Dive deeper into the concepts of entropy and free energy by exploring our comprehensive library of interactive 3D models, study guides, simulations, and more!

Chemistry

Chemistry is the branch of science that deals with the study of matter! Did you know that chemistry is also called “the central science,” because of its role in bridging physics with other natural sciences? Let's dive into learning more on the composition and the physical and chemical properties of various forms of matter!  

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AP Bio

CBSE Bio

General Chemistry

General Bio

General Physics 

Biology

Physics

## INTRODUCTION: 
You might have heard that it is not easy to make curd during the cold season! Have you ever wondered what could be the relation between room temperature and the making of curd? What could be the relation between temperature and a biological process? 

![Curd](//images.ctfassets.net/4yflszkpcwkt/5wQfO8P4ZCyCJ6EfXoM4t8/f48928266281910ea3376ee8b14ccad3/Curd.png)
[Source](https://timesofindia.indiatimes.com/life-style/food-news/why-is-it-difficult-to-set-curd-in-winters-easy-tips-on-how-to-do-it-right-/photostory/87754252.cms?picid=87754273)

Let's take another example to make it clear. All of us have dissolved sugar in water. Have you noticed that after dissolving a particular amount of sugar, it doesn't mix, and the sugar starts to settle down at the bottom of the container? But if you heat the water a bit, you can easily mix more sugar into the same solution! In fact, that’s how we make sugar syrup. 

We keep increasing the temperature, and more and more sugar gets mixed into the solution. Have you ever wondered about the relationship between increasing temperature and the amount of sugar dissolving? The answer lies in a thermodynamic concept of spontaneity. Gibbs' free energy (ΔG°) is the concept that tells us about the spontaneity or the feasibility of any process taking place near us.

![sugar-syrup-thermometer](//images.ctfassets.net/4yflszkpcwkt/3lOhasccATlO2RndHDt1fY/a71630f326157bba3839c85f5f803970/sugar-syrup-thermometer.jpg)
[Source](https://pastrymaestra.com/basic-techniques/how-to-cook-sugar-syrup/) 

### EQUILIBRIUM CONSTANT (K) AND ΔG: 
A reversible reaction's G is equivalent to 0 at equilibrium. The quantities of all chemicals in the process at equilibrium are referenced as Keq. As a result, we may construct the following equation (using a more sophisticated treatment of thermodynamics): 

![Gibbs Free Energy and Equilibrium Constant ](//images.ctfassets.net/4yflszkpcwkt/6FMt4LfkgWoUKoFxkKhrZ3/16557458997d4bdb297282711b5ad9af/thumb_540_50.jpg)
[Source](https://www.ck12.org/c/chemistry/calculations-of-free-energy-and-keq/enrichment/Relationship-between-Free-Energy-and-Equilibrium-Constant-Overview/)

The computation of the other requires knowledge of either standard Gibbs free energy or the equilibrium constants for a process. 

K and ΔG° can both be used to forecast the product-to-reactant ratio at equilibrium in a reaction. We have seen above that the expression that connects G° with K is ΔG°=−RTln⁡K. How do we predict the product to reactant ratio using this expression is explained below: 

### LET'S LOOK AT GIBBS FREE ENERGY AND EQUILIBRIUM CONSTANT PROBLEMS:

![Gibbs Free Energy Problem](//images.ctfassets.net/4yflszkpcwkt/lgLWq20e5UlYEPskpJbWQ/0d5b0ce055d6a9b2f2690331f91e4599/Gibbs_Free_Energy_Problem.png)
[Source](https://quizlet.com/217248154/principles-of-bioenergetics-flash-cards/)

## CONCLUSION: 

- The quantities of all chemicals in the process at equilibrium are referenced as Keq.
- K and ΔG° can both be used to forecast the product-to-reactant ratio at equilibrium in a reaction.
- Gibb's energy and equilibrium constant have a relationship, i.e., △Go=−RTlnKeq.

### FAQs:  

__1. What is the relation between Gibb's free energy and equilibrium constant?__

Gibb's energy and equilibrium constant have a relationship, i.e., △Go=−RTlnKeq. 
Gibb's energy and enthalpy change have a relationship, i.e., △G= △H- T△S. 

__2. How do you find the free energy from the equilibrium constant?__

The equation G°=RTlnK relates G° with K. 

