Vacuum energy

From Wikipedia, the free encyclopedia

Vacuum energy is an underlying background energy that exists in space throughout the entire Universe. One contribution to the vacuum energy may be from virtual particles which are thought to be particle pairs that blink into existence and then annihilate in a timespan too short to observe. Their behavior is codified in Heisenberg's energy–time uncertainty principle. Still, the exact effect of such fleeting bits of energy is difficult to quantify. The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum.^[1]

Unsolved problem in physics: Why does the zero-point energy of the vacuum not cause a large cosmological constant? What cancels it out?

The effects of vacuum energy can be experimentally observed in various phenomena such as spontaneous emission, the Casimir effect and the Lamb shift, and are thought to influence the behavior of the Universe on cosmological scales. Using the upper limit of the cosmological constant, the vacuum energy of free space has been estimated to be 10⁻⁹ joules (10⁻² ergs) per cubic meter.^[2] However, in both quantum electrodynamics (QED) and stochastic electrodynamics (SED), consistency with the principle of Lorentz covariance and with the magnitude of the Planck constant requires it to have a much larger value of 10¹¹³ joules per cubic meter.^[3][4] This huge discrepancy is known as the vacuum catastrophe.

Origin

Quantum field theory states that all fundamental fields, such as the electromagnetic field, must be quantized at each and every point in space^{[citation needed]}. A field in physics may be envisioned as if space were filled with interconnected vibrating balls and springs, and the strength of the field were like the displacement of a ball from its rest position. The theory requires "vibrations" in, or more accurately changes in the strength of, such a field to propagate as per the appropriate wave equation for the particular field in question. The second quantization of quantum field theory requires that each such ball-spring combination be quantized, that is, that the strength of the field be quantized at each point in space. Canonically, if the field at each point in space is a simple harmonic oscillator, its quantization places a quantum harmonic oscillator at each point. Excitations of the field correspond to the elementary particles of particle physics. Thus, according to the theory, even the vacuum has a vastly complex structure and all calculations of quantum field theory must be made in relation to this model of the vacuum.

The theory considers vacuum to implicitly have the same properties as a particle, such as spin or polarization in the case of light, energy, and so on. According to the theory, most of these properties cancel out on average leaving the vacuum empty in the literal sense of the word. One important exception, however, is the vacuum energy or the vacuum expectation value of the energy. The quantization of a simple harmonic oscillator requires the lowest possible energy, or zero-point energy of such an oscillator to be:
${\displaystyle {E}={\frac {1}{2}}h\nu .}$
Summing over all possible oscillators at all points in space gives an infinite quantity. To remove this infinity, one may argue that only differences in energy are physically measurable, much as the concept of potential energy has been treated in classical mechanics for centuries. This argument is the underpinning of the theory of renormalization. In all practical calculations, this is how the infinity is handled.

Vacuum energy can also be thought of in terms of virtual particles (also known as vacuum fluctuations) which are created and destroyed out of the vacuum. These particles are always created out of the vacuum in particle-antiparticle pairs, which in most cases shortly annihilate each other and disappear. However, these particles and antiparticles may interact with others before disappearing, a process which can be mapped using Feynman diagrams. Note that this method of computing vacuum energy is mathematically equivalent to having a quantum harmonic oscillator at each point and, therefore, suffers the same renormalization problems.

Additional contributions to the vacuum energy come from spontaneous symmetry breaking in quantum field theory.

