Symbolically, \[A\cup B=\{x:x\in A\,\,\text{or}\,\,x\in B\}.\]
(2) Intersection of sets : Let A and B be two sets. The intersection of A and B is the set of all those elements that belong to both A and B.
The intersection of A and B is denoted by \[A\cap B\] (read as “A intersection B”).
Thus, \[A\cap B=\{x\,\,:\,\,x\in \,\,and\,\,x\in B\}\].
(3) Disjoint sets : Two sets A and B are said to be disjoint, if \[A\cap B=\phi \]. If \[A\cap B\ne \phi \], then A and B are said to be non-intersecting or non-overlapping sets.
Example : Sets {1, 2}; {3, 4} are disjoint sets.
(4) Difference of sets : Let A and B be two sets. The difference of A and B written as \[A-B\], is the set of all those elements of A which do not belong to B.
Thus, \[A-B=\{x\,:\,x\in A\,\,and\,\,x\notin B\}\]
Similarly, the difference\[B-A\] is the set of all those elements of B that do not belong to A i.e., \[B-A=\{x\in B:x\notin A\}\].
Example : Consider the sets \[A=\{1,\,2,\,3\}\] and \[B=\{3,\,4,\,5\}\], then \[A-B=\{1,\,2\};\,B-A=\{4,\,5\}\].
(5) Symmetric difference of two sets : Let A and B be two sets. The symmetric difference of sets A and B is the set \[(A-B)\cup (B-A)\] and is denoted by\[A\Delta B\]. Thus, \[A\Delta B=\]\[(A-B)\cup (B-A)=\{x:x\notin A\cap B\}\].
(6) Complement of a set : Let U be the universal set and let A be a set such that \[A\subset B\]. Then, the complement of A with respect to U is denoted by \[A'\] or \[{{A}^{o}}\] or \[C(A)\] or \[U-A\] and is defined the set of all those elements of U which are not in A.
Thus, \[A'=\{x\,\in U\,:x\,\notin A\}\].
Clearly, \[x\in A'\Leftrightarrow x\notin A\]
Example : Consider \[U=\{1,\,2,......,10\}\]
and \[A=\{1,\,3,\,5,\,7,\,9\}\].
Then \[{A}'=\{2,\,4,\,6,\,8,\,10\}\] 
| Symbol | Meaning |
| \[\Rightarrow \] | Implies |
| \[\in \] | Belongs to |
| \[A\subset B\] | A is a subset of B |
| \[\Leftrightarrow \] | Implies and is implied by |
| \[\notin \] | Does not belong to |
| s.t.(: or |) \[\forall \] | Such that For every |
| \[\exists \] | There exists |
| more...
Aromatic compounds are those which contain one or more benzene rings in them. An aromatic compound has two main parts : (1) Nucleus, (2) Side chain
(1) Nucleus :The benzene ring represented by regular hexagon of six carbon atoms with three double bonds in the alternate positions is referred to as nucleus. The ring may be represented by any of the following ways,
(2) Side chain : The alkyl or any other aliphatic group containing at least one carbon atom attached to the nucleus is called side chain. These are formed by replacing one or more hydrogen atoms in the ring by alkyl radicals i.e., R (R may be \[-C{{H}_{3}}\], \[-{{C}_{2}}{{H}_{5}}\], \[-{{C}_{3}}{{H}_{7}}\] etc.)
If one atom of hydrogen of benzene molecule is replaced by another atom or group of atoms, the derivative formed is called monovalent substituted derivative. It can exist only in one form because all the six hydrogens of benzene represent equivalent positions. For example, \[{{C}_{6}}{{H}_{5}}X\], where X is a monovalent group.
When two hydrogen atoms of benzene are replaced by two monovalent atoms or group of atoms, the resulting product disubstituted benzene derivative can have three different forms. These forms are distinguished by giving the numbers. The position occupied by the principle functional group is given as 1 and the other position is numbered in a clockwise direction which gvies lower locatant to the substituents.
