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An aldohexose is a six-carbon aldose: its open-chain reference form has an aldehyde group at C1. Glucose is an example.^[ref]

The unmodified open-chain skeleton has four stereocenters, C2–C5, giving $2^4=16$ stereoisomers, or eight enantiomer pairs. Fixing the C5 hydroxy group on the right leaves $2^3=8$ D forms; D-glucose's right/left/right/right pattern selects one. An aldohexose label therefore specifies less than a particular sugar name, and a molecular formula specifies less still. The existing glucose article checks its chemical atom inventory; monosaccharide ring-chain interconversion follows those same numbered carbon positions into a ring.

An aldopentose is a five-carbon aldose: its open-chain reference form has an aldehyde group at C1. Ribose is an example; deoxyribose is its 2-deoxy derivative.^[ref]

For the unmodified open-chain aldopentose skeleton, count one $\mathrm{CHO}$, three $\mathrm{CHOH}$ and one $\mathrm{C}{\mathrm{H}}_2\mathrm{OH}$ group: ${\mathrm{C}}_5{\mathrm{H}}_{10}{\mathrm{O}}_5$. The three interior carbon positions, C2–C4, are stereocenters. Each allows two configurations, giving $2^3=8$ stereoisomers, grouped into four enantiomer pairs. The unlike chain ends prevent a meso compound identification. D-ribose selects the right/right/right hydroxy group pattern in the Fischer projection; the word aldopentose alone does not select that pattern. Compare the existing ribose and deoxyribose diagrams for the separate question of which oxygen is present.

Arachidonic acid is a twenty-carbon polyunsaturated fatty acid with four cis carbon–carbon double bonds, at positions 5, 8, 11 and 14 when counted from the carboxyl group. Its molecular formula is ${\mathrm{C}}_{20}{\mathrm{H}}_{32}{\mathrm{O}}_2$. The shorthand $20:4n-6$ records twenty carbons, four double bonds and the first double bond six carbons from the methyl end.^[ref]

The indexing conventions describe the same structure from opposite ends: the bond between carbons 14 and 15 from the acid end is the first encountered from the methyl end. The cis geometry also distinguishes this molecule from stereoisomers with the same formula. Composition, double-bond positions and geometry all belong to its chemical identity.

Asymmetric dihydroxylation adds two hydroxyl groups across an alkene while favouring one stereochemical product. In the Sharpless approach, a chiral ligand controls an osmium-based catalytic environment, turning an otherwise face-symmetric reaction into an enantioselective transformation.^[ref]

The new oxygen-bearing centres are formed in a correlated addition. Substrate geometry and the ligand's handedness jointly determine which stereoisomer is favoured.

cis-Resveratrol is the resveratrol stereoisomer with the two aryl groups on the same side of the central double bond, corresponding to the $Z$ configuration. It has the same neutral molecular formula, ${\mathrm{C}}_{14}{\mathrm{H}}_{12}{\mathrm{O}}_3$, and formula-based molar mass as trans-Resveratrol, but a different spatial arrangement.^[ref]

The isomers need different optical response factors. Brent C. Trela and Andrew L. Waterhouse measured an ethanol absorption maximum at $288\mathrm{nm}$ with molar absorption coefficient $12600\mathrm{L}\mathrm{mo}{\mathrm{l}}^{-1}\mathrm{c}{\mathrm{m}}^{-1}$ for the cis form; their stability tests also depended on light exposure and pH.^[ref]

At that maximum, an original $10\mu \mathrm{mol}{\mathrm{L}}^{-1}$ solution in a $1\mathrm{cm}$ path has ideal absorbanceThis is lower than the trans-isomer's corresponding example at its own maximum, but the two maxima occur at different wavelengths. Dividing their peak coefficients does not supply the cis/trans response ratio at one common detector wavelength.

For a mixture at a chosen wavelength $\lambda$, an additive Beer-Lambert law model isOne reading generally cannot identify both concentrations. Two wavelengths help only if their response rows are independent and the coefficients are appropriate to the solution. Multivariate calibration makes that requirement explicit; physical separation by chromatography supplies another route. Neither equal molecular formulas nor a single colour measurement establishes isomeric purity.

Diastereomers are different stereoisomers that are not enantiomers. The meso compound form of tartaric acid is a diastereomer of either member of its enantiomer pair.