If G° is less than zero, K is greater than one, then products are preferred over reactants at equilibrium. 

At equilibrium, if G° > 0, K = 1, then reactants are preferred over products. 

__3.  What is the Gibbs free energy at equilibrium?__

The disparity here between heat radiated throughout a cycle and the heat emitted for the same set of interactions in a reversible manner is the variation in free energy (G). G = 0 indicates that a system is in equilibrium. 

*We hope you enjoyed studying this lesson and learned something cool about __Gibbs’ free energy and equilibrium constant problems__! Join our Discord community to get any questions you may have answered and to engage with other students just like you! Don't forget to download our App to experience our fun, VR classrooms - we promise, it makes studying much more fun!* 😎 

## SOURCES: 
1. Calculations of Free Energy and Keq. https://www.ck12.org/c/chemistry/calculations-of-free-energy-and-keq/lesson/Calculations-of-Free-Energy-and-Keq-CHEM/. Accessed 28 Jan 2022.
2. Gibbs (Free) Energy. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Thermodynamics/Energies_and_Potentials/Free_Energy/Gibbs_(Free)_Energy. Accessed 28 Jan 2022.
3. How do you calculate Gibbs free energy from equilibrium constant?. https://socratic.org/questions/how-do-you-calculate-gibbs-free-energy-from-equilibrium-constant. Accessed 28 Jan 2022. 


K (equilibrium constant) and ΔG° (Gibbs free energy) can both be used to forecast the product-to-reactant ratio at equilibrium in a reaction. 


Calculations of Free Energy and Keq Study Guide

# Introduction
Gibbs's free energy and the equilibrium constant are integral principles in the field of thermodynamics. Before we talk about the relationship between Gibbs's free energy and the equilibrium constant and how to calculate their values, let’s quickly get some background on thermodynamics for a fuller picture of how they work through the concepts of entropy and enthalpy.

## Thermodynamics
Thermodynamics studies the relationships between __heat, work, temperature, and energy__. It describes how the energy of a system changes and whether or not that energy can be used for useful work. 

__A system__ is defined as a body of matter or radiation enclosed by permeable walls that separate it from its surroundings, for example, an air conditioner that circulates refrigerant internally and promotes the transfer of heat between itself and its surroundings.

__“Work”__ in the context of thermodynamics is the transfer of energy from a system to its surroundings, as exemplified by the air conditioner system. __“Useful” work__ refers to an exchange of energy that does not involve the expansion of a closed system, meaning that its volume remains the same.

The concepts of __entropy and enthalpy__ are also important principles to understand when learning about Gibbs free energy and the equilibrium constant. __Entropy__ is defined as the thermal energy of a system per unit of temperature which is unavailable for useful work, whereas __enthalpy__ is defined as the total heat of the system. 

Now that we’ve got that down, we’re ready to dive into our topic of the day, Gibbs free energy and the equilibrium constant!

## GIBBS FREE ENERGY
- Gibbs free energy, or free energy, is the __maximum amount of energy__ a substance can contribute to a chemical transformation or reaction. 
- It is equal to the sum of entropy and the product of temperature in a closed system. 
- In simpler words, it is the sum of entropy and enthalpy. 
- The change in energy, ΔG, can indicate the direction of chemical reaction under two conditions: constant pressure and constant temperature. 
- It can be written as:

__G = H−TS__

Or more completely as:

__G = U + PV−TS__

In both cases,

U is internal energy (SI unit: joule)
P is pressure (SI unit: pascal)
V is the volume (SI unit: m3)
T is the temperature (SI unit: kelvin)
S is entropy (SI unit: joule/kelvin)
H is the enthalpy (SI unit: joule)

![gibbs](//images.ctfassets.net/4yflszkpcwkt/013Plp3kdfMzZ2oxVDvuR9/7e1a259e1a1b489646b1e63747edd7bb/Gibb.png)
[Source](http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/helmholtz.html)

## EQUILIBRIUM CONSTANT 
- The equilibrium constant is the ratio of the concentration of products to the concentration of reactants. 
- It is denoted by K(eq). 
- The formula of the equilibrium constant is:

__K(eq) = Kf / Kb = (C)c (D)d/(A)a (B)b = K(c)__

Where K(c) indicates the equilibrium constant measured in __moles per liter__

## RELATION BETWEEN GIBBS FREE ENERGY AND EQUILIBRIUM CONSTANT

When equilibrium is reached, there is no additional free energy change, i.e., ΔG = 0, and Q is equal to the equilibrium constant (K(eq)). 
Hence the relationship between K(eq) and ΔG becomes:

  __ΔGo = –RT In K(eq)__ 
  or 
  __ΔGo = –2.303 RT log K(eq)__

- Where R is the ideal gas constant (8.314 J/K mol), 
- T is the Kelvin temperature, 
- And K(eq) is the natural logarithm of the equilibrium constant.

## FAQ’s

__1. What is the relationship between free energy and equilibrium constant?__

When equilibrium is reached, there is no additional free energy change, i.e., ΔG = 0, and Q is equal to the equilibrium constant (K(eq)). Hence the relationship between K(eq) and ΔG becomes: 

ΔGo = –RT In K(eq), or
ΔGo = –2.303 RT log K(eq)

__2. How do you calculate free energy?__

Calculation of Free energy:
ΔG = ΔH − TΔS

__3. What is the concept of free energy?__

Free Energy refers to the energy in a system that is free to do work, i.e., the internal energy minus any energy that is inaccessible to perform work.

*We hope you enjoyed studying this lesson and learned something cool about __Free Energy and Equilibrium Constant!__ Join our Discord community to get any questions you may have answered and to engage with other students just like you! Don't forget to download our app to experience our fun VR classrooms - we promise it makes studying much more fun!😎*

## SOURCE
1. Gibbs Free Energy: https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Thermodynamics/Energies_and_Potentials/Free_Energy/Gibbs_(Free)_Energy. Accessed 28 Feb 2022

2. Calculations of Free Energy: https://flexbooks.ck12.org/cbook/ck-12-chemistry-flexbook-2.0/section/20.8/primary/lesson/calculations-of-free-energy-and-keq-chem/. Accessed 28 Feb 2022.


Free energy or Gibbs free energy change ΔG is the energy available in a system to do useful work and K(eq) is the equilibrium constant. 

Free Energy and Equilibrium Constant Study Guide

# Introduction
Take an ice cube out of the refrigerator and put it in a bowl at room temperature. What happens? It melts. But the important thing here is that we had no interference during that melting process. It just happened on its own. This is a typical example of a spontaneous reaction. So, wondering what a spontaneous reaction is? Let's find out.

![ice](//images.ctfassets.net/4yflszkpcwkt/1sFeBkja15QWMqNSGvR6Vx/d7b240e6562b69b8b22074f551e8726a/ZVbDRbtU5JWioFeX2e6Cfn.jpg)
[Source](https://www.livescience.com/2171-ice-melts.html)

## What Is A Spontaneous Process?
- The term "spontaneous reaction" refers to a reaction that promotes the creation of products under the circumstances that it occurs.
- A spontaneous process can move in a specific direction without an external energy source. 
- The rules of thermodynamics (specifically the 2nd law of thermodynamics) determine the direction of a spontaneous process, assuring that if a significant number of specific interactions are engaged, the path will always be toward rising entropy.

## The Second Law Of Thermodynamics
- The second rule of thermodynamics dictates that the total (change in entropy S) ΔS must be larger than or equal to 0 for every spontaneous process; however, spontaneous chemical changes could lead to a negative change in entropy. 
- However, because such a process must have a relatively substantial negative change in enthalpy, this does not defy the second rule (heat energy). 

- The rise in temperature of the reaction environment causes a significant increase in entropy, resulting in a positive net change in entropy. 
- That is, the surroundings' (change in entropy S) ΔS increases sufficiently as a result of the reaction's exothermicity (release of heat during a chemical reaction) to counterbalance for the system's negative (change in entropy S) ΔS.

Note - A substance's entropy (S) is a thermodynamic property that is directly proportional to its degree of disorder. The more possible microstates (arrangement of molecules) for a system, the higher the disorder and the greater the entropy.

## Spontaneous Process:
Spontaneity does not entail that the reaction happens quickly. The pace of a reaction is determined by the chemical kinetics of the reaction rather than its spontaneity. 
In a spontaneous process, every reactant tends to generate the corresponding product. This pattern is linked to stability.