Implications

Vacuum energy has a number of consequences. In 1948, Dutch physicists Hendrik B. G. Casimir and Dirk Polder predicted the existence of a tiny attractive force between closely placed metal plates due to resonances in the vacuum energy in the space between them. This is now known as the Casimir effect and has since been extensively experimentally verified. It is therefore believed that the vacuum energy is "real" in the same sense that more familiar conceptual objects such as electrons, magnetic fields, etc., are real. However, alternative explanations for the Casimir effect have since been proposed.^[5]

Other predictions are harder to verify. Vacuum fluctuations are always created as particle–antiparticle pairs. The creation of these virtual particles near the event horizon of a black hole has been hypothesized by physicist Stephen Hawking to be a mechanism for the eventual "evaporation" of black holes.^[6] If one of the pair is pulled into the black hole before this, then the other particle becomes "real" and energy/mass is essentially radiated into space from the black hole. This loss is cumulative and could result in the black hole's disappearance over time. The time required is dependent on the mass of the black hole (the equations indicate that the smaller the black hole, the more rapidly it evaporates) but could be on the order of 10¹⁰⁰ years for large solar-mass black holes.^[6]

The vacuum energy also has important consequences for physical cosmology. General relativity predicts that energy is equivalent to mass, and therefore, if the vacuum energy is "really there", it should exert a gravitational force. Essentially, a non-zero vacuum energy is expected to contribute to the cosmological constant, which affects the expansion of the universe.^{[citation needed]} In the special case of vacuum energy, general relativity stipulates that the gravitational field is proportional to ρ+3p (where ρ is the mass-energy density, and p is the pressure). Quantum theory of the vacuum further stipulates that the pressure of the zero-state vacuum energy is always negative and equal in magnitude to ρ. Thus, the total is ρ+3p = ρ-3ρ = -2ρ, a negative value. If indeed the vacuum ground state has non-zero energy, the calculation implies a repulsive gravitational field, giving rise to acceleration of the expansion of the universe,^{[citation needed]}. However, the vacuum energy is mathematically infinite without renormalization, which is based on the assumption that we can only measure energy in a relative sense, which is not true if we can observe it indirectly via the cosmological constant.^{[citation needed]}

The existence of vacuum energy is also sometimes used as theoretical justification for the possibility of free-energy machines. It has been argued that due to the broken symmetry (in QED), free energy does not violate conservation of energy, since the laws of thermodynamics only apply to equilibrium systems. However, consensus amongst physicists is that this is unknown as the nature of vacuum energy remains an unsolved problem.^[7] In particular, the second law of thermodynamics is unaffected by the existence of vacuum energy.^{[citation needed]} However, in Stochastic Electrodynamics, the energy density is taken to be a classical random noise wave field which consists of real electromagnetic noise waves propagating isotropically in all directions. The energy in such a wave field would seem to be accessible, e.g., with nothing more complicated than a directional coupler.^{[citation needed]} The most obvious difficulty appears to be the spectral distribution of the energy, which compatibility with Lorentz invariance requires to take the form Kf³, where K is a constant and f denotes frequency.^[3][8] It follows that the energy and momentum flux in this wave field only becomes significant at extremely short wavelengths where directional coupler technology is currently lacking.^{[citation needed]}

History

In 1934, Georges Lemaître used an unusual perfect-fluid equation of state to interpret the cosmological constant as due to vacuum energy. In 1948, the Casimir effect was provided an experimental method for a verification of the existence of vacuum energy, however, in 1955, Evgeny Lifshitz offered a different origin for the Casimir effect. In 1957, Lee and Yang proved the concepts of broken symmetry and parity violation, for which they won the Nobel prize. In 1973, Edward Tryon proposed the zero-energy universe hypothesis: that the Universe may be a large-scale quantum-mechanical vacuum fluctuation where positive mass-energy is balanced by negative gravitational potential energy. During the 1980s, there were many attempts to relate the fields that generate the vacuum energy to specific fields that were predicted by attempts at a Grand unification theory and to use observations of the Universe to confirm one or another version. However, the exact nature of the particles (or fields) that generate vacuum energy, with a density such as that required by inflation theory, remains a mystery.

Oxidants (Redox Reactions, including Biology)

From Wikipedia, the free encyclopedia

The two parts of a redox reaction

Rust, a slow redox reaction

A bonfire; combustion is a fast redox reaction

Sodium and fluorine bonding ionically to form sodium fluoride. Sodium loses its outer electron to give it a stable electron configuration, and this electron enters the fluorine atom exothermically. The oppositely charged ions are then attracted to each other. The sodium is oxidized, and the fluorine is reduced.

