Structural Isomer
   HOME

TheInfoList



OR:

In
chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
, a structural isomer (or constitutional isomer in the
IUPAC The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
nomenclature) of a
compound Compound may refer to: Architecture and built environments * Compound (enclosure), a cluster of buildings having a shared purpose, usually inside a fence or wall ** Compound (fortification), a version of the above fortified with defensive struc ...
is another compound whose molecule has the same number of atoms of each element, but with logically distinct bonds between them. The term metamer was formerly used for the same concept. For example,
butanol Butanol (also called butyl alcohol) is a four-carbon alcohol with a formula of C4 H9 O H, which occurs in five isomeric structures (four structural isomers), from a straight-chain primary alcohol to a branched-chain tertiary alcohol; all are a b ...
,
methyl propyl ether Methoxypropane, or methyl propyl ether, is an ether once used as a general anaesthetic. It is a clear colorless flammable liquid with a boiling point of 38.8 °C.''Merck Index'', 11th edition, 6031. Marketed under the trade names Metopryl an ...
, and
diethyl ether Diethyl ether, or simply ether, is an organic compound in the ether class with the formula , sometimes abbreviated as (see Pseudoelement symbols). It is a colourless, highly volatile, sweet-smelling ("ethereal odour"), extremely flammable liq ...
have the same
molecular formula In chemistry, a chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, ...
but are three distinct structural isomers. The concept applies also to polyatomic ions with the same total charge. A classical example is the
cyanate Cyanate is an anion with the structural formula , usually written . It also refers to any salt containing it, such as ammonium cyanate. It is an isomer of the much less stable fulminate anion .William R. Martin and David W. Ball (2019): "Sma ...
ion and the
fulminate Fulminates are chemical compounds which include the fulminate ion (). The fulminate ion is a pseudohalic ion because its charge and reactivity are similar to those of the halogens. Due to the instability of the ion, fulminate salts are frictio ...
ion . It is also extended to ionic compounds, so that (for example)
ammonium cyanate Ammonium cyanate is an inorganic compound with the formula . It is a colorless, solid salt. Structure and reactions The structure of this salt was verified by X-ray crystallography. The respective C–O and C–N distances are 1.174(8) and 1.1 ...
and
urea Urea, also known as carbamide, is an organic compound with chemical formula . This amide has two amino groups (–) joined by a carbonyl functional group (–C(=O)–). It is thus the simplest amide of carbamic acid. Urea serves an important r ...
are considered structural isomers,William F. Bynum, E. Janet Browne, Roy Porter (2014): ''Dictionary of the History of Science''. 530 pages. and so are methylammonium formate and
ammonium acetate Ammonium acetate, also known as spirit of Mindererus in aqueous solution, is a chemical compound with the formula NH4CH3CO2. It is a white, hygroscopic solid and can be derived from the reaction of ammonia and acetic acid. It is available commerci ...
. Structural isomerism is the most radical type of
isomer In chemistry, isomers are molecules or polyatomic ions with identical molecular formulae – that is, same number of atoms of each element – but distinct arrangements of atoms in space. Isomerism is existence or possibility of isomers. Iso ...
ism. It is opposed to
stereoisomer In stereochemistry, stereoisomerism, or spatial isomerism, is a form of isomerism in which molecules have the same molecular formula and sequence of bonded atoms (constitution), but differ in the three-dimensional orientations of their atoms in ...
ism, in which the atoms and bonding scheme are the same, but only the relative spatial arrangement of the atoms is different. Examples of the latter are the
enantiomer In chemistry, an enantiomer ( /ɪˈnænti.əmər, ɛ-, -oʊ-/ ''ih-NAN-tee-ə-mər''; from Ancient Greek ἐνάντιος ''(enántios)'' 'opposite', and μέρος ''(méros)'' 'part') – also called optical isomer, antipode, or optical ant ...
s, whose molecules are mirror images of each other, and the ''cis'' and ''trans'' versions of 2-butene. Among the structural isomers, one can distinguish several classes including skeletal isomers, positional isomers (or regioisomers), functional isomers, tautomers, and structural topoisomers.


