Classification of organic compounds Questions in English

(C) The study of organic compounds is treated as a separate branch of chemistry because of the unique property of carbon known as $Catenation$.
$Catenation$ is the ability of carbon atoms to form long chains and rings by bonding with other carbon atoms,which leads to the existence of a vast number of organic compounds.
This unique structural diversity makes the chemistry of carbon compounds distinct and extensive compared to inorganic compounds.

(D) An alicyclic compound is an organic compound that is both aliphatic and cyclic.
They contain one or more all-carbon rings which may be either saturated or unsaturated,but do not have aromatic character.
Alicyclic compounds may have one or more aliphatic side chains attached.

(C) Organic compounds are primarily composed of carbon atoms covalently bonded to hydrogen,oxygen,nitrogen,and other elements.
$1$. Organic compounds are characterized by the presence of carbon,which has a unique ability to form stable,long chains and rings (catenation).
$2$. Due to this property of catenation,carbon can form a vast variety of complex structures,leading to the existence of a very large number of organic compounds.
$3$. They typically exhibit covalent bonding,and their reactions are generally slower compared to ionic reactions.
Therefore,the most appropriate statement is that they are found in a large number.

(B) quaternary carbon atom is a carbon atom that is bonded to four other carbon atoms.
In the given structure $^1CH_3-^2C(CH_3)_2-^3CH_2-^4CH_3$,the carbon atom at position $2$ is bonded to four other carbon atoms (the $C1$ methyl group,the $C3$ methylene group,and two methyl groups attached to $C2$).
Therefore,$C2$ is the quaternary carbon atom.

(B) The general formula for an alkane is $C_nH_{2n+2}$,while the general formula for a cycloalkane or an alkene is $C_nH_{2n}$.
For $n = 6$,the formula $C_6H_{12}$ corresponds to either an alkene or a cycloalkane.
Cyclohexane $(C_6H_{12})$ is a saturated cyclic hydrocarbon,which is classified as an alicyclic compound.
Therefore,the correct option is $(B)$.

(B) The classification of carbon atoms depends on the number of other carbon atoms to which a specific carbon is bonded:

$1^o$ (Primary)	Bonded to $1$ other carbon
$2^o$ (Secondary)	Bonded to $2$ other carbons
$3^o$ (Tertiary)	Bonded to $3$ other carbons
$4^o$ (Quaternary)	Bonded to $4$ other carbons

Let us analyze $3-$ chloro $-2, 3-$ dimethylpentane: $CH_3-CH(CH_3)-C(Cl)(CH_3)-CH_2-CH_3$.
- $1^o$ carbons: The terminal $CH_3$ groups.
- $2^o$ carbon: The $-CH_2-$ group at position $4$.
- $3^o$ carbon: The $-CH-$ group at position $2$.
- $4^o$ carbon: The carbon at position $3$ is bonded to four other atoms (three carbons and one chlorine atom),satisfying the quaternary carbon definition.

(B) homologous series is a group of organic compounds having the same functional group and similar chemical properties,where each successive member differs by a $CH_2$ unit.
In option $(B)$,$2-$Butanol $(CH_3CH(OH)CH_2CH_3)$ and $2-$Propanol $(CH_3CH(OH)CH_3)$ differ by a $CH_2$ group,thus they belong to the same homologous series.

(B) The chemical formulas for the given compounds are:
$1$. Acetic acid: $CH_3COOH$ (Total $4$ hydrogen atoms)
$2$. Glycerol: $C_3H_8O_3$ (Total $8$ hydrogen atoms)
$3$. Methane: $CH_4$ (Total $4$ hydrogen atoms)
$4$. Methanol: $CH_3OH$ (Total $4$ hydrogen atoms)
Comparing the total number of hydrogen atoms,Glycerol $(C_3H_8O_3)$ contains the maximum number of hydrogen atoms.

(D) carbocyclic ring contains only carbon atoms in the ring structure.
When one or more heteroatoms such as nitrogen,oxygen,or sulphur are present in the ring,the ring is known as a heterocyclic ring.
In the given options:
$1$. Benzene and Cyclohexane are carbocyclic compounds.
$2$. Pyridine contains a nitrogen atom in the ring,making it a heterocyclic compound.
$3$. Furan contains an oxygen atom in the ring,making it a heterocyclic compound.
Therefore,both Furan and Pyridine lack a carbocyclic ring.

