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Wednesday, May 4, 2022

Salvation

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Salvation

Salvation (from Latin: salvatio, from salva, 'safe, saved') is the state of being saved or protected from harm or a dire situation. In religion and theology, salvation generally refers to the deliverance of the soul from sin and its consequences. The academic study of salvation is called soteriology.

Meaning

In Abrahamic religions and theology, salvation is the saving of the soul from sin and its consequences. It may also be called deliverance or redemption from sin and its effects. Depending on the religion or even denomination, salvation is considered to be caused either only by the grace of God (i.e. unmerited and unearned), or by faith, good deeds (works), or a combination thereof. Religions often emphasize that man is a sinner by nature and that the penalty of sin is death (physical death, spiritual death: spiritual separation from God and eternal punishment in hell).

Judaism

In contemporary Judaism, redemption (Hebrew: גְּאוּלָּהge'ulah), refers to God redeeming the people of Israel from their various exiles. This includes the final redemption from the present exile.

Judaism holds that adherents do not need personal salvation as Christians believe. Jews do not subscribe to the doctrine of original sin. Instead, they place a high value on individual morality as defined in the law of God—embodied in what Jews know as the Torah or The Law, given to Moses by God on biblical Mount Sinai.

In Judaism, salvation is closely related to the idea of redemption, a saving from the states or circumstances that destroy the value of human existence. God, as the universal spirit and Creator of the World, is the source of all salvation for humanity, provided an individual honours God by observing his precepts. So redemption or salvation depends on the individual. Judaism stresses that salvation cannot be obtained through anyone else or by just invoking a deity or believing in any outside power or influence.

The Jewish concept of Messiah visualises the return of the prophet Elijah as the harbinger of one who will redeem the world from war and suffering, leading mankind to universal brotherhood under the fatherhood of one God. The Messiah is not considered as a future divine or supernatural being but as a dominating human influence in an age of universal peace, characterised by the spiritual regeneration of humanity. In Judaism, salvation is open to all people and not limited to those of the Jewish faith; the only important consideration being that the people must observe and practise the ethical pattern of behaviour as summarised in the Ten Commandments. When Jews refer to themselves as the chosen people of God, they do not imply they have been chosen for special favours and privileges but rather they have taken it upon themselves to show to all peoples by precept and example the ethical way of life.

When examining Jewish intellectual sources throughout history, there is clearly a spectrum of opinions regarding death versus the afterlife. Possibly an over-simplification, one source says salvation can be achieved in the following manner: Live a holy and righteous life dedicated to Yahweh, the God of Creation. Fast, worship, and celebrate during the appropriate holidays. By origin and nature, Judaism is an ethnic religion. Therefore, salvation has been primarily conceived in terms of the destiny of Israel as the elect people of Yahweh (often referred to as “the Lord”), the God of Israel.

In the biblical text of Psalms, there is a description of death, when people go into the earth or the "realm of the dead" and cannot praise God. The first reference to resurrection is collective in Ezekiel's vision of the dry bones, when all the Israelites in exile will be resurrected. There is a reference to individual resurrection in the Book of Daniel. It was not until the 2nd century BCE that there arose a belief in an afterlife, in which the dead would be resurrected and undergo divine judgment. Before that time, the individual had to be content that his posterity continued within the holy nation.

The salvation of the individual Jew was connected to the salvation of the entire people. This belief stemmed directly from the teachings of the Torah. In the Torah, God taught his people sanctification of the individual. However, he also expected them to function together (spiritually) and be accountable to one another. The concept of salvation was tied to that of restoration for Israel.

During the Second Temple Period, the Sadducees, High Priests, denied any particular existence of individuals after death because it wasn't written in the Torah, while the Pharisees, ancestors of the rabbis, affirmed both bodily resurrection and immortality of the soul, most likely based on the influence of Hellenistic ideas about body and soul and the Pharisaic belief in the Oral Torah. The Pharisees maintained that after death, the soul is connected to God until the messianic era when it is rejoined with the body in the land of Israel at the time of resurrection.

Christianity

Allegory of Salvation by Antonius Heusler (ca. 1555), National Museum in Warsaw.

Christianity's primary premise is that the incarnation and death of Jesus Christ formed the climax of a divine plan for humanity's salvation. This plan was conceived by God before the creation of the world, achieved at the cross, and it would be completed at the Last Judgment, when the Second Coming of Christ would mark the catastrophic end of the world.

For Christianity, salvation is only possible through Jesus Christ. Christians believe that Jesus' death on the cross was the once-for-all sacrifice that atoned for the sin of humanity.

The Christian religion, though not the exclusive possessor of the idea of redemption, has given to it a special definiteness and a dominant position. Taken in its widest sense, as deliverance from dangers and ills in general, most religions teach some form of it. It assumes an important position, however, only when the ills in question form part of a great system against which human power is helpless.

