Boltzmann constant

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https://en.wikipedia.org/wiki/Boltzmann_constant 

Boltzmann constant

Ludwig Boltzmann
Definition:	The proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas
Symbol:	kB
Value in joules per kelvin:	1.380649×10−23 J⋅K−1

The Boltzmann constant (k_B or k) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy. It is named after the Austrian scientist Ludwig Boltzmann.

As part of the 2019 redefinition of SI base units, the Boltzmann constant is one of the seven "defining constants" that have been given exact definitions. They are used in various combinations to define the seven SI base units. The Boltzmann constant is defined to be exactly 1.380649×10⁻²³ J⋅K⁻¹.

Roles of the Boltzmann constant

Relationships between Boyle's, Charles's, Gay-Lussac's, Avogadro's, combined and ideal gas laws, with the Boltzmann constant k_B = R/N_A = n R/N  (in each law, properties circled are variable and properties not circled are held constant)

Macroscopically, the ideal gas law states that, for an ideal gas, the product of pressure p and volume V is proportional to the product of amount of substance n (in moles) and absolute temperature T:

${\displaystyle pV=nRT,}$

where R is the molar gas constant (8.31446261815324 J⋅K⁻¹⋅mol⁻¹). Introducing the Boltzmann constant as the gas constant per molecule k = R/N_A transforms the ideal gas law into an alternative form:

${\displaystyle pV=NkT,}$

where N is the number of molecules of gas. For n = 1 mol, N is equal to the number of particles in one mole (the Avogadro number).

Role in the equipartition of energy

Main article: Equipartition of energy

Given a thermodynamic system at an absolute temperature T, the average thermal energy carried by each microscopic degree of freedom in the system is 1/2kT (i.e., about 2.07×10⁻²¹ J, or 0.013 eV, at room temperature). It's important to note that this is generally true only for classical systems with a large number of particles, and in which quantum effects are negligible.

In classical statistical mechanics, this average is predicted to hold exactly for homogeneous ideal gases. Monatomic ideal gases (the six noble gases) possess three degrees of freedom per atom, corresponding to the three spatial directions. According to the equipartition of energy this means that there is a thermal energy of 3/2kT per atom. This corresponds very well with experimental data. The thermal energy can be used to calculate the root-mean-square speed of the atoms, which turns out to be inversely proportional to the square root of the atomic mass. The root mean square speeds found at room temperature accurately reflect this, ranging from 1370 m/s for helium, down to 240 m/s for xenon.

Kinetic theory gives the average pressure p for an ideal gas as

${\displaystyle p={\frac {1}{3}}{\frac {N}{V}}m{\overline {v^{2}}}.}$

Combination with the ideal gas law

${\displaystyle pV=NkT}$

shows that the average translational kinetic energy is

${\displaystyle {\tfrac {1}{2}}m{\overline {v^{2}}}={\tfrac {3}{2}}kT.}$

Considering that the translational motion velocity vector v has three degrees of freedom (one for each dimension) gives the average energy per degree of freedom equal to one third of that, i.e. 1/2kT.

The ideal gas equation is also obeyed closely by molecular gases; but the form for the heat capacity is more complicated, because the molecules possess additional internal degrees of freedom, as well as the three degrees of freedom for movement of the molecule as a whole. Diatomic gases, for example, possess a total of six degrees of simple freedom per molecule that are related to atomic motion (three translational, two rotational, and one vibrational). At lower temperatures, not all these degrees of freedom may fully participate in the gas heat capacity, due to quantum mechanical limits on the availability of excited states at the relevant thermal energy per molecule.

Role in Boltzmann factors

More generally, systems in equilibrium at temperature T have probability P_i of occupying a state i with energy E weighted by the corresponding Boltzmann factor:

${\displaystyle P_{i}\propto {\frac {\exp \left(-{\frac {E}{kT}}\right)}{Z}},}$

where Z is the partition function. Again, it is the energy-like quantity kT that takes central importance.

Consequences of this include (in addition to the results for ideal gases above) the Arrhenius equation in chemical kinetics.

Role in the statistical definition of entropy

Further information: Entropy (statistical thermodynamics)

 

Boltzmann's grave in the Zentralfriedhof, Vienna, with bust and entropy formula.