(i) Ortho (or 1, 2-) : The compound is said to be ortho (or 1, 2-) if the two substituents are on the adjacent carbon atoms.
(ii) Meta (or 1, 3-) : The compound is said to be meta or (1, 3-) if the two substituents are on alternate carbon atoms.
(iii) Para (or 1, 4-) : The compound is said to be para or (1, 4-) if the two substituents are on diagonally situated carbon atoms.
Ortho, meta and para are generally represented as o-, m- and p- respectively as shown below,
Aryl group : The radicals obtained by removal of one or more hydrogen atoms of the aromatic hydrocarbon molecules are known as aryl radicals or aryl groups. For example,
Nomenclature of different aromatic compounds : The names of few simple aromatic compounds are given below :
Hydrocarbons
The aromatic hydrocarbons may also contain two or more benzene rings condensed together.
Halogen derivatives
Nuclear substituted
Compounds in which one carbon atom is common to two different rings are called spiro compounds. The IUPAC name for a spiro compound begins with the word spiro followed by square brackets containing the number of carbon atoms, in ascending order, in each ring connected to the common carbon atom and then by the name of the parent hydrocarbon corresponding to the total number of the carbon atoms in the two rings. The position of substituents are indicated by numbers; the numbering beginning with the carbon atom adjacent to the spiro carbon and proceeding first around the smaller ring and then to the spiro atom and finally around the larger ring For example,
Unbranched assemblies consisting of two or more identical hydrocarbon units joined by a single bond are named by placing a suitable numerical prefix such as bi for two, ter for three, quater for four, quinque for five etc. before the name of the repititive hydrocarbon unit. Starting from either end, the carbon atoms of each repititive hydrocarbon unit are numbered with unprimed and primed arabic numerals such as 1, 2, 3...., 1', 2', 3' ....., 1'', 2'', 3''..... etc. The points of attachment of the repititive hydrocarbon units are indicated by placing the appropriate locants before the name. For example,
As an exception, unbranched assemblies consisting of benzene rings are named by using appropriate prefix with the name phenyl instead of benzene. For example,
Many hydrocarbons and their derivatives contain two fused or bridged rings. The carbon atoms common to both rings are called bridge head atoms and each bond or chain of carbon atoms connecting both the bridge head atoms is called as bridge. The bridge may contain 0, 1, 2.... etc. carbon atoms. For example,
These bicyclic compounds are named by attaching the prefix 'bicyclo' to the name of the hydrocarbon having the same total number of carbon atoms as in the two rings. The number of carbon atoms in each of the three bridges connecting the two bridge head carbon atoms is indicated by arabic numerals, i.e., 0, 1, 2.....etc. These arabic numerals are arranged in descending order; separated from one another by full stops and then enclosed in square brackets. The complete IUPAC name of the hydrocarbon is then obtained by placing these square brackets containing the arabic numerals between the prefix bicyclo and the name of alkane. For example,
If a substituent is present, the bicyclic ring system is numbered. The numbering begins with one of the bridge head atoms, proceeds first along the longest bridge to the second bridge head atom, continues along the next longest bridge to the first bridge head atom and is finally completed along the shortest path. For example,
Sometimes, the bonds between carbon atoms are represented by lines. For example, n-hexane has a continuous chain of six carbon atoms which may be represented as,
\[\begin{align} & C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}-C{{H}_{2}}-C{{H}_{2}}-C{{H}_{3}} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,n-\text{Hexane} \\ \end{align}\]
In this notation, the carbon atoms are represented by line ends and intersections. It is assumed that the required number of hydrogen atoms are present wherever they are necessary to satisfy the tetravalency of carbon. A single line represents a single bond (C - C) two parallel lines represent a double bond (C = C) and three parallel lines represent a triple bond \[(C\equiv C)\]. For example,
The naming of any organic compound depends on the name of normal parent hydrocarbon from which it has been derived. IUPAC system has framed a set of rules for various types of organic compounds.