(C) $Methyl$ cyclopropane has two secondary $(2^{\circ})$ carbon atoms,one tertiary $(3^{\circ})$ carbon atom,and one primary $(1^{\circ})$ carbon atom.
$1.$ $A$ primary $(1^{\circ})$ carbon atom is attached to only one other carbon atom.
$2.$ $A$ secondary $(2^{\circ})$ carbon atom is attached to two other carbon atoms.
$3.$ $A$ tertiary $(3^{\circ})$ carbon atom is attached to three other carbon atoms.
$4.$ $A$ quaternary $(4^{\circ})$ carbon atom is attached to four other carbon atoms.
In $methyl$ cyclopropane,the two $CH_2$ groups in the ring are secondary,the $CH$ group in the ring is tertiary,and the $CH_3$ group attached to the ring is primary.

(B) heterocyclic compound is a cyclic compound that has atoms of at least two different elements as members of its ring.
$Phenol$ $(C_6H_5OH)$ contains a benzene ring with an external $-OH$ group.
$Aniline$ $(C_6H_5NH_2)$ contains a benzene ring with an external $-NH_2$ group.
$Furan$ $(C_4H_4O)$ contains an oxygen atom within the five-membered ring.
$Thiophene$ $(C_4H_4S)$ contains a sulfur atom within the five-membered ring.
Therefore,both $Furan$ and $Thiophene$ are heterocyclic compounds.

(A) Heterocyclic compounds are cyclic compounds that contain at least one atom other than carbon (heteroatom such as $S, O, N$) in the ring.
Thiophene $(C_4H_4S)$ is a heterocyclic compound containing a sulfur atom in its five-membered ring.
$HOOC-CH=CH-COOH$ (Maleic acid) is an acyclic (open-chain) compound.
Cyclopentadiene and cyclopentadienone are homocyclic (carbocyclic) compounds because their rings consist only of carbon atoms.

(D) By analyzing the structure of the given compound:
$1$. The group enclosed in box $b$ is a ketone group ($-C=O$ attached to two carbon atoms).
$2$. The group enclosed in box $a$ is an ester group ($-COO-$ linkage within the ring).
$3$. The group enclosed in box $c$ is an amide group ($-CONH-$ linkage within the ring).
$4$. There is no ether group ($-O-$ linkage between two carbon atoms) present in the molecule.
Therefore,the correct option is $D$.

(C) heterocyclic compound is a cyclic compound that has atoms of at least two different elements as members of its ring$(s)$.
$A$. Cyclopentane is a carbocyclic compound (only carbon atoms in the ring).
$B$. Cyclopentadienone is a carbocyclic compound (only carbon atoms in the ring).
$C$. Pyrrole is a heterocyclic compound because it contains a nitrogen atom within its five-membered ring.
$D$. Aminocyclopentadiene is a carbocyclic compound (the nitrogen atom is in the substituent group,not in the ring).
Therefore,the correct answer is $C$.

(C) $2^o$ Hydrogen atom is a hydrogen atom attached to a $2^o$ carbon atom (a carbon atom bonded to two other carbon atoms).
In the given structure of $1$-chloronaphthalene,there are $10$ carbon atoms in total.
The two bridgehead carbons are $3^o$ carbons (bonded to three other carbons) and have no hydrogen atoms attached.
The carbon atom attached to the chlorine atom is a $2^o$ carbon but it has no hydrogen attached.
The remaining $7$ carbon atoms are all $2^o$ carbons,and each of these is bonded to one hydrogen atom.
Therefore,there are $7$ hydrogen atoms attached to $2^o$ carbon atoms.
Thus,the total number of $2^o$ hydrogen atoms is $7$.

(A) Homologous compounds possess the same functional group and chemical properties.
Consecutive members of a homologous series differ by a $-CH_2-$ group and a molecular mass of $14 \ u$.

(D) homologous series is a group of compounds that have the same functional group and similar chemical properties,with each successive member differing by a $CH_2$ group.
$A$: Benzyl alcohol $(C_6H_5CH_2OH)$ is a primary alcohol,while $o$-cresol ($2$-methylphenol,$C_6H_4(CH_3)OH$) is a phenolic compound. They have different functional groups.
$B$: Benzylamine $(C_6H_5CH_2NH_2)$ is a primary amine,while $N$-methylaniline $(C_6H_5NHCH_3)$ is a secondary amine. They belong to different classes of amines.
$C$: Benzoic acid $(C_6H_5COOH)$ is a carboxylic acid,while Phenyl formate $(HCOOC_6H_5)$ is an ester. They have different functional groups.
Since none of the pairs represent the same homologous series,the correct answer is $D$.