Enantiomers are a pair of nonsuperposable mirror-image molecules. The D and L configurations of alanine are an example; glycine has no such pair because its amino acid alpha carbon carries two identical hydrogen chemical atoms. ^[ref]

The word names a relation between two stereoisomers. Merely finding two different spatial arrangements does not make them enantiomers: arrangements that are different but not mirror partners are diastereomers.

Two epimers are diastereomers with opposite configurations at exactly one of the two or more tetrahedral stereocenters in their molecules. Their connectivity is the same, and configurations at the other centers agree. The definition is more specific than simply calling two compounds stereoisomers.^[ref]

D-glucose and D-mannose illustrate the relationship: their configurations differ at carbon 2 while the other corresponding stereocenters agree. This local change can alter recognition by enzymes without changing the elemental composition or the carbon-chain connectivity.

For a hypothetical molecule with corresponding stereocenters 2 and 3, the configurations $(2R,3R)$ and $(2S,3R)$ differ at one center and can form an epimeric pair. Changing both to $(2S,3S)$ is a different comparison: it does not satisfy the one-center condition. These labels assume the same molecular connectivity and consistently assigned centers.

A molecule with only one stereocenter does not produce an epimer pair merely by reversing that center: its two configurations are enantiomers, whereas the epimer definition requires a diastereomeric relationship. Epimerization names a process that interconverts an epimeric pair; it does not by itself specify the reaction mechanism, rate or equilibrium ratio.

A stereoisomer distinguished by the spatial arrangement of connected groups, such as cis versus trans ligands.

Hydroxylysine is a hydroxylated derivative of the amino acid lysine. In the important collagen-associated form, a hydroxyl group is attached at carbon 5 of the side chain. Free 5-hydroxylysine has formula ${\mathrm{C}}_6{\mathrm{H}}_{14}{\mathrm{N}}_2{\mathrm{O}}_3$, and its connectivity can be writtenThis formula specifies the arrangement of the groups but does not by itself distinguish the possible stereoisomers. ^[ref]

In collagen, hydroxylysine occurs as a modified amino acid residue within a protein. A concrete example is the sulfilimine bond linking hydroxylysine-211 of one Collagen IV unit to methionine-93 of another. Mass spectrometry and nuclear magnetic resonance identified that sulfur–nitrogen connection.^[ref] The example shows why a modified side chain matters: changing a particular residue changes the chemistry available for joining protein units. Free hydroxylysine and a residue incorporated into collagen must nevertheless be distinguished, because incorporation places its backbone in peptide bonds.

Linkage isomerism occurs when complexes have the same composition but an ambidentate ligand attaches through different atoms. N-bound and O-bound nitrite provide the classical example. This is a difference in attachment connectivity, rather than the different spatial arrangements of unchanged connectivity in stereoisomers.

A meso compound is an achiral molecule despite having stereocenters. Tartaric acid, $\mathrm{HOOC}-\mathrm{CH}(\mathrm{OH})-\mathrm{CH}(\mathrm{OH})-\mathrm{COOH}$, has two tetrahedral carbon stereocenters. Its $(2R,3R)$ and $(2S,3S)$ forms are enantiomers, but $(2R,3S)$ and $(2S,3R)$ name the same meso form after equivalent ends are identified. A symmetric spatial arrangement has a mirror plane exchanging its two halves. Thus there are three stereoisomers, not four.^[ref]

Opposite R and S configurations alone do not guarantee a meso compound: the rest of the molecule must permit mirror superposition. Likewise, a meso compound is one achiral chemical compound, whereas a racemate is a mixture of two chiral molecule populations. Both can give zero optical rotation for different reasons.

There are two, two and four stereoisomers, respectively; all eight individual stereoisomers are chiral. The drawings below give the mirror pairs. Solid and hashed wedges distinguish opposite faces; ordinary changes between conformers are not counted again.

Unlike the usual rapidly inverting trialkylamine, a pyramidal phosphine can retain a phosphorus configuration on an ordinary observational timescale; its two phosphorus configurations must therefore be included.

triethylamine removes an alpha proton from nitromethane to generate a nitronate population. Its carbon attacks the cyclic ketone carbonyl of E, forming a new C–CH2NO2 bond while the C=O pi pair moves onto oxygen. protonation by triethylammonium or another proton donor gives the tertiary alcohol F and regenerates base. This is a Henry reaction, also called a nitroaldol reaction: the former ketone carbon now bears both OH and CH2NO2.