In statistical mechanics, the entropy S of an isolated system at thermodynamic equilibrium is defined as the natural logarithm of W, the number of distinct microscopic states available to the system given the macroscopic constraints (such as a fixed total energy E):

${\displaystyle S=k\,\ln W.}$

This equation, which relates the microscopic details, or microstates, of the system (via W) to its macroscopic state (via the entropy S), is the central idea of statistical mechanics. Such is its importance that it is inscribed on Boltzmann's tombstone.

The constant of proportionality k serves to make the statistical mechanical entropy equal to the classical thermodynamic entropy of Clausius:

${\displaystyle \Delta S=\int {\frac {{\rm {d}}Q}{T}}.}$

One could choose instead a rescaled dimensionless entropy in microscopic terms such that

${\displaystyle {S'=\ln W},\quad \Delta S'=\int {\frac {\mathrm {d} Q}{kT}}.}$

This is a more natural form and this rescaled entropy exactly corresponds to Shannon's subsequent information entropy.

The characteristic energy kT is thus the energy required to increase the rescaled entropy by one nat.

The thermal voltage

In semiconductors, the Shockley diode equation—the relationship between the flow of electric current and the electrostatic potential across a p–n junction—depends on a characteristic voltage called the thermal voltage, denoted by V_T. The thermal voltage depends on absolute temperature T as

$${\displaystyle V_{\mathrm {T} }={kT \over q},}$$

where q is the magnitude of the electrical charge on the electron with a value 1.602176634×10⁻¹⁹ C Equivalently,

$${\displaystyle {V_{\mathrm {T} } \over T}={k \over q}\approx 8.61733034\times 10^{-5}\ \mathrm {V/K} .}$$

At room temperature 300 K (27 °C; 80 °F), V_T is approximately 25.85 mV which can be derived by plugging in the values as follows:

$${\displaystyle V_{\mathrm {T} }={kT \over q}={\frac {1.38\times 10^{-23}\ \mathrm {J} \cdot k^{-1}\times 300\ \mathrm {K} }{1.6\times 10^{-19}\ \mathrm {C} }}\simeq 25.85\ \mathrm {mV} }$$

At the standard state temperature of 298.15 K (25.00 °C; 77.00 °F), it is approximately 25.69 mV. The thermal voltage is also important in plasmas and electrolyte solutions (e.g. the Nernst equation); in both cases it provides a measure of how much the spatial distribution of electrons or ions is affected by a boundary held at a fixed voltage.

History

The Boltzmann constant is named after its 19th century Austrian discoverer, Ludwig Boltzmann. Although Boltzmann first linked entropy and probability in 1877, the relation was never expressed with a specific constant until Max Planck first introduced k, and gave a more precise value for it (1.346×10⁻²³ J/K, about 2.5% lower than today's figure), in his derivation of the law of black-body radiation in 1900–1901. Before 1900, equations involving Boltzmann factors were not written using the energies per molecule and the Boltzmann constant, but rather using a form of the gas constant R, and macroscopic energies for macroscopic quantities of the substance. The iconic terse form of the equation S = k ln W on Boltzmann's tombstone is in fact due to Planck, not Boltzmann. Planck actually introduced it in the same work as his eponymous h.

In 1920, Planck wrote in his Nobel Prize lecture:

This constant is often referred to as Boltzmann's constant, although, to my knowledge, Boltzmann himself never introduced it — a peculiar state of affairs, which can be explained by the fact that Boltzmann, as appears from his occasional utterances, never gave thought to the possibility of carrying out an exact measurement of the constant.

This "peculiar state of affairs" is illustrated by reference to one of the great scientific debates of the time. There was considerable disagreement in the second half of the nineteenth century as to whether atoms and molecules were real or whether they were simply a heuristic tool for solving problems. There was no agreement whether chemical molecules, as measured by atomic weights, were the same as physical molecules, as measured by kinetic theory. Planck's 1920 lecture continued:

Nothing can better illustrate the positive and hectic pace of progress which the art of experimenters has made over the past twenty years, than the fact that since that time, not only one, but a great number of methods have been discovered for measuring the mass of a molecule with practically the same accuracy as that attained for a planet.

In versions of SI prior to the 2019 redefinition of the SI base units, the Boltzmann constant was a measured quantity rather than a fixed value. Its exact definition also varied over the years due to redefinitions of the kelvin (see Kelvin § History) and other SI base units (see Joule § History).