Play media

Demonstration of the reaction between a strong oxidising and a reducing agent. When few drops of glycerol (reducing agent) are added to powdered potassium permanganate (strong oxidising agent), a vigorous reaction accompanied by self-ignition starts.

Redox (short for reduction–oxidation reaction) is a chemical reaction in which the oxidation states of atoms are changed. Any such reaction involves both a reduction process and a complementary oxidation process, two key concepts involved with electron transfer processes.^[1] Redox reactions include all chemical reactions in which atoms have their oxidation state changed; in general, redox reactions involve the transfer of electrons between chemical species. The chemical species from which the electron is stripped is said to have been oxidized, while the chemical species to which the electron is added is said to have been reduced. It can be explained in simple terms:

• Oxidation is the loss of electrons or an increase in oxidation state by a molecule, atom, or ion.
• Reduction is the gain of electrons or a decrease in oxidation state by a molecule, atom, or ion.

As an example, during the combustion of wood, oxygen from the air is reduced, gaining electrons from the carbon.^[2] Although oxidation reactions are commonly associated with the formation of oxides from oxygen molecules, oxygen is not necessarily included in such reactions, as other chemical species can serve the same function.^[2]

The reaction can occur relatively slowly, as in the case of rust, or more quickly, as in the case of fire. There are simple redox processes, such as the oxidation of carbon to yield carbon dioxide (CO₂) or the reduction of carbon by hydrogen to yield methane (CH₄), and more complex processes such as the oxidation of glucose (C₆H₁₂O₆) in the human body.

Etymology

"Redox" is a portmanteau of "reduction" and "oxidation".

The word oxidation originally implied reaction with oxygen to form an oxide, since dioxygen (O₂ (g)) was historically the first recognized oxidizing agent. Later, the term was expanded to encompass oxygen-like substances that accomplished parallel chemical reactions. Ultimately, the meaning was generalized to include all processes involving loss of electrons.

The word reduction originally referred to the loss in weight upon heating a metallic ore such as a metal oxide to extract the metal. In other words, ore was "reduced" to metal. Antoine Lavoisier (1743–1794) showed that this loss of weight was due to the loss of oxygen as a gas. Later, scientists realized that the metal atom gains electrons in this process. The meaning of reduction then became generalized to include all processes involving gain of electrons. Even though "reduction" seems counter-intuitive when speaking of the gain of electrons, it might help to think of reduction as the loss of oxygen, which was its historical meaning. Since electrons are negatively charged, it is also helpful to think of this as reduction in electrical charge.

The electrochemist John Bockris has used the words electronation and deelectronation to describe reduction and oxidation processes respectively when they occur at electrodes.^[3] These words are analogous to protonation and deprotonation, but they have not been widely adopted by chemists.

The term "hydrogenation" could be used instead of reduction, since hydrogen is the reducing agent in a large number of reactions, especially in organic chemistry and biochemistry. But, unlike oxidation, which has been generalized beyond its root element, hydrogenation has maintained its specific connection to reactions that add hydrogen to another substance (e.g., the hydrogenation of unsaturated fats into saturated fats, R−CH=CH−R + H₂ → R−CH₂−CH₂−R). The word "redox" was first used in 1928.^[4]

Definitions

The processes of oxidation and reduction occur simultaneously and cannot happen independently of one another, similar to the acid–base reaction.^[2] The oxidation alone and the reduction alone are each called a half-reaction, because two half-reactions always occur together to form a whole reaction. When writing half-reactions, the gained or lost electrons are typically included explicitly in order that the half-reaction be balanced with respect to electric charge.