Skeletal isomerism

A skeletal isomer of a compound is a structural isomer that differs from it in the atoms and bonds that are considered to comprise the "skeleton" of the molecule. For
organic compound In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen or carbon-carbon bonds. Due to carbon's ability to catenate (form chains with other carbon atoms), millions of organic compounds are known. The ...
s, such as
alkanes In organic chemistry, an alkane, or paraffin (a historical trivial name that also has other meanings), is an acyclic saturated hydrocarbon. In other words, an alkane consists of hydrogen and carbon atoms arranged in a tree structure in whi ...
, that usually means the carbon atoms and the bonds between them. For example, there are three skeletal isomers of pentane: ''n''-pentane (often called simply "pentane"),
isopentane Isopentane, also called methylbutane or 2-methylbutane, is a branched-chain saturated hydrocarbon (an alkane) with five carbon atoms, with formula or . Isopentane is an extremely volatile and extremely flammable liquid at room temperature and ...
(2-methylbutane) and neopentane (dimethylpropane). If the skeleton is acyclic, as in the above example, one may use the term chain isomerism.


Position isomerism (regioisomerism)

Position isomers (also positional isomers or regioisomers) are structural isomers that can be viewed as differing only on the position of a
functional group In organic chemistry, a functional group is a substituent or moiety in a molecule that causes the molecule's characteristic chemical reactions. The same functional group will undergo the same or similar chemical reactions regardless of the rest ...
,
substituent A substituent is one or a group of atoms that replaces (one or more) atoms, thereby becoming a moiety in the resultant (new) molecule. (In organic chemistry and biochemistry, the terms ''substituent'' and ''functional group'', as well as ''side ...
, or some other feature on a "parent" structure. For example, replacing one of the 12 hydrogen atoms –H by a
hydroxyl In chemistry, a hydroxy or hydroxyl group is a functional group with the chemical formula and composed of one oxygen atom covalently bonded to one hydrogen atom. In organic chemistry, alcohols and carboxylic acids contain one or more hydroxy ...
group –OH on the ''n''-pentane parent molecule can give any of three different position isomers:


Functional isomerism

Functional isomers are structural isomers which have different
functional group In organic chemistry, a functional group is a substituent or moiety in a molecule that causes the molecule's characteristic chemical reactions. The same functional group will undergo the same or similar chemical reactions regardless of the rest ...
s, resulting in significantly different chemical and physical properties. An example is the pair
propanal Propionaldehyde or propanal is the organic compound with the formula CH3CH2CHO. It is the 3-carbon aldehyde. It is a colourless, flammable liquid with a slightly fruity odour. It is produced on a large scale industrially. Production Propionalde ...
H3C–CH2–C(=O)-H and
acetone Acetone (2-propanone or dimethyl ketone), is an organic compound with the formula . It is the simplest and smallest ketone (). It is a colorless, highly volatile and flammable liquid with a characteristic pungent odour. Acetone is miscib ...
H3C–C(=O)–CH3: the first has a –C(=O)H functional group, which makes it an
aldehyde In organic chemistry, an aldehyde () is an organic compound containing a functional group with the structure . The functional group itself (without the "R" side chain) can be referred to as an aldehyde but can also be classified as a formyl grou ...
, whereas the second has a C–C(=O)–C group, that makes it a
ketone In organic chemistry, a ketone is a functional group with the structure R–C(=O)–R', where R and R' can be a variety of carbon-containing substituents. Ketones contain a carbonyl group –C(=O)– (which contains a carbon-oxygen double bo ...
. Another example is the pair
ethanol Ethanol (abbr. EtOH; also called ethyl alcohol, grain alcohol, drinking alcohol, or simply alcohol) is an organic compound. It is an Alcohol (chemistry), alcohol with the chemical formula . Its formula can be also written as or (an ethyl ...
H3C–CH2–OH (an alcohol) and
dimethyl ether Dimethyl ether (DME; also known as methoxymethane) is the organic compound with the formula CH3OCH3, (sometimes ambiguously simplified to C2H6O as it is an isomer of ethanol). The simplest ether, it is a colorless gas that is a useful precursor ...
H3C–O–CH2H (an
ether In organic chemistry, ethers are a class of compounds that contain an ether group—an oxygen atom connected to two alkyl or aryl groups. They have the general formula , where R and R′ represent the alkyl or aryl groups. Ethers can again be c ...
). In contrast, 1-propanol and
2-propanol Isopropyl alcohol (IUPAC name propan-2-ol and also called isopropanol or 2-propanol) is a colorless, flammable organic compound with a pungent alcoholic odor. As an isopropyl group linked to a hydroxyl group (chemical formula ) it is the sim ...
are structural isomers, but not functional isomers, since they have the same significant functional group (the
hydroxyl In chemistry, a hydroxy or hydroxyl group is a functional group with the chemical formula and composed of one oxygen atom covalently bonded to one hydrogen atom. In organic chemistry, alcohols and carboxylic acids contain one or more hydroxy ...
–OH) and are both alcohols. Besides the different chemistry, functional isomers typically have very different infrared spectra. The infrared spectrum is largely determined by the vibration modes of the molecule, and functional groups like hydroxyl and esters have very different vibration modes. Thus 1-propanol and 2-propanol have relatively similar infrared spectra because of the hydroxyl group, which are fairly different from that of methyl ethyl ether.