Allegory of Salvation by Wolf Huber (ca. 1543), Kunsthistorisches Museum in Vienna

According to Christian belief, sin as the human predicament is considered to be universal. For example, in Romans 1:18-3:20 the Apostle Paul declared everyone to be under sin—Jew and Gentile alike. Salvation is made possible by the life, death, and resurrection of Jesus, which in the context of salvation is referred to as the "atonement". Christian soteriology ranges from exclusive salvation to universal reconciliation concepts. While some of the differences are as widespread as Christianity itself, the overwhelming majority agrees that salvation is made possible by the work of Jesus Christ, the Son of God, dying on the cross.

At the heart of Christian faith is the reality and hope of salvation in Jesus Christ. Christian faith is faith in the God of salvation revealed in Jesus of Nazareth. The Christian tradition has always equated this salvation with the transcendent, eschatological fulfillment of human existence in a life freed from sin, finitude, and mortality and united with the triune God. This is perhaps the non-negotiable item of Christian faith. What has been a matter of debate is the relation between salvation and our activities in the world.

— Anselm Kyongsuk Min, Dialectic of Salvation: Issues in Theology of Liberation (2009)

The Bible presents salvation in the form of a story that describes the outworking of God's eternal plan to deal with the problem of human sin. The story is set against the background of the history of God's people and reaches its climax in the person and work of Christ. The Old Testament part of the story shows that people are sinners by nature, and describes a series of covenants by which God sets people free and makes promises to them. His plan includes the promise of blessing for all nations through Abraham and the redemption of Israel from every form of bondage. God showed his saving power throughout Israel's history, but he also spoke about a Messianic figure who would save all people from the power, guilt, and penalty of sin. This role was fulfilled by Jesus, who will ultimately destroy all the devil's work, including suffering, pain, and death.

— Macmillan Dictionary of the Bible.

Variant views on salvation are among the main fault lines dividing the various Christian denominations, both between Roman Catholicism and Protestantism and within Protestantism, notably in the Calvinist–Arminian debate, and the fault lines include conflicting definitions of depravity, predestination, atonement, but most pointedly justification.

A bumper sticker asking if one has found salvation

Salvation, according to most denominations, is believed to be a process that begins when a person first becomes a Christian, continues through that person's life, and is completed when they stand before Christ in judgment. Therefore, according to Catholic apologist James Akin, the faithful Christian can say in faith and hope, "I have been saved; I am being saved; and I will be saved."

Christian salvation concepts are varied and complicated by certain theological concepts, traditional beliefs, and dogmas. Scripture is subject to individual and ecclesiastical interpretations. While some of the differences are as widespread as Christianity itself, the overwhelming majority agrees that salvation is made possible by the work of Jesus Christ, the Son of God, dying on the cross.

The purpose of salvation is debated, but in general most Christian theologians agree that God devised and implemented his plan of salvation because he loves them and regards human beings as his children. Since human existence on Earth is said to be "given to sin," salvation also has connotations that deal with the liberation of human beings from sin, and the suffering associated with the punishment of sin—i.e., "the wages of sin are death."

Christians believe that salvation depends on the grace of God. Stagg writes that a fact assumed throughout the Bible is that humanity is in, "serious trouble from which we need deliverance…. The fact of sin as the human predicament is implied in the mission of Jesus, and it is explicitly affirmed in that connection." By its nature, salvation must answer to the plight of humankind as it actually is. Each individual's plight as sinner is the result of a fatal choice involving the whole person in bondage, guilt, estrangement, and death. Therefore, salvation must be concerned with the total person. "It must offer redemption from bondage, forgiveness for guilt, reconciliation for estrangement, renewal for the marred image of God."

Mormonism

According to doctrine of the Church of Jesus Christ of Latter-day Saints]], the plan of salvation is God's plan to save, redeem, and exalt all humankind who chose, either in this life, or in the world of spirits of the dead, to accept the grace of Jesus Christ by exercising faith in Him, repenting of their sins, and by making and keeping sacred covenants (including baptism). Since the vast majority of God's children depart this life without that opportunity, Christ's gospel is preached to the unbelieving spirits in spirit prison (1 Peter 3: 19) so that they might be judged by the same standards as the living and live by following God in their spirit form (1 Peter 4: 6). If they accept Christ, sincerely repent of their sins, and accept ordinances done on their behalf, they can, by the grace of Christ, receive salvation on the same terms as the living. For this reason, members of the Church of Jesus Christ of Latter-day Saints do vicarious work for the dead in sacred temples. The elements of this plan are drawn from various sources, including the Bible, Book of Mormon, Doctrine & Covenants, Pearl of Great Price, and numerous statements made by the leadership of The Church of Jesus Christ of Latter-day Saints (LDS Church).

Islam

In Islam, salvation refers to the eventual entrance to Paradise. Islam teaches that people who die disbelieving in God do not receive salvation. It also teaches that non-Muslims who die believing in God but disbelieving in His message (Islam), are left to His will. Those who die believing in the one God and His message (Islam) receive salvation.