(B) Homologues are members of a homologous series that differ by a $CH_2$ group and have the same general formula. Isomers are compounds with the same molecular formula but different structural arrangements. Since homologues have different molecular formulas (differing by $CH_2$),they cannot be isomers.

The first five members of each homologous series are generated by adding successive $-CH_{2}-$ units:
$(a)$ $HCOOH$ (Methanoic acid),$CH_{3}COOH$ (Ethanoic acid),$CH_{3}CH_{2}COOH$ (Propanoic acid),$CH_{3}CH_{2}CH_{2}COOH$ (Butanoic acid),$CH_{3}CH_{2}CH_{2}CH_{2}COOH$ (Pentanoic acid).
$(b)$ $CH_{3}COCH_{3}$ (Propanone),$CH_{3}COCH_{2}CH_{3}$ (Butanone),$CH_{3}COCH_{2}CH_{2}CH_{3}$ (Pentan$-2-$one),$CH_{3}COCH_{2}CH_{2}CH_{2}CH_{3}$ (Hexan$-2-$one),$CH_{3}COCH_{2}CH_{2}CH_{2}CH_{2}CH_{3}$ (Heptan$-2-$one).
$(c)$ $CH_{2}=CH_{2}$ (Ethene),$CH_{3}CH=CH_{2}$ (Propene),$CH_{3}CH_{2}CH=CH_{2}$ (But$-1-$ene),$CH_{3}CH_{2}CH_{2}CH=CH_{2}$ (Pent$-1-$ene),$CH_{3}CH_{2}CH_{2}CH_{2}CH=CH_{2}$ (Hex$-1-$ene).

(N/A) The functional groups present in the given compounds are:
$(a)$ Aldehyde $(-CHO)$,Hydroxyl $(-OH)$,Methoxy $(-OCH_3)$,and Aromatic ring.
$(b)$ Primary amine $(-NH_2)$,Ester $(-COO-)$,and Tertiary amine $(-N(C_2H_5)_2)$.
$(c)$ Nitro group $(-NO_2)$ and Alkene $(C=C)$.

(N/A) The history of organic chemistry began with the belief in $Vital \ Force \ Theory$,which suggested that organic compounds could only be produced by living organisms.
In $1828$,$Friedrich \ Wöhler$ disproved this by synthesizing urea $(NH_2CONH_2)$ from an inorganic compound,ammonium cyanate $(NH_4OCN)$,by heating it.
This discovery marked the beginning of modern organic chemistry,shifting the focus from vitalism to the study of carbon-based compounds.
Later,$Kolbe$ synthesized acetic acid and $Berthelot$ synthesized methane,further establishing that organic compounds could be prepared in the laboratory from inorganic precursors.
Today,organic chemistry is defined as the study of carbon compounds,excluding simple oxides like $CO$,$CO_2$,carbides,and carbonates.

(N/A) The classification of organic compounds based on their structure is as follows:
Organic compounds are primarily divided into two categories:
$1$. Acyclic or Open chain compounds $(I)$
$2$. Cyclic or Closed chain or Ring compounds $(II)$
Cyclic compounds are further classified into:
$1$. Homocyclic or Carbocyclic compounds
$2$. Heterocyclic compounds
Homocyclic or Carbocyclic compounds are further divided into:
$1$. Alicyclic compounds
$2$. Aromatic compounds (which are further classified into Benzenoid and Non-benzenoid compounds).

(N/A) Definition: These compounds are also called aliphatic compounds and consist of straight or branched chain structures.
$(a)$ Examples of acyclic or straight chain compounds:
$(i)$ $CH_3CH_3$ (ethane)
(ii) $CH_3CH_2CH_3$ (propane)
(iii) $CH_3CH_2CH_2CH_3$ ($n$-butane)
(iv) $CH_3CHO$ (acetaldehyde)
$(v)$ $CH_3COOH$ (acetic acid)
(vi) $CH_3CH_2CH_2CH_2Cl$ ($1$-chlorobutane)
$(b)$ Acyclic or branched chain compounds:
$(i)$ $(CH_3)_2CHCH_3$ (isobutane)
(ii) $C(CH_3)_4$ (neopentane)
(iii) $CH_3CH(CH_3)CH_2CH_3$ (isopentane)
(iv) $CH_3CH(CH_3)CH_2Cl$ (isobutyl chloride)

(N/A) Alicyclic (aliphatic cyclic) compounds: These are organic compounds that contain carbon atoms joined in the form of a ring. They resemble aliphatic compounds in their properties. Examples include cyclopropane,cyclohexene,and cyclohexane.
$(b)$ Heterocyclic compounds: These are cyclic compounds in which the ring contains one or more atoms other than carbon (such as $O$,$N$,or $S$). An example is tetrahydrofuran.