The nitro group remains attached to its original nitromethane carbon; attack through oxygen would give a different connectivity. The methyl acetal and the original alcohol substituents need not be cleaved or displaced. This addition produces the isolated connectivity without requiring dehydration to a nitroalkene. The stated complex mixture is compatible with competing additions or stereoisomers, but the scheme supplies no basis for claiming F is the unique or kinetically dominant product. Only its formation is being explained.

Treat each semiquinonate ligand as a symmetric O,O chelate, with the free radical delocalized over the dioxolene framework. The ideal octahedral donor-connectivity structures are one trans form and two mirror-related cis forms, giving three stereoisomers. Trans refers to the two pyridine N donors, not to the two O atoms of a chelate, which must remain adjacent.

In the diagram, coloured curves join the two O donors belonging to one ligand. For an unambiguous coordinate specification, the trans form has Py at $+z,-z$, with chelate pairs $(+x,+y)$ and $(-x,-y)$. A cis pair has Py at $+z,+x$, with chelates $(-z,+y)$ and $(-x,-y)$; reflecting $y\mapsto -y$ gives the other cis form. Proper rotations cannot superpose those two cis arrangements. Ring conformations and pyridine rotations are not extra donor-connectivity isomers.

Treat the two donors of 2-Picolylamine as distinct: $P$ denotes pyridyl N and $A$ denotes amino N. Each ligand must join two adjacent octahedral positions because its five-membered chelate ring cannot span a trans pair. The three $P$ sites can either occupy a triangular face, giving a facial isomer, or a meridian containing a trans pair, giving a meridional isomer. Each geometry has a pair of nonsuperposable mirror images. Therefore there are four configurational stereoisomers: fac-$\Delta$, fac-$\Lambda$, mer-$\Delta$ and mer-$\Lambda$. Rapid ring puckering or amine inversion does not introduce additional persistent configurations in this count.

The mer geometry is the reasonable steric prediction for the more stable form. It spreads the bulky pyridyl rings farther apart, allowing one pyridyl–pyridyl trans relationship, whereas the fac geometry groups all three pyridyl donors on one face. This is a qualitative preference, not a proof independent of counterions and solvent: hydrogen bonding and packing can favor the alternative. Primary structures of different salts contain both geometries, so neither should be claimed impossible.^[ref]

The mirror-image facial complex and the meridional complex provide the two requested stereoisomers. Let O, N and P denote the three attached atoms of the same unsymmetrical chelate. The original has these atoms on one octahedral face and the three chlorides on the opposite face. Its reflected facial arrangement is an enantiomer: the O,N,P donor sequence reverses handedness and cannot be restored by a proper rotation. In the meridional arrangement, O and P are trans, and the two adjacent chelate links O–N and N–P remain cis. The following original coordination diagrams specify the ligand positions; lines joining donor labels represent the ligand's connectivity, with its organic backbone suppressed.

The meridional structure is a geometric isomer, not the reflected facial structure. Distorting chelate rings without changing these donor positions does not by itself supply a new coordination stereoisomer.

Secondary amines normally favor non-geminal disubstitution, putting the second amino substituent on a different phosphorus. The first installed $\mathrm{N}{\mathrm{R}}_2$ group donates electron density to the P–N framework and deactivates its own phosphorus toward further attack. It is also bulkier than an initially installed primary-amino group. Crucially, $\mathrm{P}-\mathrm{N}{\mathrm{R}}_2$ has no N–H proton, so the proton-abstraction/chloride-elimination pathway that can direct a primary amine geminally is unavailable. Direct attack at a less-deactivated $\mathrm{PC}{\mathrm{l}}_2$ site is favored. The resulting non-geminal products can have cis or trans relative orientations around the ring; non-geminal substitution alone does not select one of these stereoisomers. These are useful trends, with known substituent-dependent exceptions in experimentally characterized mixed derivatives.^[ref]

Stereoisomers have the same chemical bond connectivity but different spatial arrangements. A mirror pair of distinct stereoisomers comprises enantiomers; diastereomers have no mirror-pair relation.

Preferential formation of one stereoisomer over another.