Narrated Anas, that Muhammad said:

Whoever said "None has the right to be worshipped but Allah" and has in his heart good (faith) equal to the weight of a barley grain will be taken out of Hell. And whoever said, "None has the right to be worshipped but Allah" and has in his heart good (faith) equal to the weight of a wheat grain will be taken out of Hell. And whoever said, "None has the right to be worshipped but Allah" and has in his heart good (faith) equal to the weight of an atom will be taken out of Hell.

— Muhammad, Sahih al-Bukhari, 1:2:43

Islam teaches that all who enter into Islam must remain so in order to receive salvation.

"If anyone desires a religion other than Islam (submission to Allah), never will it be accepted of him; and in the Hereafter He will be in the ranks of those who have lost (all spiritual good)."

— Quran, sura 3 (Al Imran), ayat 85

For those who have not been granted Islam or to whom the message has not been brought:

Those who believe (in the Qur'an), those who follow the Jewish (scriptures), and the Sabians and the Christians,- any who believe in Allah and the Last Day, and work righteousness,- on them shall be no fear, nor shall they grieve."

Tawhid

Belief in the “One God”, also known as the Tawhid (التَوْحيدْ) in Arabic, consists of two parts (or principles):

  1. Tawḥīdu r-Rubūbiyya (تَوْحيدُ الرُبوبِيَّة): Believing in the attributes of God and attributing them to no other but God. Such attributes include Creation, having no beginning, and having no end. These attributes are what make a God. Islam also teaches 99 names for God, and each of these names defines one attribute. One breaks this principle, for example, by believing in an Idol as an intercessor to God. The idol, in this case, is thought of having powers that only God should have, thereby breaking this part of Tawheed. No intercession is required to communicate with, or worship, God.
  2. Tawḥīdu l-'ulūhiyya (تَوْحيدُ الأُلوهيَّة): Directing worship, prayer, or deed to God, and God only. For example, worshiping an idol or any saint or prophet is also considered Shirk.

Sin and repentance

Islam also stresses that in order to gain salvation, one must also avoid sinning along with performing good deeds. Islam acknowledges the inclination of humanity towards sin. Therefore, Muslims are constantly commanded to seek God's forgiveness and repent. Islam teaches that no one can gain salvation simply by virtue of their belief or deeds, instead it is the Mercy of God, which merits them salvation. However, this repentance must not be used to sin any further. Islam teaches that God is Merciful.

Allah accepts the repentance of those who do evil in ignorance and repent soon afterwards; to them will Allah turn in mercy: For Allah is full of knowledge and wisdom. Of no effect is the repentance of those who continue to do evil, until death faces one of them, and he says, "Now have I repented indeed;" nor of those who die rejecting Faith: for them have We prepared a punishment most grievous.

— Qur'an, sura 4 (An-Nisa), ayat 17

Allah forgiveth not that partners should be set up with Him; but He forgiveth anything else, to whom He pleaseth; to set up partners with Allah is to devise a sin Most heinous indeed.

— Qur'an, sura 4 (An-Nisa), ayat 48

Islam describes a true believer to have Love of God and Fear of God. Islam also teaches that every person is responsible for their own sins. The Quran states;

If ye reject (Allah), truly Allah hath no need of you; but He liketh not ingratitude from His servants: if ye are grateful, He is pleased with you. No bearer of burdens can bear the burden of another. In the end, to your Lord is your Return, when He will tell you the truth of all that ye did (in this life). for He knoweth well all that is in (men's) hearts.

— Qur'an, sura 39 (Az-Zumar), ayat 7

Al-Agharr al-Muzani, a companion of Mohammad, reported that Ibn 'Umar stated to him that Mohammad said,

O people, seek repentance from Allah. Verily, I seek repentance from Him a hundred times a day.

— Prophet Mohammad, Sahih Muslim, 35:6523

Sin in Islam is not a state, but an action (a bad deed); Islam teaches that a child is born sinless, regardless of the belief of his parents, dies a Muslim; he enters heaven, and does not enter hell.

Narrated Aisha, that Mohammad said, "Do good deeds properly, sincerely and moderately, and receive good news because one's good deeds will not make him enter Paradise." They asked, "Even you, O Allah's Apostle?" He said, "Even I, unless and until Allah bestows His pardon and Mercy on me."

Five Pillars

Islam is built on five principles, acts of worship that Islam teaches to be mandatory. Not performing the mandatory acts of worship may deprive Muslims of the chance of salvation. According to Ibn 'Umar, Muhammad said that Islam is based on the following five principles:

  1. To testify that none has the right to be worshipped but Allah and Muhammad is Allah's Apostle.
  2. To offer the compulsory prayers dutifully and perfectly.
  3. To pay Zakat to poor and needy (i.e. obligatory charity of 2.5% annually of surplus wealth).
  4. To perform Hajj. (i.e. Pilgrimage to Mecca)
  5. To observe fast during the month of Ramadhan.