## Non-Spontaneous Process:
- A chemical reaction known as an endergonic reaction (also known as a nonspontaneous reaction) is one in which the standard change in free energy is positive, and energy is absorbed. Because the whole quantity of energy represents a loss, the net outcome is negative. 
- Endergonic processes can also be driven by connecting them through a common intermediate to a highly exergonic reaction.

For example: Photosynthesis
During photosynthesis, plants use energy from the sun to turn carbon dioxide (CO2) and water (H2O) into sugar (C6H12O6) and oxygen (O2).
6 CO2 (g) + 6 H2O (l) + energy → C6H12O6 (s) + 6 O2 (g)

![reactions](//images.ctfassets.net/4yflszkpcwkt/3U0rManQihEirgpHtidTa8/ad43dc83ae503faddb6c2f023b1020b8/reactioncoo.jpg)
[Source](https://bio.libretexts.org/Under_Construction/Purgatory/Core_(Britt%27s_page)/Endergonic_and_Exergonic_Reactions%23)

# Summary 
- A spontaneous reaction happens in a given set of conditions without any interruptions.
- The nonspontaneous reaction takes place with the help of external agents like heat or energy.

## FAQs: 
__1. What is a spontaneous and nonspontaneous reaction?__

A spontaneous reaction takes place without any external agent. An example is the melting of ice. This doesn't require any external agent. Happens slowly and steadily. A non-spontaneous reaction requires an external agent like heat or light or energy of some sort to make the reaction start. For example, photosynthesis. A plant absorbs water and carbon dioxide. But for it to get converted, sunlight is required. This is a nonspontaneous reaction.

__2. How do you know if a reaction is spontaneous or nonspontaneous?__

If the reaction takes place without any external agent, it's a spontaneous reaction. If the reaction takes place with the help of an external agent, then it's a nonspontaneous reaction.

*We hope you enjoyed studying this lesson and learned something cool about __Spontaneous and non-spontaneous reactions!__ Join our Discord community to get any questions you may have answered and to engage with other students just like you! Don't forget to download our App to experience our fun, VR classrooms - we promise, it makes studying much more fun!😎* 

## Sources:
1. Spontaneous and Nonspontaneous reaction. https://www.ck12.org/c/chemistry/spontaneous-and-nonspontaneous-reactions/lesson/Spontaneous-and-Nonspontaneous-Reactions-CHEM/. Accessed on 26th Jan 2022.
2. Spontaneous and Nonspontaneous reaction. https://www.chemistrylearner.com/chemical-reactions/spontaneous-and-non-spontaneous-reaction. Accessed on 26th Jan 2022.
3. Spontaneity https://byjus.com/chemistry/spontaneity/, Accessed on 26th Jan 2022.


The term "spontaneous reaction" refers to a reaction that promotes the creation of products under the circumstances that it occurs.

Spontaneous And Non-Spontaneous Reactions Study Guide

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## INTRODUCTION
Have you ever spent a day organizing your room only to find it back in the same state of disarray a few days or weeks later? Nature has the tendency to decline gradually from order to disorder and randomness, a concept known as entropy. Entropy is utilized in many fields, including cosmology, thermodynamics, economics, and chemistry. It exists not only in concept, but also as a measurable physical property that is always related to uncertainty in one way or another.

### WHAT IS ENTROPY IN CHEMISTRY?

Entropy is the measurement of systemic disorder. It is considered an extensive property of a thermodynamic system, and its value changes depending on the amount of matter the system contains. The entropy of a system is the sum of all entropies within said system, and any change in entropy results from interactions between the system and its surroundings. In equations, entropy is represented by the letter “S” with the unit joules per kelvin (J/K). A system that is highly ordered has very low entropy. 

### REVERSIBLE PROCESS ENTROPY

![Boltzmann distribution](//images.ctfassets.net/4yflszkpcwkt/FXyeqjPtmO8L5GyEsnyGJ/fb9255ecf02e35391eb764fefa5d7c1a/112316_fig1_pp123_cockcroft_july09_tcm18-154952.jpg)
[Source](https://edu.rsc.org/feature/what-is-entropy/2020274.article) 

In thermodynamics, a reversible process is a process that occurs between a system and its surroundings that can be reversed by a change in the properties of the surroundings, such as temperature or pressure. In a reversible process, the system remains in physical and chemical equilibrium, meaning its entropy value is always zero.