(N/A) functional group is defined as an atom or a group of atoms joined in a specific manner,which is responsible for the characteristic chemical properties of organic compounds.
Examples:
$(i)$ $(-OH)$ Hydroxyl group,e.g.,$CH_3OH$
$(ii)$ $(-CHO)$ Aldehyde group,e.g.,$CH_3CHO$
$(iii)$ $(-COOH)$ Carboxylic acid group,e.g.,$CH_3COOH$
Some important functional groups containing carbon-carbon multiple bonds are given in the table below:

Series	Group	Characteristic
Alkene	$ >C=C< $	$C-C$ double bond
Alkyne	$-C \equiv C-$	$C-C$ triple bond
Arene	$C_6H_6$ (Benzene ring)	Six-membered ring with alternate $C=C$ and $C-C$ bonds (aromatic ring)

(N/A) homologous series is a group or a series of organic compounds that have the same functional group and similar chemical properties,and in which the successive members differ by a $-CH_{2}-$ unit.
$(I)$ The members of a homologous series can be represented by a general molecular formula.
$(II)$ The successive members differ from each other in molecular formula by a $-CH_{2}-$ unit.
$(III)$ All compounds of a homologous series contain the same functional group.
$(IV)$ The compounds of a homologous series are prepared by general methods and exhibit similar chemical properties.
$(V)$ The physical properties of members of a homologous series change gradually with an increase in molecular mass.

Homologous series / General formula	Examples
Alkane series: $C_{n}H_{2n+2}$	$C_{2}H_{6}, C_{3}H_{8}, C_{4}H_{10}$
Alkene series: $C_{n}H_{2n}$	$C_{2}H_{4}, C_{3}H_{6}, C_{4}H_{8}$
Alkyne series: $C_{n}H_{2n-2}$	$C_{2}H_{2}, C_{3}H_{4}, C_{4}H_{6}$
Alcohol series: $C_{n}H_{2n+1}OH$	$CH_{3}OH, C_{2}H_{5}OH, C_{3}H_{7}OH$
Acid series: $C_{n}H_{2n+1}COOH$	$CH_{3}COOH, C_{2}H_{5}COOH$

(N/A) Definition: $A$ functional group is an atom or a group of atoms bonded together in a unique manner,which is usually the site of chemical reactivity in an organic molecule.
Characteristics: Compounds containing the same functional group undergo similar chemical reactions. For example,$CH_{3}OH$,$CH_{3}CH_{2}OH$,and $(CH_{3})_{2}CHOH$,all containing the $-OH$ functional group,liberate hydrogen gas upon reaction with sodium metal.
Uses: Functional groups allow for the systematic classification of organic compounds into different classes based on their chemical behavior and structural features.

(N/A) Organic chemistry is the branch of chemistry that deals with the study of carbon compounds. Carbon atoms form stable covalent bonds with other carbon atoms and with elements such as hydrogen,oxygen,nitrogen,sulfur,phosphorus,and halogens. The study of these compounds and their properties constitutes organic chemistry.

(N/A) Carbon atoms possess the unique ability to form stable covalent bonds with other carbon atoms (catenation) and with various other elements such as hydrogen,oxygen,nitrogen,sulfur,phosphorus,and halogens. The vast number of compounds resulting from these diverse bonding patterns necessitated the creation of a specialized branch of chemistry dedicated to their study,which is known as organic chemistry.

(N/A) The classification of the given compounds is as follows:
$1$. Acyclic (Open chain): {Acetic acid,Ethane,Butene,Propane}
$2$. Alicyclic: {Tetrahydrofuran,Cyclohexene,Cyclobutane}
$3$. Benzenoid: {Naphthalene,Benzene}
$4$. Non-benzenoid: {Tropolone}

(N/A) $(i)$ Alicyclic compounds: These are cyclic organic compounds that contain carbon atoms arranged in a ring,but they do not possess aromatic character. They resemble aliphatic compounds in their properties. Example: Cyclopropane,Cyclohexane.
$(ii)$ Heterocyclic compounds: These are cyclic compounds in which the ring contains one or more atoms other than carbon (such as $N$,$O$,or $S$). These are called heteroatoms. Example: Furan,Pyridine,Thiophene.
$(iii)$ Non-benzenoid compounds: These are cyclic compounds that possess aromatic character but do not contain a benzene ring. They exhibit aromaticity due to the presence of a cyclic conjugated system following $H$ückel's rule $(4n+2) \pi$ electrons. Example: Azulene,Tropolone.

