneous processes and the second law
All spontaneous processes actually yield increased entropy. Even when it appears that the amount of order is increasing, the entropy level is actually increasing when you take the entire system into account.
One example is that molecules can assemble themselves into a living organism. This would appear to be an increase in order and thus a decrease in entropy, but this is not the case. When you consider the entire system, including the environment, entropy is actually increasing overall.
In another scientific example, when you evaporate water from a salt solution, crystals can form. This may seem like increased order; in a way, it is, because crystals are more orderly than salt molecules that are moving around in the solution. However, the vaporized water that’s now traveling through the air is a lot more disorderly than the liquid water that was initially there.
If you need an example that seems more familiar to you, think about your room. If you aren’t making some sort of conscious effort to keep it clean, won’t it just get messier and messier over time?
When you clean your room, you appear to be increasing order, but you’re putting work into that process. The effort that you’re putting into cleaning your room has resulted in a decrease in entropy in your room. But, keep in mind, this is not a spontaneous process.
If you allow only spontaneous processes to dictate the cleanliness of your room, it will naturally get more disorderly over time.
It’s the second law of thermodynamics that involves how to calculate Delta S.
According to the third law of thermodynamics, as the temperature of a system approaches absolute zero, the entropy of that system will approach a constant value. Typically, this will be zero. The entropy of a pure crystalline substance, which would be in perfect order, would be zero at the temperature of absolute zero.
What Is Delta S?
We’ve already told you that the second law of thermodynamics is the one that involves how to calculate Delta S. How, you ask?
In the world of chemistry, S is the symbol for entropy. Also, in case you didn’t know this, scientists use the “delta” symbol to denote a change in a quantity. It follows from this that Delta S is the change in the entropy of a given system and surroundings.
As you already know, the second law of thermodynamics says that the entropy of the universe will increase for any spontaneous process. A spontaneous process is a process that takes place without the addition of external energy.
In order for a process to be spontaneous, it doesn’t have to take place quickly. For example, carbon spontaneously goes from diamond form to graphite form. It’s just that the process is so slow, no human being can observe this taking place during his or her lifetime.
It’s also important to remember that spontaneous processes can either be exothermic or endothermic. This means that in order for a process to be spontaneous, it doesn’t matter whether it releases heat (exothermic) or absorbs heat (endothermic).
How can you tell whether a process is spontaneous? It may not make much sense right now, but you actually use the second law of thermodynamics.
You know that any spontaneous process will increase the entropy in the universe, meaning that the increase in entropy of the universe is equal to the increase in entropy in the system plus the increasing entropy in the surroundings. And that that increase in entropy is going to be greater than zero.
But you can’t really measure the entropy change in the entire universe. Theoretically, it’s probably possible, but no one person would really be able to do that. Luckily, they don’t have to.
Gibbs free energy
In order to determine whether or not a process is spontaneous and thus has a positive value for Delta S, you actually don’t need to know how to calculate Delta S for the entire universe. You just need to be able to calculate Gibbs free energy.
When a process occurs at a constant pressure and temperature, you can calculate Gibbs free energy. In order to do this, you just multiply the entropy by the temperature in Kelvins and then subtract that quantity from the enthalpy (H). Enthalpy is another word for heat, in this case meaning the heat in the system.
Calculating Delta G
The change in Gibbs free energy for any chemical process is actually written as Delta G. Given that the temperature (T) and pressure (P) of the system are constant, you can write the equation for Gibbs free energy as follows:
Delta G = Delta H – (T)(Delta S)
When you calculate Delta G, you can use the sign of your result to figure out whether the reaction is spontaneous or not. Every reaction will be spontaneous in one direction or the other. It’s just that some reactions will be spontaneous in the reverse direction.
With any given chemical reaction, on a molecular level, there will be some molecules going back to the reactants form. It’s just that if the process is spontaneous in the forward direction, there will be more turning into products than turning back into reactants.
If Delta G is less than zero, meaning negative, the process is exergonic. This means it’s going to proceed spontaneously in the forward direction and create something new. However, if Delta G has a positive value, the process is endergonic, meaning that it will proceed spontaneously in the reverse direction and break down something to create more starting materials. If Delta G is zero, the system is in equilibrium, meaning the concentrations of both the products and reactants are going to remain constant.
As you can see from the above equation, in order to calculate Delta G, you just need to know Delta H, Delta S, and the temperature in Kelvins.
How to Calculate Delta S
Many people will focus only on calculating Gibbs free energy and not worry about calculating Delta S. In fact, many scientists simply obtain Delta S values from a table of standard values. They can do this, given that they know the value of Delta G in that situation.
Calculating Delta S
However, you can easily learn how to calculate Delta S just by looking at the equation for Gibbs free energy.
Since Delta G = Delta H – (T)(Delta S), all you need to do is rearrange the equation if you’re trying to figure out how to calculate Delta S. You just need to isolate Delta S in that equation. Once you do that using basic algebra, you’ll see that:
Delta S = (Delta G – Delta H) / -T
The units for Delta S are quite complicated. It’s typically kJ/(mol-rxn)*K). In other words, this is kilojoules per mole of reaction times temperature. You don’t necessarily need to know exactly what these units mean unless you’re in the field of chemistry. The main takeaway is that the higher the Delta S value, the more disordered the system is becoming.
Delta S and spontaneity
If the process is spontaneous, the Delta S value is always going to be positive. The higher it is, the more entropy the reaction is producing.
Most of the time, even if you’re studying thermodynamics, you’ll just have to calculate Delta G in order to assess whether or not the reaction is spontaneous. Entropy is kind of a difficult concept to pin down, so a lot of people find it easier to just focus on Delta G.
However, it’s still good to know how to calculate Delta S. It’s relatively straightforward because all you really need to do is rearrange the equation that chemists use to calculate Delta G. The concept of quantities of entropy may not be very straightforward, but fortunately, the process of calculating it is.
If you want to learn how to calculate Delta S, you can easily do so just by following the above equation. However, it doesn’t mean much unless you understand the science behind it. You should know what entropy means, and you should understand the concept of a spontaneous process for the quantity of Delta S to mean anything other than some random number in front of you.
Calculating and Recalculating…
You may not have thought that much before about how to calculate Delta S. You probably don’t even think about entropy that much, despite the fact that you experience it every single day. One of the wonders of science is that it governs so much of what we do and experience without us really having to think much about it.
Learning the chemistry and math that is behind so many of the chemical reactions that we experience every day can be quite fascinating. It’s so important in our lives on a daily basis. However, so many people are entirely unaware of the mechanisms that underlie all of it.
How to calculate Delta S is just one small part of understanding chemistry and thermodynamics. However, now that you have a better understanding of this concept, hopefully, you have a better appreciation for just how intricate and complex these processes are. After all, the world wouldn’t be the same without them. In fact, it wouldn’t be at all!
What do you think of everything we’ve just told you about how to calculate Delta S? Tell us about it in the comments section!