Structural isotopomers

In chemistry, one usually ignores distinctions between
isotope Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numbers) ...
s of the same element. However, in some situations (for instance in Raman,
NMR Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with ...
, or
microwave spectroscopy Microwave spectroscopy is the spectroscopy method that employs microwaves, i.e. electromagnetic radiation at GHz frequencies, for the study of matter. History The ammonia molecule NH3 is shaped like a pyramid 0.38 Å in height, with an equilatera ...
) one may treat different isotopes of the same element as different elements. In the second case, two molecules with the same number of atoms of each isotope but distinct bonding schemes are said to be structural isotopomers. Thus, for example,
ethene Ethylene (IUPAC name: ethene) is a hydrocarbon which has the formula or . It is a colourless, flammable gas with a faint "sweet and musky" odour when pure. It is the simplest alkene (a hydrocarbon with carbon-carbon double bonds). Ethylene i ...
would have no structural isomers under the first interpretation; but replacing two of the hydrogen atoms (1H) by
deuterium Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two Stable isotope ratio, stable isotopes of hydrogen (the other being Hydrogen atom, protium, or hydrogen-1). The atomic nucleus, nucleus of a deuterium ato ...
atoms (2H) may yield any of two structural isotopomers (1,1-dideuteroethene and 1,2-dideuteroethene), if both carbon atoms are the same isotope. If, in addition, the two carbons are different isotopes (say, 12C and 13C), there would be three distinct structural isotopomers, since 1-13C-1,1-dideuteroethene would be different from 1-13C-2,2-dideuteroethene.) And, in both cases, the 1,2-dideutero structural isotopomer would occur as two stereo isotopoomers, ''cis'' and ''trans''.


Structural equivalence and symmetry


Structural equivalence

Two molecules (including polyatomic ions) A and B have the same structure if each atom of A can be paired with an atom of B of the same element, in a one-to-one way, so that for every bond in A there is a bond in B, of the same type, between corresponding atoms; and vice versa. This requirement applies also complex bonds that involve three or more atoms, such as the
delocalized bond In theoretical chemistry, a conjugated system is a system of connected p-orbitals with delocalized electrons in a molecule, which in general lowers the overall energy of the molecule and increases stability. It is conventionally represented a ...
ing in the benzene molecule and other aromatic compounds. Depending on the context, one may require that each atom be paired with an atom of the same isotope, not just of the same element. Two molecules then can be said to be structural isomers (or, if isotopes matter, structural isotopomers) if they have the same molecular formula but do not have the same structure.


