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mathematics

Ether

Ether is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Ether rather than just read about it. In short: In organic chemistry, ethers are a class of compounds that contain an ether group, a single oxygen atom bonded to two separate carbon atoms, each part of an organyl group (e.g., alkyl or aryl). They have the general formula R−O−R′, where R and R′ represent the organyl groups.

Ether — main illustration
Ether — illustration

Key takeaways

  • Ether belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Ether to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Ether from memory before moving on to harder problems.

Reference excerpt

In organic chemistry, ethers are a class of compounds that contain an ether group, a single oxygen atom bonded to two separate carbon atoms, each part of an organyl group (e.g., alkyl or aryl). They have the general formula R−O−R′, where R and R′ represent the organyl groups. Ethers can again be classified into two varieties: if the organyl groups are the same on both sides of the oxygen atom, then it is a simple or symmetrical ether, whereas if they are different, the ethers are called mixed or unsymmetrical ethers. A typical example of the first group is the solvent and anaesthetic diethyl ether, commonly referred to simply as "ether" (CH3−CH2−O−CH2−CH3). Ethers are common in organic chemistry and even more prevalent in biochemistry, as they are common linkages in carbohydrates and lignin.

History Ethers were first isolated by Pierre-François-Guillaume Boullay and his son in the early 19th century.

Structure and bonding Ethers feature bent C−O−C linkages. In dimethyl ether, the bond angle is 111° and C–O distances are 141 pm. The barrier to rotation about the C–O bonds is low. The bonding of oxygen in ethers, alcohols, and water is similar. In the language of valence bond theory, the hybridization at oxygen is sp3. Ethers can be symmetrical of the type ROR or unsymmetrical of the type ROR'. Examples of the former are dimethyl ether, diethyl ether, dipropyl ether etc. Illustrative unsymmetrical ethers are anisole (methoxybenzene) and dimethoxyethane.

Vinyl- and acetylenic ethers Vinyl- and acetylenic ethers are far less common than alkyl or aryl ethers. Vinylethers, often called enol ethers, are important intermediates in organic synthesis. Acetylenic ethers are especially rare. Di-tert-butoxyacetylene is the most common example of this rare class of compounds.

Nomenclature In the IUPAC Nomenclature system, ethers are named using the general formula "alkoxyalkane", for example CH3–CH2–O–CH3 is methoxyethane. If the ether is part of a more-complex molecule, it is described as an alkoxy substituent, so –OCH3 would be considered a "methoxy-" group. The simpler alkyl radical is written in front, so CH3–O–CH2CH3 would be given as methoxy(CH3O)ethane(CH2CH3).

Trivial names IUPAC rules are often not followed for simple ethers. The trivial names for simple ethers (i.e., those with none or few other functional groups) are a composite of the two substituents followed by "ether". For example, ethyl methyl ether (CH3OC2H5), diphenylether (C6H5OC6H5). As for other organic compounds, very common ethers acquired names before rules for nomenclature were formalized. Diethyl ether is simply called ether, but was once called sweet oil of vitriol. Methyl phenyl ether is anisole, because it was originally found in aniseed. The aromatic ethers include furans. Acetals (α-alkoxy ethers R–CH(–OR)–O–R) are another class of ethers with characteristic properties.

Polyethers Polyethers are generally polymers containing ether linkages in their main chain. The term polyol generally refers to polyether polyols with one or more functional end-groups such as a hydroxyl group. The term "oxide" or other terms are used for high molar mass polymer when end-groups no longer affect polymer properties. Crown ethers are cyclic polyethers. Some toxins produced by dinoflagellates such as brevetoxin and ciguatoxin are extremely large and are known as cyclic or ladder polyethers.

The phenyl ether polymers are a class of aromatic polyethers containing aromatic cycles in their main chain: polyphenyl ether (PPE) and poly(p-phenylene oxide) (PPO).

Related compounds Many classes of compounds with C–O–C linkages are not considered ethers: Esters (R–C(=O)–O–R′), hemiacetals (R–CH(–OH)–O–R′), carboxylic acid anhydrides (RC(=O)–O–C(=O)R′). There are compounds which, instead of C in the C−O−C linkage, contain heavier group 14 chemical elements (e.g., Si, Ge, Sn, Pb). Such compounds are considered ethers as well. Examples of such ethers are silyl enol ethers R3Si−O−CR=CR2 (containing the Si−O−C linkage), disiloxane H3Si−O−SiH3 (the other name of this compound is disilyl ether, containing the Si−O−Si linkage) and stannoxanes R3Sn−O−SnR3 (containing the Sn−O−Sn linkage).