When it comes to calculating the entropy of a reversible process, there are quite a few assumptions to keep in mind (the assumption that each configuration within the process is equally probable for example). Considering the outcomes having equal probability, entropy equals Boltzmann’s constant multiplied by the natural logarithm of all possible numbers of states (W). In equation form, this is written as:

S = kB ln W

Where kB = 1.38065 × 10⁻²³ J/K.

### ISOTHERMAL PROCESS ENTROPY 

An isothermal process is a reversible process in which the temperature of the system remains constant as its pressure is increased. The change in entropy of an isothermal process is calculated by dividing the change in energy by the temperature of a system. In simpler terms, the change in entropy equals the change in heat. In equation form, this is written as:

ΔS = ΔQ / T

Where ΔQ = the change in the heat energy of the system (J), T = the absolute temperature of the system (K), and ΔS = the entropy of an isothermal process (J/K).

### INTERNAL ENERGY AND ENTROPY 

Internal energy is the energy contained within a thermodynamic system. It is an extensive property and thus cannot be measured directly. To find the value of a system’s internal energy, we can use the following equation:

ΔU = q + w

Where, ΔU = the change in the internal energy of a system, q = the heat energy exchanged between a system and its surroundings, and w = the work done by the system.

### SECOND LAW OF THERMODYNAMICS AND ENTROPY

The second law of thermodynamics states that the total entropy within a closed system does not decrease. However, in a system, the entropy of one system could decrease while raising the entropy of another system.

![Entropy](//images.ctfassets.net/4yflszkpcwkt/7a9aT75GGEcQqsx1Ey3IZH/d48720ad70787b6e6c59b881dc3fe50b/CNX_Chem_16_03_Entropies.jpg)
[Source](https://courses.lumenlearning.com/chemistryformajors/chapter/entropy/) 

### EXAMPLES OF ENTROPY IN EVERYDAY LIFE 

Melting ice is an excellent example of entropy. In the form of ice, water molecules exist in a fixed, highly-organized crystalline lattice structure. As ice melts, the water molecules become free to move and break away from their lattice structure into a state of relative disorder. In this scenario, the entropy of the ice increases.

## CONCLUSION 
- Entropy is regarded as the measurement of systemic disorder. 
- An example of entropy is melting ice.
- Entropy is an extensive property. 
- The SI unit of entropy is J/Kmol.
- To calculate the entropy of a reversible process, use the following equation: S = kB ln W
- To calculate the entropy of an isothermal process, use the following equation: ΔS = ΔQ / T
- To calculate internal energy, use the following equation: ΔU = q + w

### FAQs

__1. What is an example of entropy in everyday life?__

Melting ice is an example of entropy in everyday life.

__2. What are some examples of entropy?__

Some examples of entropy would be the melting of ice, sugar dissolving, and a campfire. 

*We hope you enjoyed studying this lesson and learned something cool about __Entropy__! Join our Discord community to get any questions you may have answered and to engage with other students just like you! Don't forget to download our App to experience our fun VR classrooms - we promise, it makes studying much more fun!* 😎

## SOURCES:
1. Example of Entropy: https://socratic.org/questions/what-is-an-example-of-entropy-from-everyday-life#:~:text=A%20campfire%20is%20an%20example,increasing%20entropy%20in%20your%20kitchen.Accessed 10th March 2022.
2. Entropy in Chemistry: https://study.com/academy/lesson/entropy-in-chemistry-definition-lesson.html.Accessed 10th March 2022.
3. What Is Entropy? https://www.thoughtco.com/definition-of-entropy-604458.Accessed 10th March 2022.
4. Entropy: https://byjus.com/jee/entropy/.Accessed 10th March 2022.


Entropy in everyday life is a crucial concept that you would come across while studying chemistry and physics. It is defined in various ways and serves various purposes. 


Entropy Study Guide

TL;DR Free Energy and Equilibrium Constant

TL;DR Entropy

TL;DR Calculations Of Free Energy And Keq

Ice that melts at 25 degree Celcius, the burning of wood and formation of rust that we observe all about us are examples of an amazing reaction that we shall learn in this cheat sheet! 