Indian religions

Hinduism, Buddhism, Jainism and Sikhism share certain key concepts, which are interpreted differently by different groups and individuals. In these religions one is not liberated from sin and its consequences, but from the saṃsāra (cycle of rebirth) perpetuated by passions and delusions and its resulting karma. They differ however on the exact nature of this liberation.

Salvation is always self-attained in Dharmic traditions, and a more appropriate term would be moksha ('liberation') or mukti ('release'). This state and the conditions considered necessary for its realization is described in early texts of Indian religion such as the Upanishads and the Pāli Canon, and later texts such the Yoga Sutras of Patanjali and the Vedanta tradition. Moksha can be attained by sādhanā, literally 'means of accomplishing something'. It includes a variety of disciplines, such as yoga and meditation.

Nirvana is the profound peace of mind that is acquired with moksha. In Buddhism and Jainism, it is the state of being free from suffering. In Hindu philosophy, it is union with the Brahman (Supreme Being). The word literally means 'blown out' (as in a candle) and refers, in the Buddhist context, to the blowing out of the fires of desire, aversion, and delusion, and the imperturbable stillness of mind acquired thereafter.

In Theravada Buddhism the emphasis is on one's own liberation from samsara. The Mahayana traditions emphasize the bodhisattva path, in which "each Buddha and Bodhisattva is a redeemer," assisting the Buddhist in seeking to achieve the redemptive state. The assistance rendered is a form of self-sacrifice on the part of the teachers, who would presumably be able to achieve total detachment from worldly concerns, but have instead chosen to remain engaged in the material world to the degree that this is necessary to assist others in achieving such detachment.

Jainism

In Jainism, salvation, moksha, and nirvana are one and the same. When a soul (atman) achieves moksha, it is released from the cycle of births and deaths, and achieves its pure self. It then becomes a siddha ('one who has accomplished his ultimate objective'). Attaining Moksha requires annihilation of all karmas, good and bad, because if karma is left, it must bear fruit.

Deadly Venom From Spiders and Snakes May Cure What Ails You

Efforts to tease apart the vast swarm of proteins in venom — a field called venomics — have burgeoned in recent years, leading to important drug discoveries.

TUCSON, Ariz. — In a small room in a building at the Arizona-Sonora Desert Museum, the invertebrate keeper, Emma Califf, lifts up a rock in a plastic box. “This is one of our desert hairies,” she said, exposing a three-inch-long scorpion, its tail arced over its back. “The largest scorpion in North America.”

This captive hairy, along with a swarm of inch-long bark scorpions in another box, and two dozen rattlesnakes of varying species and sub- species across the hall, are kept here for the coin of the realm: their venom.

Efforts to tease apart the vast swarm of proteins in venom — a field called venomics — have burgeoned in recent years, and the growing catalog of compounds has led to a number of drug discoveries. As the components of these natural toxins continue to be assayed by evolving technologies, the number of promising molecules is also growing.

“A century ago we thought venom had three or four components, and now we know just one type of venom can have thousands,” said Leslie V. Boyer, a professor emeritus of pathology at the University of Arizona. “Things are accelerating because a small number of very good laboratories have been pumping out information that everyone else can now use to make discoveries.”

She added, “There’s a pharmacopoeia out there waiting to be explored.”

It is a striking case of modern-day scientific alchemy: The most highly evolved of natural poisons on the planet are creating a number of effective medicines with the potential for many more.

Leslie V. Boyer, founder of the Venom Immunochemistry, Pharmacology, and Emergency Response Institute, calls Arizona “venom central.”
A giant hairy scorpion at the Arizona-Sonora Desert Museum.
One of the most promising venom-derived drugs to date comes from the deadly Fraser Island funnel web spider of Australia, which halts cell death after a heart attack.

Blood flow to the heart is reduced after a heart attack, which makes the cell environment more acidic and leads to cell death. The drug, a protein called Hi1A, is scheduled for clinical trials next year. In the lab, it was tested on the cells of beating human hearts. It was found to block their ability to sense acid, “so the death message is blocked, cell death is reduced, and we see improved heart cell survival,” said Nathan Palpant, a researcher at the University of Queensland in Australia who helped make the discovery.

If proven in trials, it could be administered by emergency medical workers, and might prevent the damage that occurs after heart attacks and possibly improve outcomes in heart transplants by keeping the donor heart healthier longer.

“It looks like it’s going to be a heart attack wonder drug,” said Bryan Fry, an associate professor of toxicology at the University of Queensland, who is familiar with the research but was not involved in it. “And it’s from one of the most vilified creatures” in Australia.