Structural symmetry and equivalent atoms

Structural symmetry of a molecule can be defined mathematically as a
permutation In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or proc ...
of the atoms that exchanges at least two atoms but does not change the molecule's structure. Two atoms then can be said to be structurally
equivalent Equivalence or Equivalent may refer to: Arts and entertainment *Album-equivalent unit, a measurement unit in the music industry * Equivalence class (music) *'' Equivalent VIII'', or ''The Bricks'', a minimalist sculpture by Carl Andre *''Equiva ...
if there is a structural symmetry that takes one to the other. Thus, for example, all four hydrogen atoms of
methane Methane ( , ) is a chemical compound with the chemical formula (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas. The relative abundance of methane on Eart ...
are structurally equivalent, because any permutation of them will preserve all the bonds of the molecule. Likewise, all six hydrogens of
ethane Ethane ( , ) is an organic chemical compound with chemical formula . At standard temperature and pressure, ethane is a colorless, odorless gas. Like many hydrocarbons, ethane is isolated on an industrial scale from natural gas and as a petr ...
() are structurally equivalent to each other, as are the two carbons; because any hydrogen can be switched with any other, either by a permutation that swaps just those two atoms, or by a permutation that swaps the two carbons and each hydrogen in one methyl group with a different hydrogen on the other methyl. Either operation preserves the structure of the molecule. That is the case also for the hydrogen atoms
cyclopentane Cyclopentane (also called C pentane) is a highly flammable alicyclic hydrocarbon with chemical formula C5H10 and CAS number 287-92-3, consisting of a ring of five carbon atoms each bonded with two hydrogen atoms above and below the plane. It occur ...
,
allene In organic chemistry, allenes are organic compounds in which one carbon atom has double bonds with each of its two adjacent carbon centres (). Allenes are classified as cumulated dienes. The parent compound of this class is propadiene, which ...
, 2-butyne,
hexamethylenetetramine Hexamethylenetetramine, also known as methenamine, hexamine, or urotropin, is a heterocyclic organic compound with the formula (CH2)6N4. This white crystalline compound is highly soluble in water and polar organic solvents. It has a cage-like s ...
,
prismane Prismane or 'Ladenburg benzene' is a polycyclic hydrocarbon with the formula C6H6. It is an isomer of benzene, specifically a valence isomer. Prismane is far less stable than benzene. The carbon (and hydrogen) atoms of the prismane molecule are ...
,
cubane Cubane () is a synthetic hydrocarbon compound that consists of eight carbon atoms arranged at the corners of a cube, with one hydrogen atom attached to each carbon atom. A solid crystalline substance, cubane is one of the Platonic hydrocarbons an ...
,
dodecahedrane Dodecahedrane is a chemical compound, a hydrocarbon with formula , whose carbon atoms are arranged as the vertices (corners) of a regular dodecahedron. Each carbon is bound to three neighbouring carbon atoms and to a hydrogen atom. This compound ...
, etc. On the other hand, the hydrogen atoms of
propane Propane () is a three-carbon alkane with the molecular formula . It is a gas at standard temperature and pressure, but compressible to a transportable liquid. A by-product of natural gas processing and petroleum refining, it is commonly used a ...
are not all structurally equivalent. The six hydrogens attached to the first and third carbons are equivalent, as in ethane, and the two attached to the middle carbon are equivalent to each other; but there is no equivalence between these two
equivalence class In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation), then one may naturally split the set S into equivalence classes. These equivalence classes are constructed so that elements a ...
es.