In 2017, the most accurate measures of the Boltzmann constant were obtained by acoustic gas thermometry, which determines the speed of sound of a monatomic gas in a triaxial ellipsoid chamber using microwave and acoustic resonances. This decade-long effort was undertaken with different techniques by several laboratories; it is one of the cornerstones of the 2019 redefinition of SI base units. Based on these measurements, the CODATA recommended 1.380649×10⁻²³ J/K to be the final fixed value of the Boltzmann constant to be used for the International System of Units.

Value in different units

Values of kB	Units	Comments
1.380649×10−23	J/K	SI by definition, J/K = m2⋅kg/(s2⋅K) in SI base units
8.617333262×10−5	eV/K
2.083661912×1010	Hz/K	(k/h)
1.380649×10−16	erg/K	CGS system, 1 erg = 1×10−7 J
3.297623483×10−24	cal/K	1 calorie = 4.1868 J
1.832013046×10−24	cal/°R
5.657302466×10−24	ft lb/°R
0.695034800	cm−1/K	(k/(hc))
3.166811563×10−6	Eh/K	(Eh = Hartree)
1.987204259×10−3	kcal/(mol⋅K)	(kNA)
8.314462618×10−3	kJ/(mol⋅K)	(kNA)
−228.5991672	dB(W/K/Hz)	10 log10(k/(1 W/K/Hz)), used for thermal noise calculations

Since k is a proportionality factor between temperature and energy, its numerical value depends on the choice of units for energy and temperature. The small numerical value of the Boltzmann constant in SI units means a change in temperature by 1 K only changes a particle's energy by a small amount. A change of 1 °C is defined to be the same as a change of 1 K. The characteristic energy kT is a term encountered in many physical relationships.

The Boltzmann constant sets up a relationship between wavelength and temperature (dividing hc/k by a wavelength gives a temperature) with one micrometer being related to 14387.777 K, and also a relationship between voltage and temperature (multiplying the voltage by k in units of eV/K) with one volt being related to 11604.518 K. The ratio of these two temperatures, 14387.777 K / 11604.518 K ≈ 1.239842, is the numerical value of hc in units of eV⋅μm.

Natural units

The Boltzmann constant provides a mapping from this characteristic microscopic energy E to the macroscopic temperature scale T = E/k. In physics research another definition is often encountered in setting k to unity, resulting in temperature and energy quantities of the same type. In this context temperature is measured effectively in units of energy and the Boltzmann constant is not explicitly needed.

The equipartition formula for the energy associated with each classical degree of freedom then becomes

${\displaystyle E_{\mathrm {dof} }={\tfrac {1}{2}}T}$

The use of natural units simplifies many physical relationships; in this form the definition of thermodynamic entropy coincides with the form of information entropy:

${\displaystyle S=-\sum _{i}P_{i}\ln P_{i}.}$

where P_i is the probability of each microstate.

Alcohol (chemistry)

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Alcohol_(chemistry) 

Ball-and-stick model of an alcohol molecule (R₃COH). The red and white balls represent the hydroxyl group (-OH). The three "R's" stand for carbon substituents or hydrogen atoms.

 

The bond angle between a hydroxyl group (-OH) and a chain of carbon atoms (R)

In chemistry, an alcohol is a type of organic compound that carries at least one hydroxyl functional group (−OH) bound to a saturated carbon atom. The term alcohol originally referred to the primary alcohol ethanol (ethyl alcohol), which is used as a drug and is the main alcohol present in alcoholic drinks. An important class of alcohols, of which methanol and ethanol are the simplest members, includes all compounds for which the general formula is C_nH_2n+1OH. Simple monoalcohols that are the subject of this article include primary (RCH₂OH), secondary (R₂CHOH) and tertiary (R₃COH) alcohols.

The suffix -ol appears in the IUPAC chemical name of all substances where the hydroxyl group is the functional group with the highest priority. When a higher priority group is present in the compound, the prefix hydroxy- is used in its IUPAC name. The suffix -ol in non-IUPAC names (such as paracetamol or cholesterol) also typically indicates that the substance is an alcohol. However, many substances that contain hydroxyl functional groups (particularly sugars, such as glucose and sucrose) have names which include neither the suffix -ol, nor the prefix hydroxy-.