The techniques used to process venom compounds have become so powerful that they are creating new opportunities. “We can do assays nowadays using only a couple of micrograms of venom that 10 or 15 years ago would have required hundreds of micrograms,” or more, Dr. Fry said. “What this has done is open up all the other venomous lineages out there that produce tiny amounts of material.”

There is an enormous natural library to sort through. Hundreds of thousands of species of reptile, insect, spider, snail and jellyfish, among other creatures, have mastered the art of chemical warfare with venom. Moreover, the makeup of venom varies from animal to animal. There is a kind of toxic terroir: Venom differs in quantity, potency and proportion and types of toxin, according to habitat and diet, and even by changing temperatures due to climate change.

Venom is made of a complex mix of toxins, which are composed of proteins with unique characteristics. They are so deadly because evolution has honed their effectiveness for so long — some 54 million years for snakes and 600 million for jellyfish.

Howard Byrne, a curator at the Arizona desert museum, handling a Gila monster, from which the drug exenatide, for Type 2 diabetes, is derived.
A tiger rattlesnake at the Arizona Sonoran Desert Museum.

Venom is the product of a biological arms race over that time; as venom becomes more deadly, victims evolve more resistance, which in turn makes venom even deadlier. Humans are included in that dynamic. “We are made of protein and our protein has little complex configurations on it that make us human,” said Dr. Boyer, who founded the Venom Immunochemistry, Pharmacology, and Emergency Response Institute, or VIPER. “And those little configurations are targets of the venom.”

The specific cellular proteins that the venom molecules have evolved to target with pinpoint accuracy are what make the drugs derived from them — which use the same pathways — so effective. Some proteins, however, have inherent problems that can make new drugs from them unworkable.

There is usually no need to gather venom to make these drugs. Once they are identified, they can be synthesized.

There are three main effects from venom. Neurotoxins attack the nervous system, paralyzing the victim. Hemotoxins target the blood and local tissue toxins attack the area around the site of poison exposure.

Numerous venom-derived drugs are on the market. Captopril, the first, was created in the 1970s from the venom of a Brazilian jararaca pit viper to treat high blood pressure. It has been successful commercially. Another drug, exenatide, is derived from Gila monster venom and is prescribed for Type 2 diabetes. Draculin is an anticoagulant from vampire bat venom and is used to treat stroke and heart attack.

The venom of the Israeli deathstalker scorpion is the source of a compound in clinical trials that finds and illuminates breast and colon tumors.

“Things are accelerating because a small number of very good laboratories have been pumping out information that everyone else can now use,” Dr. Boyer said.

Some proteins have been flagged as potential candidates for new drugs, but they have to journey through the long process of manufacture and clinical trials, which can take many years and cost millions of dollars. In March, researchers at the University of Utah announced that they had discovered a fast-acting molecule in cone snails. Cone snails fire their venom into fish, which causes the victims’ insulin levels to drop so rapidly it kills them. It holds promise as a drug for diabetes. Bee venom appears to work with a wide range of pathologies and has recently been found to kill aggressive breast cancer cells.

In Brazil researchers have been looking at the venom of the Brazilian wandering spider as a possible source of a new drug for erectile dysfunction — because of what happens to human victims when they are bit. “A characteristic of their envenomation is that males get extraordinary painful, incredibly long-lasting erections,” Dr. Fry said. “They have to separate it from its lethal factor, of course, and find a way to dial it back.”

Some scientists have long suspected that important secrets are locked up in venom. Scientific interest first surfaced in the 17th century. In the mid-18th century the Italian physician and polymath Felice Fontana added to the body of knowledge with his treatise, and in 1860 the first research to look at venom components was conducted by S. Weir Mitchell in Philadelphia.

The medicinal use of venom has a long history, often without scientific support. Venom-dipped needles are a traditional form of acupuncture. Bee sting therapy, in which a swarm of bees is placed on the skin, is used by some natural healers. The rock musician Steve Ludwin claims to have routinely injected himself with diluted venom, believing it to be a tonic that builds his immune system and boosts his energy.

The demand for venom is increasing. Ms. Califf of the Arizona-Sonora Desert Museum said she had to travel to the desert to find more bark scorpions, which she hunts at night with a black light because they glow in the dark. Arizona, Dr. Boyer said, is “venom central,” with more venomous creatures than in any other U.S. state, making it well suited for this kind of production.

Venom, made of a complex mix of toxins, are so deadly because evolution has honed their effectiveness for so long — some 54 million years for snakes.
The Arizona bark scorpion, which glows in the dark is hunted at night with a black light.

Scorpion venom is harvested by applying a tiny electrical current to the arachnid, which causes it to excrete a small drop of the amber liquid at the tip of its tail. With snakes, venom glands are gently massaged as they bare their fangs over a martini glass. After they surrender their venom, the substance is sent to researchers around the globe.

Pit vipers, including rattlesnakes, have other unusual adaptations. The “pit” is the site of the biological equipment that allows snakes to sense the heat of their prey. “You can blindfold a snake and it will still strike the target,” Dr. Boyer said.