Symmetry and positional isomerism

Structural equivalences between atoms of a parent molecule reduce the number of positional isomers that can be obtained by replacing those atoms for a different element or group. Thus, for example, the structural equivalence between the six hydrogens of
ethane Ethane ( , ) is an organic chemical compound with chemical formula . At standard temperature and pressure, ethane is a colorless, odorless gas. Like many hydrocarbons, ethane is isolated on an industrial scale from natural gas and as a petr ...
means that there is just one structural isomer of
ethanol Ethanol (abbr. EtOH; also called ethyl alcohol, grain alcohol, drinking alcohol, or simply alcohol) is an organic compound. It is an Alcohol (chemistry), alcohol with the chemical formula . Its formula can be also written as or (an ethyl ...
, not 6. The eight hydrogens of
propane Propane () is a three-carbon alkane with the molecular formula . It is a gas at standard temperature and pressure, but compressible to a transportable liquid. A by-product of natural gas processing and petroleum refining, it is commonly used a ...
are partitioned into two structural equivalence classes (the six on the methyl groups, and the two on the central carbon); therefore there are only two positional isomers of propanol ( 1-propanol and
2-propanol Isopropyl alcohol (IUPAC name propan-2-ol and also called isopropanol or 2-propanol) is a colorless, flammable organic compound with a pungent alcoholic odor. As an isopropyl group linked to a hydroxyl group (chemical formula ) it is the sim ...
). Likewise there are only two positional isomers of
butanol Butanol (also called butyl alcohol) is a four-carbon alcohol with a formula of C4 H9 O H, which occurs in five isomeric structures (four structural isomers), from a straight-chain primary alcohol to a branched-chain tertiary alcohol; all are a b ...
, and three of pentanol or
hexanol Hexanol may refer to any of the following isomeric organic compounds with the formula C6H13OH: : See also * Cyclohexanol * Amyl alcohol An amyl alcohol is any of eight alcohols with the formula C5H12O. A mixture of amyl alcohols (also called a ...
.


Symmetry breaking by substitutions

Once a substitution is made on a parent molecule, its structural symmetry is usually reduced, meaning that atoms that were formerly equivalent may no longer be so. Thus substitution of two or more equivalent atoms by the same element may generate more than one positional isomer. The classical example is the derivatives of
benzene Benzene is an organic chemical compound with the molecular formula C6H6. The benzene molecule is composed of six carbon atoms joined in a planar ring with one hydrogen atom attached to each. Because it contains only carbon and hydrogen atoms, ...
. Its six hydrogens are all structurally equivalent, and so are the six carbons; because the structure is not changed if the atoms are permuted in ways that correspond to flipping the molecule over or rotating it by multiples of 60 degrees. Therefore, replacing any hydrogen by chlorine yields only one
chlorobenzene Chlorobenzene is an aromatic organic compound with the chemical formula C6H5Cl. This colorless, flammable liquid is a common solvent and a widely used intermediate in the manufacture of other chemicals. Uses Historical The major use of chlorob ...
. However, with that replacement, the atom permutations that moved that hydrogen are no longer valid. Only one permutation remains, that corresponds to flipping the molecule over while keeping the chlorine fixed. The five remaining hydrogens then fall into three different equivalence classes: the one opposite to the chlorine is a class by itself (called the ''para'' position), the two closest to the chlorine form another class (''ortho''), and the remaining two are the third class (''meta''). Thus a second substitution of hydrogen by chlorine can yield three positional isomers: 1,2- or ''ortho''-, 1,3- or ''meta''-, and 1,4- or ''para''-dichlorobenzene. For the same reason, there is only one
phenol Phenol (also called carbolic acid) is an aromatic organic compound with the molecular formula . It is a white crystalline solid that is volatile. The molecule consists of a phenyl group () bonded to a hydroxy group (). Mildly acidic, it req ...
(hydroxybenzene), but three
benzenediol In organic chemistry, dihydroxybenzenes (benzenediols) are organic compounds in which two hydroxyl groups () are Arene substitution reaction, substituted onto a benzene ring (). These aromatic compounds are classed as phenols. There are three str ...
s; and one
toluene Toluene (), also known as toluol (), is a substituted aromatic hydrocarbon. It is a colorless, water-insoluble liquid with the smell associated with paint thinners. It is a mono-substituted benzene derivative, consisting of a methyl group (CH3) at ...
(methylbenzene), but three
toluol Toluene (), also known as toluol (), is a substituted aromatic hydrocarbon. It is a colorless, water-insoluble liquid with the smell associated with paint thinners. It is a mono-substituted benzene derivative, consisting of a methyl group (CH3) at ...
s, and three
xylene In organic chemistry, xylene or xylol (; IUPAC name: dimethylbenzene) are any of three organic compounds with the formula . They are derived from the substitution of two hydrogen atoms with methyl groups in a benzene ring; which hydrogens are s ...
s. On the other hand, the second replacement (by the same substituent) may preserve or even increase the symmetry of the molecule, and thus may preserve or reduce the number of equivalence classes for the next replacement. Thus, the four remaining hydrogens in ''meta''-dichlorobenzene still fall into three classes, while those of ''ortho''- fall into two, and those of ''para''- are all equivalent again. Still, some of these 3 + 2 + 1 = 6 substitutions end up yielding the same structure, so there are only three structurally distinct
trichlorobenzene Trichlorobenzene (TCB) may refer to any of three isomeric chlorinated derivatives of benzene with the molecular formula C6H3Cl3. Trichlorobenzenes are man-made chemical compounds that occur in three different forms. Even though the forms have the ...
s: 1,2,3-, 1,2,4-, and 1,3,5-. If the substituents at each step are different, there will usually be more structural isomers.
Xylenol Xylenols are organic compounds with the formula (CH3)2C6H3OH. They are volatile colorless solids or oily liquids. They are derivatives of phenol with two methyl groups at various positions relative to the hydroxyl group. Six isomers exist, of whi ...
, which is benzene with one hydroxyl substituent and two methyl substituents, has a total of 6 isomers:


Isomer enumeration and counting

Enumerating or counting structural isomers in general is a difficult problem, since one must take into account several bond types (including delocalized ones), cyclic structures, and structures that cannot possibly be realized due to valence or geometric constraints, and non-separable tautomers. For example, there are nine structural isomers with molecular formula C3H6O having different bond connectivities. Seven of them are air-stable at room temperature, and these are given in the table below. Two structural isomers are the
enol In organic chemistry, alkenols (shortened to enols) are a type of reactive structure or intermediate in organic chemistry that is represented as an alkene ( olefin) with a hydroxyl group attached to one end of the alkene double bond (). The t ...
tautomer Tautomers () are structural isomers (constitutional isomers) of chemical compounds that readily interconvert. The chemical reaction interconverting the two is called tautomerization. This conversion commonly results from the relocation of a hyd ...
s of the carbonyl isomers (propionaldehyde and acetone), but these are not stable.
CRC Handbook of Chemistry and Physics The ''CRC Handbook of Chemistry and Physics'' is a comprehensive one-volume reference resource for science research. First published in 1914, it is currently () in its 103rd edition, published in 2022. It is sometimes nicknamed the "Rubber Bible ...
65Th Ed.


See also

* Coordination isomerism *
Descriptor (chemistry) A descriptor is in chemical nomenclature a prefix placed before the systematic substance name, which describes the configuration or the stereochemistry of the molecule. Some listed descriptors are only of historical interest and should not be us ...
*
Stereoisomer In stereochemistry, stereoisomerism, or spatial isomerism, is a form of isomerism in which molecules have the same molecular formula and sequence of bonded atoms (constitution), but differ in the three-dimensional orientations of their atoms in ...
* Metamerism (disambiguation)


References

Frederick A. Bettelheim, William H. Brown, Mary K. Campbell, Shawn O. Farrell (2009): ''Introduction to Organic and Biochemistry''. 752 pages. Peter P. Mumba (2018): ''Useful Principles in Chemistry for Agriculture and Nursing Students'', 2nd Edition. 281 pages. Jim Clark (2000)
"Structural isomerism"
in ''Chemguide'', n.l.
D. Brynn Hibbert, A.M. James (1987): ''Macmillan Dictionary of Chemistry''. 532 pages. Zdenek Slanina (1986):
Contemporary Theory of Chemical Isomerism
'. 254 pages.
H. Stephen Stoker (2015): ''General, Organic, and Biological Chemistry'', 7th edition. 1232 pages. Jean-Loup Faulon, Andreas Bender (2010): ''Handbook of Chemoinformatics Algorithms''. 454 pages. Barry G. Hinwood (1997): ''A Textbook of Science for the Health Professions''. 489 pages. {{isbn, 9780748733774
Isomerism es:Isomería estructural he:איזומרים מרחביים