History

The inflammable nature of the exhalations of wine was already known to ancient natural philosophers such as Aristotle (384–322 BCE), Theophrastus (c. 371–287 BCE), and Pliny the Elder (23/24–79 CE). However, this did not immediately lead to the isolation of alcohol, even despite the development of more advanced distillation techniques in second- and third-century Roman Egypt. An important recognition, first found in one of the writings attributed to Jābir ibn Ḥayyān (ninth century CE), was that by adding salt to boiling wine, which increases the wine's relative volatility, the flammability of the resulting vapors may be enhanced. The distillation of wine is attested in Arabic works attributed to al-Kindī (c. 801–873 CE) and to al-Fārābī (c. 872–950), and in the 28th book of al-Zahrāwī's (Latin: Abulcasis, 936–1013) Kitāb al-Taṣrīf (later translated into Latin as Liber servatoris). In the twelfth century, recipes for the production of aqua ardens ("burning water", i.e., alcohol) by distilling wine with salt started to appear in a number of Latin works, and by the end of the thirteenth century it had become a widely known substance among Western European chemists.

The works of Taddeo Alderotti (1223–1296) describe a method for concentrating alcohol involving repeated fractional distillation through a water-cooled still, by which an alcohol purity of 90% could be obtained. The medicinal properties of ethanol were studied by Arnald of Villanova (1240–1311 CE) and John of Rupescissa (c. 1310–1366), the latter of whom regarded it as a life-preserving substance able to prevent all diseases (the aqua vitae or "water of life", also called by John the quintessence of wine).

Nomenclature

Etymology

The word "alcohol" is from the Arabic kohl (Arabic: الكحل, romanized: al-kuḥl), a powder used as an eyeliner. Al- is the Arabic definite article, equivalent to the in English. Alcohol was originally used for the very fine powder produced by the sublimation of the natural mineral stibnite to form antimony trisulfide Sb₂S₃. It was considered to be the essence or "spirit" of this mineral. It was used as an antiseptic, eyeliner, and cosmetic. The meaning of alcohol was extended to distilled substances in general, and then narrowed to ethanol, when "spirits" was a synonym for hard liquor.

Bartholomew Traheron, in his 1543 translation of John of Vigo, introduces the word as a term used by "barbarous" authors for "fine powder." Vigo wrote: "the barbarous auctours use alcohol, or (as I fynde it sometymes wryten) alcofoll, for moost fine poudre."

The 1657 Lexicon Chymicum, by William Johnson glosses the word as "antimonium sive stibium." By extension, the word came to refer to any fluid obtained by distillation, including "alcohol of wine," the distilled essence of wine. Libavius in Alchymia (1594) refers to "vini alcohol vel vinum alcalisatum". Johnson (1657) glosses alcohol vini as "quando omnis superfluitas vini a vino separatur, ita ut accensum ardeat donec totum consumatur, nihilque fæcum aut phlegmatis in fundo remaneat. "The word's meaning became restricted to "spirit of wine" (the chemical known today as ethanol) in the 18th century and was extended to the class of substances so-called as "alcohols" in modern chemistry after 1850.

The term ethanol was invented in 1892, blending "ethane" with the "-ol" ending of "alcohol", which was generalized as a libfix.

Systematic names

IUPAC nomenclature is used in scientific publications and where precise identification of the substance is important, especially in cases where the relative complexity of the molecule does not make such a systematic name unwieldy. In naming simple alcohols, the name of the alkane chain loses the terminal e and adds the suffix -ol, e.g., as in "ethanol" from the alkane chain name "ethane". When necessary, the position of the hydroxyl group is indicated by a number between the alkane name and the -ol: propan-1-ol for CH₃CH₂CH₂OH, propan-2-ol for CH₃CH(OH)CH₃. If a higher priority group is present (such as an aldehyde, ketone, or carboxylic acid), then the prefix hydroxy-is used, e.g., as in 1-hydroxy-2-propanone (CH₃C(O)CH₂OH).

Some examples of simple alcohols and how to name them

CH3−CH2−CH2−OH
n-propyl alcohol, propan-1-ol, or 1-propanol	isopropyl alcohol, propan-2-ol, or 2-propanol	cyclohexanol	isobutyl alcohol, 2-methylpropan-1-ol, or 2-methyl-1-propanol	tert-amyl alcohol, 2-methylbutan-2-ol, or 2-methyl-2-butanol
A primary alcohol	A secondary alcohol	A secondary alcohol	A primary alcohol	A tertiary alcohol

In cases where the hydroxy group is bonded to an sp² carbon on an aromatic ring, the molecule is classified separately as a phenol and is named using the IUPAC rules for naming phenols. Phenols have distinct properties and are not classified as alcohols.