But it’s not just venom that’s far better understood these days. In the last few years, there has been a well-heeled and concerted search for antivenom.

In 2019 the Wellcome Trust created a $100 million fund toward the pursuit. Since then there have been numerous research efforts around the world looking for a single universal treatment — one that can be carried into remote areas to immediately help someone bitten by any type of venomous snake. Currently, different types of snakebites have different antivenom.

It has been difficult. The wide array of ingredients in venom that benefit new drug research has also made it difficult to find a drug that can neutralize them. One promising universal antivenom, varespladib, is in clinical trials.

Experts hope the role of venom will lead to more respect for the fear-inducing creatures who create them. Dr. Fry, for his work on anticoagulants, is studying the venom of Komodo dragons, which, at 10 feet long and more than 300 pounds, is the largest lizard in the world. It is also highly endangered.

Work on the Komodo, “allows us to talk about the broader conservation message,” he said.

“You want nature around because it’s a biobank,” he added. “We can only find these interesting compounds from these magnificent creatures if they are not extinct.”

Chemical potential

From Wikipedia, the free encyclopedia

In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species in a mixture is defined as the rate of change of free energy of a thermodynamic system with respect to the change in the number of atoms or molecules of the species that are added to the system. Thus, it is the partial derivative of the free energy with respect to the amount of the species, all other species' concentrations in the mixture remaining constant. When both temperature and pressure are held constant, and the number of particles is expressed in moles, the chemical potential is the partial molar Gibbs free energy. At chemical equilibrium or in phase equilibrium, the total sum of the product of chemical potentials and stoichiometric coefficients is zero, as the free energy is at a minimum. In a system in diffusion equilibrium, the chemical potential of any chemical species is uniformly the same everywhere throughout the system.

In semiconductor physics, the chemical potential of a system of electrons at zero absolute temperature is known as the Fermi energy.

Overview

Particles tend to move from higher chemical potential to lower chemical potential because this reduces the free energy. In this way, chemical potential is a generalization of "potentials" in physics such as gravitational potential. When a ball rolls down a hill, it is moving from a higher gravitational potential (higher internal energy thus higher potential for work) to a lower gravitational potential (lower internal energy). In the same way, as molecules move, react, dissolve, etc., they will always tend naturally to go from a higher chemical potential to a lower one, changing the particle number, which is conjugate variable to chemical potential.

A simple example is a system of dilute molecules diffusing in a homogeneous environment. In this system, the molecules tend to move from areas with high concentration to low concentration, until eventually, the concentration is the same everywhere. The microscopic explanation for this is based on kinetic theory and the random motion of molecules. However, it is simpler to describe the process in terms of chemical potentials: For a given temperature, a molecule has a higher chemical potential in a higher-concentration area and a lower chemical potential in a low concentration area. Movement of molecules from higher chemical potential to lower chemical potential is accompanied by a release of free energy. Therefore, it is a spontaneous process.

Another example, not based on concentration but on phase, is an ice cube on a plate above 0 °C. An H2O molecule that is in the solid phase (ice) has a higher chemical potential than a water molecule that is in the liquid phase (water) above 0 °C. When some of the ice melts, H2O molecules convert from solid to the warmer liquid where their chemical potential is lower, so the ice cube shrinks. At the temperature of the melting point, 0 °C, the chemical potentials in water and ice are the same; the ice cube neither grows nor shrinks, and the system is in equilibrium.

A third example is illustrated by the chemical reaction of dissociation of a weak acid HA (such as acetic acid, A = CH3COO):

HA ⇌ H+ + A

Vinegar contains acetic acid. When acid molecules dissociate, the concentration of the undissociated acid molecules (HA) decreases and the concentrations of the product ions (H+ and A) increase. Thus the chemical potential of HA decreases and the sum of the chemical potentials of H+ and A increases. When the sums of chemical potential of reactants and products are equal the system is at equilibrium and there is no tendency for the reaction to proceed in either the forward or backward direction. This explains why vinegar is acidic, because acetic acid dissociates to some extent, releasing hydrogen ions into the solution.

Chemical potentials are important in many aspects of multi-phase equilibrium chemistry, including melting, boiling, evaporation, solubility, osmosis, partition coefficient, liquid-liquid extraction and chromatography. In each case the chemical potential of a given species at equilibrium is the same in all phases of the system.

In electrochemistry, ions do not always tend to go from higher to lower chemical potential, but they do always go from higher to lower electrochemical potential. The electrochemical potential completely characterizes all of the influences on an ion's motion, while the chemical potential includes everything except the electric force. (See below for more on this terminology.)