Though sufficient for many purposes, these general descriptions are not precisely correct. Although oxidation and reduction properly refer to a change in oxidation state — the actual transfer of electrons may never occur. The oxidation state of an atom is the fictitious charge that an atom would have if all bonds between atoms of different elements were 100% ionic. Thus, oxidation is best defined as an increase in oxidation state, and reduction as a decrease in oxidation state. In practice, the transfer of electrons will always cause a change in oxidation state, but there are many reactions that are classed as "redox" even though no electron transfer occurs (such as those involving covalent bonds).

Oxidizing and reducing agents

In redox processes, the reductant transfers electrons to the oxidant. Thus, in the reaction, the reductant or reducing agent loses electrons and is oxidized, and the oxidant or oxidizing agent gains electrons and is reduced. The pair of an oxidizing and reducing agent that are involved in a particular reaction is called a redox pair. A redox couple is a reducing species and its corresponding oxidizing form, e.g., Fe²⁺/Fe³⁺.

Oxidizers

The international pictogram for oxidizing chemicals.

Substances that have the ability to oxidize other substances (cause them to lose electrons) are said to be oxidative or oxidizing and are known as oxidizing agents, oxidants, or oxidizers. That is, the oxidant (oxidizing agent) removes electrons from another substance, and is thus itself reduced. And, because it "accepts" electrons, the oxidizing agent is also called an electron acceptor. Oxygen is the quintessential oxidizer.

Oxidants are usually chemical substances with elements in high oxidation states (e.g., H
2O
2, MnO−
4, CrO
3, Cr
2O2−
7, OsO
4), or else highly electronegative elements (O₂, F₂, Cl₂, Br₂) that can gain extra electrons by oxidizing another substance.

Reducers

Substances that have the ability to reduce other substances (cause them to gain electrons) are said to be reductive or reducing and are known as reducing agents, reductants, or reducers. The reductant (reducing agent) transfers electrons to another substance, and is thus itself oxidized. And, because it "donates" electrons, the reducing agent is also called an electron donor. Electron donors can also form charge transfer complexes with electron acceptors.

Reductants in chemistry are very diverse. Electropositive elemental metals, such as lithium, sodium, magnesium, iron, zinc, and aluminium, are good reducing agents. These metals donate or give away electrons readily. Hydride transfer reagents, such as NaBH₄ and LiAlH₄, are widely used in organic chemistry,^[5][6] primarily in the reduction of carbonyl compounds to alcohols. Another method of reduction involves the use of hydrogen gas (H₂) with a palladium, platinum, or nickel catalyst. These catalytic reductions are used primarily in the reduction of carbon-carbon double or triple bonds.

Standard electrode potentials (reduction potentials)

Each half-reaction has a standard electrode potential (E0
cell), which is equal to the potential difference or voltage at equilibrium under standard conditions of an electrochemical cell in which the cathode reaction is the half-reaction considered, and the anode is a standard hydrogen electrode where hydrogen is oxidized:

 ¹⁄₂ H₂ → H⁺ + e⁻.

The electrode potential of each half-reaction is also known as its reduction potential E0
red, or potential when the half-reaction takes place at a cathode. The reduction potential is a measure of the tendency of the oxidizing agent to be reduced. Its value is zero for H⁺ + e⁻ →  ¹⁄₂ H₂ by definition, positive for oxidizing agents stronger than H⁺ (e.g., +2.866 V for F₂) and negative for oxidizing agents that are weaker than H⁺ (e.g., −0.763 V for Zn²⁺).^[7]

For a redox reaction that takes place in a cell, the potential difference is:

E0
cell = E0
cathode – E0
anode

However, the potential of the reaction at the anode was sometimes expressed as an oxidation potential:

E0
ox = –E0
red.