Common names

In other less formal contexts, an alcohol is often called with the name of the corresponding alkyl group followed by the word "alcohol", e.g., methyl alcohol, ethyl alcohol. Propyl alcohol may be n-propyl alcohol or isopropyl alcohol, depending on whether the hydroxyl group is bonded to the end or middle carbon on the straight propane chain. As described under systematic naming, if another group on the molecule takes priority, the alcohol moiety is often indicated using the "hydroxy-" prefix.

Alcohols are then classified into primary, secondary (sec-, s-), and tertiary (tert-, t-), based upon the number of carbon atoms connected to the carbon atom that bears the hydroxyl functional group. (The respective numeric shorthands 1°, 2°, and 3° are also sometimes used in informal settings.) The primary alcohols have general formulas RCH₂OH. The simplest primary alcohol is methanol (CH₃OH), for which R=H, and the next is ethanol, for which R=CH₃, the methyl group. Secondary alcohols are those of the form RR'CHOH, the simplest of which is 2-propanol (R=R'=CH₃). For the tertiary alcohols the general form is RR'R"COH. The simplest example is tert-butanol (2-methylpropan-2-ol), for which each of R, R', and R" is CH₃. In these shorthands, R, R', and R" represent substituents, alkyl or other attached, generally organic groups.

In archaic nomenclature, alcohols can be named as derivatives of methanol using "-carbinol" as the ending. For instance, (CH₃)₃COH can be named trimethylcarbinol.

Type	Formula	IUPAC Name	Common name
Monohydric alcohols	CH3OH	Methanol	Wood alcohol
	C2H5OH	Ethanol	Alcohol
	C3H7OH	Propan-2-ol	Isopropyl alcohol, Rubbing alcohol
	C4H9OH	Butan-1-ol	Butanol, Butyl alcohol
	C5H11OH	Pentan-1-ol	Pentanol, Amyl alcohol
	C16H33OH	Hexadecan-1-ol	Cetyl alcohol
Polyhydric alcohols	C2H4(OH)2	Ethane-1,2-diol	Ethylene glycol
	C3H6(OH)2	Propane-1,2-diol	Propylene glycol
	C3H5(OH)3	Propane-1,2,3-triol	Glycerol
	C4H6(OH)4	Butane-1,2,3,4-tetraol	Erythritol, Threitol
	C5H7(OH)5	Pentane-1,2,3,4,5-pentol	Xylitol
	C6H8(OH)6	hexane-1,2,3,4,5,6-hexol	Mannitol, Sorbitol
	C7H9(OH)7	Heptane-1,2,3,4,5,6,7-heptol	Volemitol
Unsaturated aliphatic alcohols	C3H5OH	Prop-2-ene-1-ol	Allyl alcohol
	C10H17OH	3,7-Dimethylocta-2,6-dien-1-ol	Geraniol
	C3H3OH	Prop-2-yn-1-ol	Propargyl alcohol
Alicyclic alcohols	C6H6(OH)6	Cyclohexane-1,2,3,4,5,6-hexol	Inositol
	C10H19OH	5-Methyl-2-(propan-2-yl)cyclohexan-1-ol	Menthol

Applications

Total recorded alcohol per capita consumption (15+), in litres of pure ethanol

Alcohols have a long history of myriad uses. For simple mono-alcohols, which is the focus on this article, the following are most important industrial alcohols:

• methanol, mainly for the production of formaldehyde and as a fuel additive
• ethanol, mainly for alcoholic beverages, fuel additive, solvent
• 1-propanol, 1-butanol, and isobutyl alcohol for use as a solvent and precursor to solvents
• C6–C11 alcohols used for plasticizers, e.g. in polyvinylchloride
• fatty alcohol (C12–C18), precursors to detergents

Methanol is the most common industrial alcohol, with about 12 million tons/y produced in 1980. The combined capacity of the other alcohols is about the same, distributed roughly equally.

Toxicity

Main articles: Ethanol and Methanol

With respect to acute toxicity, simple alcohols have low acute toxicities. Doses of several milliliters are tolerated. For pentanols, hexanols, octanols and longer alcohols, LD50 range from 2–5 g/kg (rats, oral). Methanol and ethanol are less acutely toxic. All alcohols are mild skin irritants.

The metabolism of methanol (and ethylene glycol) is affected by the presence of ethanol, which has a higher affinity for liver alcohol dehydrogenase. In this way methanol will be excreted intact in urine.