Physical properties Ethers have boiling points similar to those of the analogous alkanes. Simple ethers are generally colorless.

Reactions

The C-O bonds that comprise simple ethers are strong. They are unreactive toward all but the strongest bases. Although generally of low chemical reactivity, they are more reactive than alkanes. Specialized ethers such as epoxides, ketals, and acetals are unrepresentative classes of ethers and are discussed in separate articles. Important reactions are listed below.

Cleavage

Although ethers resist hydrolysis, they are cleaved by hydrobromic acid and hydroiodic acid. Hydrogen chloride cleaves ethers only slowly. Methyl ethers typically afford methyl halides:

ROCH3 + HBr → CH3Br + ROH These reactions proceed via onium intermediates, i.e. [RO(H)CH3]+Br−. Some ethers undergo rapid cleavage with boron tribromide (even aluminium chloride is used in some cases) to give the alkyl halide. Depending on the substituents, some ethers can be cleaved with a variety of reagents, e.g. strong base. Despite these difficulties the chemical paper pulping processes are based on cleavage of ether bonds in the lignin.

Peroxide formation When stored in the presence of air or oxygen, ethers tend to form explosive peroxides, such as diethyl ether hydroperoxide. The reaction is accelerated by light, metal catalysts, and aldehydes. In addition to avoiding storage conditions likely to form peroxides, it is recommended, when an ether is used as a solvent, not to distill it to dryness, as any peroxides that may have formed, being less volatile than the original ether, will become concentrated in the last few drops of liquid. The presence of peroxide in old samples of ethers may be detected by shaking them with freshly prepared solution of a ferrous sulfate followed by addition of KSCN. Appearance of blood red color indicates presence of peroxides. The dangerous properties of ether peroxides are the reason that diethyl ether and other peroxide forming ethers like tetrahydrofuran (THF) or ethylene glycol dimethyl ether (1,2-dimethoxyethane) are avoided in industrial processes.

Lewis bases

… excerpt ends here. Continue reading the full article.

Illustrations

Ether: The general structure of an ether. R and R' represent most organyl substituents.
The general structure of an ether. R and R' represent most organyl substituents.
Ether: Structure of the polymeric diethyl ether peroxide[citation needed]
Structure of the polymeric diethyl ether peroxide[citation needed]
Ether: Structure of VCl3(thf)3.[8].mw-parser-output .legend{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .legend-color{display:inline-block;min-width:1.25em;height:1.25em;line-height:1.25;margin:1px 0;text-align:center;border:1px solid black;background-color:transparent;color:black}.mw-parser-output .legend-text{}  Vanadium, V  Chlorine, Cl  Carbon, C  Hydrogen, H  Oxygen, O
Structure of VCl3(thf)3.[8].mw-parser-output .legend{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .legend-color{display:inline-block;min-width:1.25em;height:1.25em;line-height:1.25;margin:1px 0;text-align:center;border:1px solid black;background-color:transparent;color:black}.mw-parser-output .legend-text{}  Vanadium, V  Chlorine, Cl  Carbon, C  Hydrogen, H  Oxygen, O
Ether: 2 R–OH → R–O–R + H2O
2 R–OH → R–O–R + H2O
Ether illustration

Worked examples

Example 1 — a first encounter with Ether

Start with the simplest possible case. Write down what Ether claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Ether before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Ether ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Ether

In research
Ether appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Ether in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Ether is common in secondary-school and first-year university syllabi. It links to neighbouring topics Ethers, Functional groups, Impression material, so understanding it makes those chapters shorter.
In everyday life
Look for Ether outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Ether in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Ether means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Ether out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Ether in simple terms?

In organic chemistry, ethers are a class of compounds that contain an ether group, a single oxygen atom bonded to two separate carbon atoms, each part of an organyl group (e.g., alkyl or aryl). They have the general formula R−O−R′, where R and R′ represent the organyl groups.

Why does Ether matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Ether?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Ether.

Tags

  • Ethers
  • Functional groups
  • Impression material

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