The oxidation potential is a measure of the tendency of the reducing agent to be oxidized, but does not represent the physical potential at an electrode. With this notation, the cell voltage equation is written with a plus sign

E0
cell = E0
red(cathode) + E0
ox(anode)

Examples of redox reactions

Illustration of a redox reaction

A good example is the reaction between hydrogen and fluorine in which hydrogen is being oxidized and fluorine is being reduced:

H
2 + F
2 → 2 HF

We can write this overall reaction as two half-reactions:

the oxidation reaction:

H
2 → 2 H⁺ + 2 e⁻

and the reduction reaction:

F
2 + 2 e⁻ → 2 F⁻

Analyzing each half-reaction in isolation can often make the overall chemical process clearer. Because there is no net change in charge during a redox reaction, the number of electrons in excess in the oxidation reaction must equal to the number consumed by the reduction reaction (as shown above).

Elements, even in molecular form, always have an oxidation state of zero. In the first half-reaction, hydrogen is oxidized from an oxidation state of zero to an oxidation state of +1. In the second half-reaction, fluorine is reduced from an oxidation state of zero to an oxidation state of −1.

When adding the reactions together the electrons are canceled:

H 2	→	2 H+ + 2 e−
F 2 + 2 e−	→	2 F−
H2 + F2	→	2 H+ + 2 F−

And the ions combine to form hydrogen fluoride:

2 H⁺ + 2 F⁻ → 2 HF

The overall reaction is:

H
2 + F
2 → 2 HF

Metal displacement

A redox reaction is the force behind an electrochemical cell like the Galvanic cell pictured. The battery is made out of a zinc electrode in a ZnSO₄ solution connected with a wire and a porous disk to a copper electrode in a CuSO₄ solution.

In this type of reaction, a metal atom in a compound (or in a solution) is replaced by an atom of another metal. For example, copper is deposited when zinc metal is placed in a copper(II) sulfate solution:

Zn(s)+ CuSO₄(aq) → ZnSO₄(aq) + Cu(s)

In the above reaction, zinc metal displaces the copper(II) ion from copper sulfate solution and thus liberates free copper metal.

The ionic equation for this reaction is:

Zn + Cu²⁺ → Zn²⁺ + Cu

As two half-reactions, it is seen that the zinc is oxidized:

Zn → Zn²⁺ + 2 e⁻

And the copper is reduced:

Cu²⁺ + 2 e⁻ → Cu

Other examples

• The reduction of nitrate to nitrogen in the presence of an acid (denitrification):

  2 NO−
  3 + 10 e⁻ + 12 H⁺ → N₂ + 6 H₂O

• The combustion of hydrocarbons, such as in an internal combustion engine, which produces water, carbon dioxide, some partially oxidized forms such as carbon monoxide, and heat energy. Complete oxidation of materials containing carbon produces carbon dioxide.
• In organic chemistry, the stepwise oxidation of a hydrocarbon by oxygen produces water and, successively, an alcohol, an aldehyde or a ketone, a carboxylic acid, and then a peroxide.

Corrosion and rusting

Oxides, such as iron(III) oxide or rust, which consists of hydrated iron(III) oxides Fe₂O₃·nH₂O and iron(III) oxide-hydroxide (FeO(OH), Fe(OH)₃), form when oxygen combines with other elements

Iron rusting in pyrite cubes

• The term corrosion refers to the electrochemical oxidation of metals in reaction with an oxidant such as oxygen. Rusting, the formation of iron oxides, is a well-known example of electrochemical corrosion; it forms as a result of the oxidation of iron metal. Common rust often refers to iron(III) oxide, formed in the following chemical reaction:

  4 Fe + 3 O₂ → 2 Fe₂O₃

• The oxidation of iron(II) to iron(III) by hydrogen peroxide in the presence of an acid:

  Fe²⁺ → Fe³⁺ + e⁻

  H₂O₂ + 2 e⁻ → 2 OH⁻

Overall equation:

2 Fe²⁺ + H₂O₂ + 2 H⁺ → 2 Fe³⁺ + 2 H₂O

Redox reactions in industry

Cathodic protection is a technique used to control the corrosion of a metal surface by making it the cathode of an electrochemical cell. A simple method of protection connects protected metal to a more easily corroded "sacrificial anode" to act as the anode. The sacrificial metal instead of the protected metal, then, corrodes. A common application of cathodic protection is in galvanized steel, in which a sacrificial coating of zinc on steel parts protects them from rust.