Physical properties

In general, the hydroxyl group makes alcohols polar. Those groups can form hydrogen bonds to one another and to most other compounds. Owing to the presence of the polar OH alcohols are more water-soluble than simple hydrocarbons. Methanol, ethanol, and propanol are miscible in water. Butanol, with a four-carbon chain, is moderately soluble.

Because of hydrogen bonding, alcohols tend to have higher boiling points than comparable hydrocarbons and ethers. The boiling point of the alcohol ethanol is 78.29 °C, compared to 69 °C for the hydrocarbon hexane, and 34.6 °C for diethyl ether.

Occurrence in nature

Simple alcohols are found widely in nature. Ethanol is the most prominent because it is the product of fermentation, a major energy-producing pathway. Other simple alcohols, chiefly fusel alcohols, are formed in only trace amounts. More complex alcohols however are pervasive, as manifested in sugars, some amino acids, and fatty acids.

Production

Ziegler and oxo processes

In the Ziegler process, linear alcohols are produced from ethylene and triethylaluminium followed by oxidation and hydrolysis. An idealized synthesis of 1-octanol is shown:

Al(C₂H₅)₃ + 9 C₂H₄ → Al(C₈H₁₇)₃

Al(C₈H₁₇)₃ + 3 O + 3 H₂O → 3 HOC₈H₁₇ + Al(OH)₃

The process generates a range of alcohols that are separated by distillation.

Many higher alcohols are produced by hydroformylation of alkenes followed by hydrogenation. When applied to a terminal alkene, as is common, one typically obtains a linear alcohol:

RCH=CH₂ + H₂ + CO → RCH₂CH₂CHO

RCH₂CH₂CHO + 3 H₂ → RCH₂CH₂CH₂OH

Such processes give fatty alcohols, which are useful for detergents.

Hydration reactions

Some low molecular weight alcohols of industrial importance are produced by the addition of water to alkenes. Ethanol, isopropanol, 2-butanol, and tert-butanol are produced by this general method. Two implementations are employed, the direct and indirect methods. The direct method avoids the formation of stable intermediates, typically using acid catalysts. In the indirect method, the alkene is converted to the sulfate ester, which is subsequently hydrolyzed. The direct hydration using ethylene (ethylene hydration) or other alkenes from cracking of fractions of distilled crude oil.

Hydration is also used industrially to produce the diol ethylene glycol from ethylene oxide.

Biological routes

Ethanol is obtained by fermentation using glucose produced from sugar from the hydrolysis of starch, in the presence of yeast and temperature of less than 37 °C to produce ethanol. For instance, such a process might proceed by the conversion of sucrose by the enzyme invertase into glucose and fructose, then the conversion of glucose by the enzyme complex zymase into ethanol and carbon dioxide.

Several species of the benign bacteria in the intestine use fermentation as a form of anaerobic metabolism. This metabolic reaction produces ethanol as a waste product. Thus, human bodies contain some quantity of alcohol endogenously produced by these bacteria. In rare cases, this can be sufficient to cause "auto-brewery syndrome" in which intoxicating quantities of alcohol are produced.

Like ethanol, butanol can be produced by fermentation processes. Saccharomyces yeast are known to produce these higher alcohols at temperatures above 75 °F (24 °C). The bacterium Clostridium acetobutylicum can feed on cellulose to produce butanol on an industrial scale.

Substitution

Primary alkyl halides react with aqueous NaOH or KOH mainly to primary alcohols in nucleophilic aliphatic substitution. (Secondary and especially tertiary alkyl halides will give the elimination (alkene) product instead). Grignard reagents react with carbonyl groups to secondary and tertiary alcohols. Related reactions are the Barbier reaction and the Nozaki-Hiyama reaction.

Reduction

Aldehydes or ketones are reduced with sodium borohydride or lithium aluminium hydride (after an acidic workup). Another reduction by aluminiumisopropylates is the Meerwein-Ponndorf-Verley reduction. Noyori asymmetric hydrogenation is the asymmetric reduction of β-keto-esters.

Hydrolysis

Alkenes engage in an acid catalysed hydration reaction using concentrated sulfuric acid as a catalyst that gives usually secondary or tertiary alcohols. The hydroboration-oxidation and oxymercuration-reduction of alkenes are more reliable in organic synthesis. Alkenes react with NBS and water in halohydrin formation reaction. Amines can be converted to diazonium salts, which are then hydrolyzed.

