# Entropy

If you've heard of entropy before, you might know that it's a way to measure the amount of messiness in a thermodynamic system. But did you know that entropy is actually more complicated than that?

Entropy, or S, is all about how energy can be spread out among molecules. It's like a measure of how many ways you can rearrange a bunch of puzzle pieces. In this article, we'll dive deeper into the world of entropy. We'll explore why it's all about energy distribution, and how it relates to spontaneous reactions. We'll even show you how to calculate the entropy change of a reaction using standard entropy values. So if you're ready to learn about the meaning of total entropy and more, keep reading! And don't worry if you're not a science whiz - we'll explain everything in simple terms that anyone can understand. Plus, did you know that understanding entropy can help you better understand the world around you? So let's get started!

## What is entropy?

To get a better grasp of entropy, imagine a group of molecules in a system that are in equilibrium. Even though they all have the same average energy, if you were to take snapshots of these molecules at different times, you'd see that their energy levels are constantly changing. This is because molecules interact and share energy with each other. For example, think of gas particles bouncing around in a container. Every time they collide with each other or the walls of the container, some particles gain energy while others lose it. The faster particles have more energy than the slower ones. So, if you were to take a snapshot of these particles at one moment, you might find that one molecule has a certain amount of energy. But if you were to take another snapshot a moment later, that same molecule might have less energy. This constant random motion and energy transfer between molecules is what leads to entropy. The more ways energy can be distributed among the molecules, the higher the entropy. So, even though the molecules may be in equilibrium, the distribution of their energy is constantly changing, leading to a higher level of disorder and randomness in the system.

Energy exists in ‘packets’ which we call quanta. A particle can only have a whole number of quanta, never fractions of quanta. You must imagine that as the particles interact with each other, the quanta get distributed (or spread out) among them. In other words, every time you take a snapshot, there is a new arrangement of quanta between the molecules. The amount of quanta available to a particle in a system is limited to the total energy of the system. If you were to increase the amount of total energy in the system, for example by heating a gas, you would increase the number of available quanta that a particle can have.

To sum it up, when we talk about entropy, we are referring to the number of ways that energy can be distributed among the molecules in a system. The more energy a system has, the more ways there are to distribute that energy randomly.

Think of it like spreading out a deck of cards. The more you shuffle them, the more ways the cards can be arranged. In the same way, the more ways there are to distribute energy among the molecules in a system, the higher the entropy. When the particles in a system have more freedom to move around, the energy gets spread out more, and the system becomes more stable. This is why liquids and gases have a higher entropy than solids. In a liquid or gas, the particles have more disorder or freedom to move around, which leads to a higher number of possible energy distributions among the particles. So, understanding entropy can help us better understand how energy is distributed in different systems, and why some systems are more stable than others.

### Units of entropy

Entropy is measure in joules, and not kilojoules. This is because a unit of entropy is smaller (in order of magnitude) than a unit of enthalpy. The official unit for entropy is .

## Entropy changes

To further elaborate, entropy change is a measure of the change in disorder or randomness of a reaction. Entropy is a state function, meaning that it depends only on the initial and final states of a system and not on the path taken to get there. However, unlike enthalpy, we cannot directly measure entropy. Instead, we measure the change in entropy (∆S) between the initial and final states of a system.

Standard entropy is the entropy of a substance under standard conditions (25°C and 1 atm). In exams, you will be provided with standard entropy values for various substances. It is important to note that the standard entropy values for elements are not zero, unlike the standard enthalpy of formation of an element.

To calculate the entropy change for a reaction, we use the standard entropy values and the following equation:

∆S = ∑S(products) - ∑S(reactants)

where the sigma symbol (∑) means "sum of". The value of ∆S will tell us whether a reaction increases or decreases in disorder. A positive ∆S means that the reaction results in an increase in disorder, while a negative ∆S means that the reaction results in a decrease in disorder.

It is also important to note that a chemical reaction not only affects the system (the species involved in the reaction) but also the surroundings (the test-tube or beaker and the air in the laboratory). However, in the context of calculating entropy change, we only consider the change in entropy of the system.

### What is total entropy change?

To explain the backwards endothermic reaction of dinitrogen tetroxide decomposing to nitrogen dioxide, we need to consider the second law of thermodynamics. As we mentioned before, the second law of thermodynamics states that in a spontaneous process, the total entropy change must be positive.

In the case of the dimerisation of nitrogen dioxide, the forward reaction is exothermic and results in a decrease in enthalpy. This means that the forward reaction is energetically favorable and will occur spontaneously. However, at room temperature, the system will reach equilibrium where some of the dinitrogen tetroxide will spontaneously decompose back to nitrogen dioxide. This is because the total entropy change for the reaction is positive, meaning that the overall disorder of the system and surroundings is increasing.

The increase in entropy occurs because the decomposition of dinitrogen tetroxide to nitrogen dioxide results in an increase in the number of gas molecules, which increases the number of possible ways the energy can be distributed among the molecules. This leads to an increase in disorder and an increase in entropy.

Therefore, even though the backwards reaction is endothermic and absorbs heat from the surroundings, it still occurs spontaneously because the total entropy change is positive. This highlights the importance of considering both enthalpy and entropy changes when predicting the feasibility of a reaction.

### What is the second law of thermodynamics?

To summarize, the second law of thermodynamics states that in a spontaneous process, the total entropy change for a system and its surroundings is positive. Entropy is a measure of the disorder or randomness in a system, and the total entropy change takes into account both the system and the surroundings.

When predicting the feasibility of a reaction, we need to consider both enthalpy and entropy changes. Gibbs free energy is another way of measuring the spontaneity of a reaction, taking into account the enthalpy change, entropy change, and temperature.

The equation for Gibbs free energy is ΔG = ΔH - TΔS, where ΔG is the free energy, ΔH is the change in enthalpy, T is the temperature, and ΔS is the change in entropy. By calculating the value of ΔG, we can determine whether a reaction is spontaneous or not.

Overall, understanding the relationship between entropy, enthalpy, and feasibility is crucial in the field of thermodynamics and can help us predict and understand the behavior of chemical reactions.

Additionally, when predicting the feasibility of a reaction, we need to consider both enthalpy and entropy changes. Gibbs free energy is another way of measuring the spontaneity of a reaction, taking into account the enthalpy change, entropy change, and temperature. The equation for Gibbs free energy is ΔG = ΔH - TΔS, where ΔG is the free energy, ΔH is the change in enthalpy, T is the temperature, and ΔS is the change in entropy.

## Entropy

How do you calculate change in entropy?

Total entropy change is the sum of entropy change in the system and the surroundings. We calculate it using the following equation:∆S (total) = ∆S (system) + ∆S (surroundings)

What is entropy in A-Level Chemistry?

Entropy is the number of possible ways quanta (packets of energy) can be distributed between the particles in a system. The more ways there are, the higher the entropy. Quanta get distributed when the particles in a system interact with each other and transfer energy. The more freely moving the particles in a system are, the more energy is spread about the system. We say liquids have a higher entropy than solids because the particles in a liquid move about more than in a solid i.e., the particles in a liquid are more disordered. So there is a higher distribution of quanta between the particles.

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