The primary process of reducing ore at high temperature to produce metals is known as smelting.

Oxidation is used in a wide variety of industries such as in the production of cleaning products and oxidizing ammonia to produce nitric acid, which is used in most fertilizers.

Redox reactions are the foundation of electrochemical cells, which can generate electrical energy or support electrosynthesis.

The process of electroplating uses redox reactions to coat objects with a thin layer of a material, as in chrome-plated automotive parts, silver plating cutlery, and gold-plated jewelry.

The production of compact discs depends on a redox reaction, which coats the disc with a thin layer of metal film.^{[clarification needed]}

Redox reactions in biology

Top: ascorbic acid (reduced form of Vitamin C)
Bottom: dehydroascorbic acid (oxidized form of Vitamin C)

Many important biological processes involve redox reactions.

Cellular respiration, for instance, is the oxidation of glucose (C₆H₁₂O₆) to CO₂ and the reduction of oxygen to water. The summary equation for cell respiration is:

C₆H₁₂O₆ + 6 O₂ → 6 CO₂ + 6 H₂O

The process of cell respiration also depends heavily on the reduction of NAD⁺ to NADH and the reverse reaction (the oxidation of NADH to NAD⁺). Photosynthesis and cellular respiration are complementary, but photosynthesis is not the reverse of the redox reaction in cell respiration:

6 CO₂ + 6 H₂O + light energy → C₆H₁₂O₆ + 6 O₂

Biological energy is frequently stored and released by means of redox reactions. Photosynthesis involves the reduction of carbon dioxide into sugars and the oxidation of water into molecular oxygen. The reverse reaction, respiration, oxidizes sugars to produce carbon dioxide and water. As intermediate steps, the reduced carbon compounds are used to reduce nicotinamide adenine dinucleotide (NAD⁺), which then contributes to the creation of a proton gradient, which drives the synthesis of adenosine triphosphate (ATP) and is maintained by the reduction of oxygen. In animal cells, mitochondria perform similar functions. See the Membrane potential article.

Free radical reactions are redox reactions that occur as a part of homeostasis and killing microorganisms, where an electron detaches from a molecule and then reattaches almost instantaneously. Free radicals are a part of redox molecules and can become harmful to the human body if they do not reattach to the redox molecule or an antioxidant. Unsatisfied free radicals can spur the mutation of cells they encounter and are, thus, causes of cancer.

The term redox state is often used to describe the balance of GSH/GSSG, NAD⁺/NADH and NADP⁺/NADPH in a biological system such as a cell or organ. The redox state is reflected in the balance of several sets of metabolites (e.g., lactate and pyruvate, beta-hydroxybutyrate, and acetoacetate), whose interconversion is dependent on these ratios. An abnormal redox state can develop in a variety of deleterious situations, such as hypoxia, shock, and sepsis. Redox mechanism also control some cellular processes. Redox proteins and their genes must be co-located for redox regulation according to the CoRR hypothesis for the function of DNA in mitochondria and chloroplasts.

Redox cycling

A wide variety of aromatic compounds are enzymatically reduced to form free radicals that contain one more electron than their parent compounds. In general, the electron donor is any of a wide variety of flavoenzymes and their coenzymes. Once formed, these anion free radicals reduce molecular oxygen to superoxide, and regenerate the unchanged parent compound. The net reaction is the oxidation of the flavoenzyme's coenzymes and the reduction of molecular oxygen to form superoxide. This catalytic behavior has been described as futile cycle or redox cycling.

Examples of redox cycling-inducing molecules are the herbicide paraquat and other viologens and quinones such as menadione.^[8]

Redox reactions in geology

Mi Vida uranium mine, near Moab, Utah. The alternating red and white/green bands of sandstone correspond to oxidized and reduced conditions in groundwater redox chemistry.