The formation of a secondary alcohol via reduction and hydration is shown:

Reactions

Deprotonation

With aqueous pK_a values of around 16–19, they are, in general, slightly weaker acids than water. With strong bases such as sodium hydride or sodium they form salts called alkoxides, with the general formula RO⁻ M⁺.

2 R−OH + 2 NaH → 2 R−O⁻Na⁺ + 2 H₂

2 R−OH + 2 Na → 2 R−O⁻Na⁺ + H₂

The acidity of alcohols is strongly affected by solvation. In the gas phase, alcohols are more acidic than in water. In DMSO, alcohols (and water) have a pK_a of around 29–32. As a consequence, alkoxides (and hydroxide) are powerful bases and nucleophiles (e.g., for the Williamson ether synthesis) in this solvent. In particular, RO^– or HO^– in DMSO can be used to generate significant equilibrium concentrations of acetylide ions through the deprotonation of alkynes (see Favorskii reaction).

Nucleophilic substitution

The OH group is not a good leaving group in nucleophilic substitution reactions, so neutral alcohols do not react in such reactions. However, if the oxygen is first protonated to give R⁻OH+2, the leaving group (water) is much more stable, and the nucleophilic substitution can take place. For instance, tertiary alcohols react with hydrochloric acid to produce tertiary alkyl halides, where the hydroxyl group is replaced by a chlorine atom by unimolecular nucleophilic substitution. If primary or secondary alcohols are to be reacted with hydrochloric acid, an activator such as zinc chloride is needed. In alternative fashion, the conversion may be performed directly using thionyl chloride.

Alcohols may, likewise, be converted to alkyl bromides using hydrobromic acid or phosphorus tribromide, for example:

3 R−OH + PBr₃ → 3 RBr + H₃PO₃

In the Barton-McCombie deoxygenation an alcohol is deoxygenated to an alkane with tributyltin hydride or a trimethylborane-water complex in a radical substitution reaction.

Dehydration

Meanwhile, the oxygen atom has lone pairs of nonbonded electrons that render it weakly basic in the presence of strong acids such as sulfuric acid. For example, with methanol:

Upon treatment with strong acids, alcohols undergo the E1 elimination reaction to produce alkenes. The reaction, in general, obeys Zaitsev's Rule, which states that the most stable (usually the most substituted) alkene is formed. Tertiary alcohols eliminate easily at just above room temperature, but primary alcohols require a higher temperature.

This is a diagram of acid catalysed dehydration of ethanol to produce ethylene:

A more controlled elimination reaction requires the formation of the xanthate ester.

Protonolysis

Tertiary alcohols react with strong acids to generate carbocations. The reaction is related to their dehydration, e.g. isobutylene from tert-butyl alcohol. A special kind of dehydration reaction involves triphenylmethanol and especially its amine-substituted derivatives. When treated with acid, these alcohols lose water to give stable carbocations, which are commercial dyes.

Preparation of crystal violet by protonolysis of the tertiary alcohol.

Esterification

Alcohol and carboxylic acids react in the so-called Fischer esterification. The reaction usually requires a catalyst, such as concentrated sulfuric acid:

R−OH + R'−CO₂H → R'−CO₂R + H₂O

Other types of ester are prepared in a similar manner – for example, tosyl (tosylate) esters are made by reaction of the alcohol with p-toluenesulfonyl chloride in pyridine.

Oxidation

Main article: Alcohol oxidation

Primary alcohols (R−CH₂OH) can be oxidized either to aldehydes (R-CHO) or to carboxylic acids (R−CO₂H). The oxidation of secondary alcohols (R¹R²CH-OH) normally terminates at the ketone (R¹R²C=O) stage. Tertiary alcohols (R¹R²R³C-OH) are resistant to oxidation.

The direct oxidation of primary alcohols to carboxylic acids normally proceeds via the corresponding aldehyde, which is transformed via an aldehyde hydrate (R−CH(OH)₂) by reaction with water before it can be further oxidized to the carboxylic acid.

Mechanism of oxidation of primary alcohols to carboxylic acids via aldehydes and aldehyde hydrates

Reagents useful for the transformation of primary alcohols to aldehydes are normally also suitable for the oxidation of secondary alcohols to ketones. These include Collins reagent and Dess-Martin periodinane. The direct oxidation of primary alcohols to carboxylic acids can be carried out using potassium permanganate or the Jones reagent.