(1) Rules for Naming complex aliphatic compounds when no functional group is present (saturated hydrocarbon or paraffins or Alkanes)
(i) Longest chain rule : The first step in naming an organic compound is to select the longest continuous chain of carbon atoms which may or may not be horizontal (straight). This continuous chain is called parent chain or main chain and other carbon chains attached to it are known as side chains (substituents). Examples :
If two different chains of equal length are possible, the chain with maximum number of side chains or alkyl groups is selected.
(ii) Position of the substituent : Number of the carbon atoms in the parent chain as 1, 2, 3,....... etc. starting from the end which gives lower number to the carbon atoms carrying the substituents. For examples,
\[\underset{\text{A}\,\text{(Correct)}}{\mathop{\overset{5}{\mathop{C}}\,-\overset{4}{\mathop{C}}\,-\overset{3}{\mathop{C}}\,-\overset{X}{\mathop{\overset{2|}{\mathop{C}}\,}}\,-\overset{1}{\mathop{C}}\,}}\,\] \[\underset{\text{B}\,\text{(Wrong)}}{\mathop{\overset{1}{\mathop{C}}\,-\overset{2}{\mathop{C}}\,-\overset{3}{\mathop{C}}\,-\overset{X}{\mathop{\overset{4|}{\mathop{C}}\,}}\,-\overset{5}{\mathop{C}}\,}}\,\]
The number that indicates the position of the substituent or side chain is called locant. \[\underset{2-\text{Methylpentane}}{\mathop{\underset{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,C{{H}_{3}}}{\mathop{\underset{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,|}{\mathop{\overset{5}{\mathop{C}}\,{{H}_{3}}-\overset{4}{\mathop{C}}\,{{H}_{2}}-\overset{3}{\mathop{C}}\,{{H}_{2}}-\overset{2}{\mathop{C}}\,H-\overset{1}{\mathop{C}}\,{{H}_{3}}}}\,}}\,}}\,\] \[\underset{3-\text{Ethylhexane}}{\mathop{\underset{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,C{{H}_{2}}-C{{H}_{2}}-C{{H}_{3}}}{\mathop{\underset{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5\,\,\,\,\,\,\,\,\,\,\,\,6\,\,\,\,\,\,\,\,\,\,\,}{\mathop{\overset{1}{\mathop{C}}\,{{H}_{3}}-\overset{2}{\mathop{C}}\,{{H}_{2}}-\overset{3}{\mathop{C}}\,H-\overset{{}}{\mathop{C}}\,H-\overset{{}}{\mathop{C}}\,{{H}_{3}}}}\,}}\,}}\,\]
(iii) Lowest set of locants : When two or more substituents are present, then end of the parent chain which gives the lowest set of the locants is preferred for numbering.