In geology, redox is important to both the formation of minerals and the mobilization of minerals, and is also important in some depositional environments. In general, the redox state of most rocks can be seen in the color of the rock. The rock forms in oxidizing conditions, giving it a red color. It is then "bleached" to a green—or sometimes white—form when a reducing fluid passes through the rock. The reduced fluid can also carry uranium-bearing minerals. Famous examples of redox conditions affecting geological processes include uranium deposits and Moqui marbles.

Balancing redox reactions

Describing the overall electrochemical reaction for a redox process requires a balancing of the component half-reactions for oxidation and reduction. In general, for reactions in aqueous solution, this involves adding H⁺, OH⁻, H₂O, and electrons to compensate for the oxidation changes.

Acidic media

In acidic media, H⁺ ions and water are added to half-reactions to balance the overall reaction.
For instance, when manganese(II) reacts with sodium bismuthate:

Unbalanced reaction:	Mn2+(aq) + NaBiO3(s) → Bi3+(aq) + MnO− 4 (aq)
Oxidation:	4 H2O(l) + Mn2+(aq) → MnO− 4(aq) + 8 H+(aq) + 5 e−
Reduction:	2 e− + 6 H+ + BiO− 3(s) → Bi3+(aq) + 3 H2O(l)

The reaction is balanced by scaling the two half-cell reactions to involve the same number of electrons (multiplying the oxidation reaction by the number of electrons in the reduction step and vice versa):

8 H₂O(l) + 2 Mn²⁺(aq) → 2 MnO−
4(aq) + 16 H⁺(aq) + 10 e⁻

10 e⁻ + 30 H⁺ + 5 BiO−
3(s) → 5 Bi³⁺(aq) + 15 H₂O(l)

Adding these two reactions eliminates the electrons terms and yields the balanced reaction:

14 H⁺(aq) + 2 Mn²⁺(aq) + 5 NaBiO₃(s) → 7 H₂O(l) + 2 MnO−
4(aq) + 5 Bi³⁺(aq) + 5 Na+(aq)

Basic media

In basic media, OH⁻ ions and water are added to half reactions to balance the overall reaction.

For example, in the reaction between potassium permanganate and sodium sulfite:

Unbalanced reaction:	KMnO4 + Na2SO3 + H2O → MnO2 + Na2SO4 + KOH
Reduction:	3 e− + 2 H2O + MnO− 4 → MnO2 + 4 OH−
Oxidation:	2 OH− + SO2− 3 → SO2− 4 + H2O + 2 e−

Balancing the number of electrons in the two half-cell reactions gives:

6 e⁻ + 4 H₂O + 2 MnO−
4 → 2 MnO₂ + 8 OH⁻

6 OH⁻ + 3 SO2−
3 → 3 SO2−
4 + 3 H₂O + 6 e⁻

Adding these two half-cell reactions together gives the balanced equation:

2 KMnO₄ + 3 Na₂SO₃ + H₂O → 2 MnO₂ + 3 Na₂SO₄ + 2 KOH

Memory aids

The key terms involved in redox are often confusing to students.^[9][10] For example, an element that is oxidized loses electrons; however, that element is referred to as the reducing agent. Likewise, an element that is reduced gains electrons and is referred to as the oxidizing agent.^[11] Acronyms or mnemonics are commonly used^[12] to help remember the terminology:

• "OIL RIG" — oxidation is loss of electrons, reduction is gain of electrons.^{[9][10][11][12]}
• "LEO the lion says GER" — loss of electrons is oxidation, gain of electrons is reduction.^{[9][10][11][12]}
• "LEORA says GEROA" — loss of electrons is oxidation (reducing agent), gain of electrons is reduction (oxidizing agent).^[11]
• "RED CAT" and "AN OX", or "AnOx RedCat" ("an ox-red cat") — reduction occurs at the cathode and the anode is for oxidation.
• "RED CAT gains what AN OX loses" – reduction at the cathode gains (electrons) what anode oxidation loses (electrons).