Thermodynamic definition

The chemical potential μi of species i (atomic, molecular or nuclear) is defined, as all intensive quantities are, by the phenomenological fundamental equation of thermodynamics expressed in the form, which holds for both reversible and irreversible infinitesimal processes:

where dU is the infinitesimal change of internal energy U, dS the infinitesimal change of entropy S, and dV is the infinitesimal change of volume V for a thermodynamic system in thermal equilibrium, and dNi is the infinitesimal change of particle number Ni of species i as particles are added or subtracted. T is absolute temperature, S is entropy, P is pressure, and V is volume. Other work terms, such as those involving electric, magnetic or gravitational fields may be added.

From the above equation, the chemical potential is given by

This is an inconvenient expression for condensed-matter systems, such as chemical solutions, as it is hard to control the volume and entropy to be constant while particles are added. A more convenient expression may be obtained by making a Legendre transformation to another thermodynamic potential: the Gibbs free energy . From the differential and using the above expression for , a differential relation for is obtained:

As a consequence, another expression for results:

and the change in Gibbs free energy of a system that is held at constant temperature and pressure is simply

In thermodynamic equilibrium, when the system concerned is at constant temperature and pressure but can exchange particles with its external environment, the Gibbs free energy is at its minimum for the system, that is . It follows that

Use of this equality provides the means to establish the equilibrium constant for a chemical reaction.

By making further Legendre transformations from U to other thermodynamic potentials like the enthalpy and Helmholtz free energy , expressions for the chemical potential may be obtained in terms of these:

These different forms for the chemical potential are all equivalent, meaning that they have the same physical content and may be useful in different physical situations.

Applications

The Gibbs–Duhem equation is useful because it relates individual chemical potentials. For example, in a binary mixture, at constant temperature and pressure, the chemical potentials of the two participants A and B are related by

where is the number of moles of A and is the number of moles of B. Every instance of phase or chemical equilibrium is characterized by a constant. For instance, the melting of ice is characterized by a temperature, known as the melting point at which solid and liquid phases are in equilibrium with each other. Chemical potentials can be used to explain the slopes of lines on a phase diagram by using the Clapeyron equation, which in turn can be derived from the Gibbs–Duhem equation. They are used to explain colligative properties such as melting-point depression by the application of pressure. Henry's law for the solute can be derived from Raoult's law for the solvent using chemical potentials.

History

Chemical potential was first described by the American engineer, chemist and mathematical physicist Josiah Willard Gibbs. He defined it as follows:

If to any homogeneous mass in a state of hydrostatic stress we suppose an infinitesimal quantity of any substance to be added, the mass remaining homogeneous and its entropy and volume remaining unchanged, the increase of the energy of the mass divided by the quantity of the substance added is the potential for that substance in the mass considered.

Gibbs later noted also that for the purposes of this definition, any chemical element or combination of elements in given proportions may be considered a substance, whether capable or not of existing by itself as a homogeneous body. This freedom to choose the boundary of the system allows the chemical potential to be applied to a huge range of systems. The term can be used in thermodynamics and physics for any system undergoing change. Chemical potential is also referred to as partial molar Gibbs energy (see also partial molar property). Chemical potential is measured in units of energy/particle or, equivalently, energy/mole.

In his 1873 paper A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces, Gibbs introduced the preliminary outline of the principles of his new equation able to predict or estimate the tendencies of various natural processes to ensue when bodies or systems are brought into contact. By studying the interactions of homogeneous substances in contact, i.e. bodies, being in composition part solid, part liquid, and part vapor, and by using a three-dimensional volumeentropyinternal energy graph, Gibbs was able to determine three states of equilibrium, i.e. "necessarily stable", "neutral", and "unstable", and whether or not changes will ensue. In 1876, Gibbs built on this framework by introducing the concept of chemical potential so to take into account chemical reactions and states of bodies that are chemically different from each other. In his own words from the aforementioned paper, Gibbs states:

If we wish to express in a single equation the necessary and sufficient condition of thermodynamic equilibrium for a substance when surrounded by a medium of constant pressure P and temperature T, this equation may be written:

Where δ refers to the variation produced by any variations in the state of the parts of the body, and (when different parts of the body are in different states) in the proportion in which the body is divided between the different states. The condition of stable equilibrium is that the value of the expression in the parenthesis shall be a minimum.

In this description, as used by Gibbs, ε refers to the internal energy of the body, η refers to the entropy of the body, and ν is the volume of the body.

Electrochemical, internal, external, and total chemical potential

The abstract definition of chemical potential given above—total change in free energy per extra mole of substance—is more specifically called total chemical potential. If two locations have different total chemical potentials for a species, some of it may be due to potentials associated with "external" force fields (electric potential energy, gravitational potential energy, etc.), while the rest would be due to "internal" factors (density, temperature, etc.) Therefore, the total chemical potential can be split into internal chemical potential and external chemical potential:

where

i.e., the external potential is the sum of electric potential, gravitational potential, etc. (where q and m are the charge and mass of the species, Vele and h are the electric potential and height of the container, respectively, and g is the acceleration due to gravity). The internal chemical potential includes everything else besides the external potentials, such as density, temperature, and enthalpy. This formalism can be understood by assuming that the total energy of a system, , is the sum of two parts: an internal energy, , and an external energy due to the interaction of each particle with an external field, . The definition of chemical potential applied to yields the above expression for .