This rule is called lowest set of locants. This means that when two or more different sets of locants are possible, that set of locants which when compared term by term with other sets, each in order of increasing magnitude, has the lowest term at the first point of difference. This rule is used irrespective of the nature of the substituent. For example, \[\underset{\text{Set of locants : 2, 3, 5 (Correct)}}{\mathop{\underset{\,\,\,\,\,\,\,\,\,\,\,C{{H}_{3}}}{\mathop{\underset{\,\,\,\,\,\,\,\,|}{\mathop{{{H}_{3}}\overset{6}{\mathop{C}}\,-\overset{5}{\mathop{C}}\,H-}}\,}}\,\underset{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,C{{H}_{3}}}{\mathop{\underset{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,|}{\mathop{\overset{4}{\mathop{C}}\,{{H}_{2}}-\overset{3}{\mathop{C}}\,H}}\,}}\,-\underset{C{{H}_{3}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,}{\mathop{\underset{|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}{\mathop{\overset{2}{\mathop{C}}\,H-\overset{1}{\mathop{C}}\,{{H}_{3}}}}\,}}\,}}\,\] \[\underset{\text{Set of locants : 2, 4, 5 (Wrong)}}{\mathop{\underset{\,\,\,\,\,\,\,\,\,\,\,C{{H}_{3}}}{\mathop{\underset{\,\,\,\,\,\,\,\,|}{\mathop{{{H}_{3}}\overset{1}{\mathop{C}}\,-\overset{2}{\mathop{C}}\,H-}}\,}}\,\underset{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,C{{H}_{3}}}{\mathop{\underset{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,|}{\mathop{\overset{3}{\mathop{C}}\,{{H}_{2}}-\overset{4}{\mathop{C}}\,H}}\,}}\,-\underset{C{{H}_{3}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,}{\mathop{\underset{|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}{\mathop{\overset{5}{\mathop{C}}\,H-\overset{6}{\mathop{C}}\,{{H}_{3}}}}\,}}\,}}\,\]
The correct set of locants is 2, 3, 5 and not 2, 4, 5. The first set is lower than the second set because at the first difference 3 is less than 4. (Note that first locant is same in both sets 2; 2 and the first difference is with the second locant 3, 4. We can compare term by term as 2-2, 3-4 (first difference), 5-5. Only first point of difference is considered for preference. Similarly for the compounds, \[\underset{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\ \ \,C{{H}_{3}}}{\mathop{\underset{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\ \ \,\,\,\,\,\,\,|}{\mathop{\overset{10}{\mathop{C}}\,{{H}_{3}}-\overset{9}{\mathop{C}}\,{{H}_{2}}-\overset{8}{\mathop{C}}\,H-}}\,}}\,\underset{C{{H}_{3}}\,\,\,\,\,\ \ \ \ \ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}{\mathop{\underset{|\,\,\,\,\,\,\ \ \ \ \,\,\,\,\,\,\,\,\,\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}{\mathop{\overset{7}{\mathop{C}}\,H-\overset{6}{\mathop{C}}\,{{H}_{2}}-\overset{5}{\mathop{C}}\,{{H}_{2}}-\overset{4}{\mathop{C}}\,{{H}_{2}}}}\,}}\,\underset{\,\,\,\,C{{H}_{3}}}{\mathop{\underset{|\ }{\mathop{-\overset{3}{\mathop{C}}\,{{H}_{2}}-\overset{2}{\mathop{C}}\,H-\overset{1}{\mathop{C}}\,{{H}_{3}}}}\,}}\,\] Set of locants : 2, 7, 8 (Correct) \[\underset{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,C{{H}_{3}}}{\mathop{\underset{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,|}{\mathop{\overset{1}{\mathop{C}}\,{{H}_{3}}-\overset{2}{\mathop{C}}\,{{H}_{2}}-\overset{3}{\mathop{C}}\,H-}}\,}}\,\underset{C{{H}_{3}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}{\mathop{\underset{|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}{\mathop{\overset{4}{\mathop{C}}\,H-\overset{5}{\mathop{C}}\,{{H}_{2}}-\overset{6}{\mathop{C}}\,{{H}_{2}}-\overset{7}{\mathop{C}}\,{{H}_{2}}}}\,}}\,\underset{\,\,\,\,\,C{{H}_{3}}}{\mathop{\underset{|}{\mathop{-\overset{8}{\mathop{C}}\,{{H}_{2}}-\overset{9}{\mathop{C}}\,H-\overset{10}{\mathop{C}}\,{{H}_{3}}}}\,}}\,\] Set of locants : 3, 4, 9 (Wrong)
First set of locants 2, 7, 8 is lower than second set 3, 4, 9 because at the first point of difference 2 is lower than 3.
Lowest sum rule : It may be noted that earlier, the numbering of the parent chain containing two or more substituents was done in such a way that sum of the locants more... Current Affairs CategoriesArchive
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