The phrase "chemical potential" sometimes means "total chemical potential", but that is not universal. In some fields, in particular electrochemistry, semiconductor physics, and solid-state physics, the term "chemical potential" means internal chemical potential, while the term electrochemical potential is used to mean total chemical potential.

Systems of particles

Electrons in solids

Electrons in solids have a chemical potential, defined the same way as the chemical potential of a chemical species: The change in free energy when electrons are added or removed from the system. In the case of electrons, the chemical potential is usually expressed in energy per particle rather than energy per mole, and the energy per particle is conventionally given in units of electronvolt (eV).

Chemical potential plays an especially important role in solid-state physics and is closely related to the concepts of work function, Fermi energy, and Fermi level. For example, n-type silicon has a higher internal chemical potential of electrons than p-type silicon. In a p–n junction diode at equilibrium the chemical potential (internal chemical potential) varies from the p-type to the n-type side, while the total chemical potential (electrochemical potential, or, Fermi level) is constant throughout the diode.

As described above, when describing chemical potential, one has to say "relative to what". In the case of electrons in semiconductors, internal chemical potential is often specified relative to some convenient point in the band structure, e.g., to the bottom of the conduction band. It may also be specified "relative to vacuum", to yield a quantity known as work function, however, work function varies from surface to surface even on a completely homogeneous material. Total chemical potential, on the other hand, is usually specified relative to electrical ground.

In atomic physics, the chemical potential of the electrons in an atom is sometimes said to be the negative of the atom's electronegativity. Likewise, the process of chemical potential equalization is sometimes referred to as the process of electronegativity equalization. This connection comes from the Mulliken electronegativity scale. By inserting the energetic definitions of the ionization potential and electron affinity into the Mulliken electronegativity, it is seen that the Mulliken chemical potential is a finite difference approximation of the electronic energy with respect to the number of electrons., i.e.,

Sub-nuclear particles

In recent years, thermal physics has applied the definition of chemical potential to systems in particle physics and its associated processes. For example, in a quark–gluon plasma or other QCD matter, at every point in space there is a chemical potential for photons, a chemical potential for electrons, a chemical potential for baryon number, electric charge, and so forth.

In the case of photons, photons are bosons and can very easily and rapidly appear or disappear. Therefore, at thermodynamic equilibrium, the chemical potential of photons is always and everywhere zero. The reason is, if the chemical potential somewhere was higher than zero, photons would spontaneously disappear from that area until the chemical potential went back to zero; likewise, if the chemical potential somewhere was less than zero, photons would spontaneously appear until the chemical potential went back to zero. Since this process occurs extremely rapidly (at least, it occurs rapidly in the presence of dense charged matter), it is safe to assume that the photon chemical potential is never different from zero.

Electric charge is different because it is conserved, i.e. it can be neither created nor destroyed. It can, however, diffuse. The "chemical potential of electric charge" controls this diffusion: Electric charge, like anything else, will tend to diffuse from areas of higher chemical potential to areas of lower chemical potential. Other conserved quantities like baryon number are the same. In fact, each conserved quantity is associated with a chemical potential and a corresponding tendency to diffuse to equalize it out.

In the case of electrons, the behaviour depends on temperature and context. At low temperatures, with no positrons present, electrons cannot be created or destroyed. Therefore, there is an electron chemical potential that might vary in space, causing diffusion. At very high temperatures, however, electrons and positrons can spontaneously appear out of the vacuum (pair production), so the chemical potential of electrons by themselves becomes a less useful quantity than the chemical potential of the conserved quantities like (electrons minus positrons).

The chemical potentials of bosons and fermions is related to the number of particles and the temperature by Bose–Einstein statistics and Fermi–Dirac statistics respectively.

Ideal vs. non-ideal solutions

The chemical potential of component i in solution for (left) ideal [incorrectly linearized] and (right) real solutions

Generally the chemical potential is given as a sum of an ideal contribution and an excess contribution:

In an ideal solution, the chemical potential of species ii) is dependent on temperature and pressure. μi0(TP) is defined as the chemical potential of pure species i. Given this definition, the chemical potential of species i in an ideal solution is

where R is the gas constant, and is the mole fraction of species i contained in the solution. The chemical potential becomes negative infinity when , but this does not lead to unphysical results because means that species i is not present in the system.

This equation assumes that only depends on the mole fraction () contained in the solution. This neglects intermolecular interaction between species i with itself and other species [i–(ji)]. This can be corrected for by factoring in the coefficient of activity of species i, defined as γi. This correction yields

The plots above give a very rough picture of the ideal and non-ideal situation.

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