(N/A) The classification of a carbon atom as primary $(1^{\circ})$,secondary $(2^{\circ})$,tertiary $(3^{\circ})$,or quaternary $(4^{\circ})$ depends on the number of other carbon atoms directly attached to it.
$1^{\circ}$ (Primary): $A$ carbon atom attached to no other carbon atom (as in methane) or only one other carbon atom (as in ethane) is called a primary carbon.
$2^{\circ}$ (Secondary): $A$ carbon atom attached to two other carbon atoms is known as a secondary carbon.
$3^{\circ}$ (Tertiary): $A$ carbon atom attached to three other carbon atoms is known as a tertiary carbon.
$4^{\circ}$ (Quaternary): $A$ carbon atom attached to four other carbon atoms is known as a quaternary carbon.
Examples:

Structure	Forms of carbon
$H_3C-CH(CH_3)-CH_2-CH_3$ ($2$-Methylbutane)	Terminal $-CH_3$ groups are $1^{\circ}$. The $CH$ carbon is $3^{\circ}$ (attached to $3$ carbons). The $-CH_2-$ carbon is $2^{\circ}$ (attached to $2$ carbons).
$C(CH_3)_4$ ($2$,$2$-Dimethylpropane)	The central carbon is $4^{\circ}$ (attached to $4$ carbons). The four terminal $-CH_3$ carbons are $1^{\circ}$.

(N/A) Based on the number of other carbon atoms attached to a specific carbon atom,it is classified as primary $(1^{\circ})$,secondary $(2^{\circ})$,tertiary $(3^{\circ})$,or quaternary $(4^{\circ})$.
$1^{\circ}$ (Primary) Carbon: $A$ carbon atom attached to no other carbon atom (as in methane) or to only one other carbon atom (as in ethane).
$2^{\circ}$ (Secondary) Carbon: $A$ carbon atom attached to two other carbon atoms.
$3^{\circ}$ (Tertiary) Carbon: $A$ carbon atom attached to three other carbon atoms.
$4^{\circ}$ (Quaternary) Carbon: $A$ carbon atom attached to four other carbon atoms.
Examples:
| Structure | Forms of Carbon |
| :--- | :--- |
| $H_3C-CH(CH_3)-CH_2-CH_3$ ($2$-Methylbutane) | Terminal $CH_3$ groups are $1^{\circ}$. The $CH$ carbon is $3^{\circ}$ as it is attached to $3$ other carbons. The $CH_2$ carbon is $2^{\circ}$ as it is attached to $2$ other carbons. |
| $C(CH_3)_4$ ($2$,$2$-Dimethylpropane) | The four terminal $CH_3$ groups are $1^{\circ}$. The central carbon is $4^{\circ}$ as it is attached to $4$ other carbon atoms. |

(N/A) quaternary carbon atom is a carbon atom that is bonded to four other carbon atoms. Since carbon has a valency of $4$,all its bonding sites are occupied by carbon atoms. Therefore,there is no space for a hydrogen atom to bond with a quaternary carbon. Consequently,the existence of a quaternary hydrogen atom is impossible.

(A) $(i)$ Aromatic compounds contain a benzene ring or satisfy $H$ückel's rule. Aniline is a benzenoid aromatic compound. So,$(i-d)$.
$(ii)$ Branched acyclic compounds are open-chain structures with branches. Neopentane is a branched alkane. So,$(ii-b)$.
$(iii)$ Alicyclic compounds are cyclic compounds that behave like aliphatic compounds. Cyclohexene is an alicyclic compound. So,$(iii-c)$.
$(iv)$ Non-benzenoid aromatic compounds are aromatic but do not contain a benzene ring. Tropolone is a non-benzenoid aromatic compound. So,$(iv-a)$.
Therefore,the correct match is $(i-d, ii-b, iii-c, iv-a)$.

(D) Cyclohexene is a cyclic compound that does not contain a benzene ring and does not exhibit aromaticity. \\ Such cyclic compounds that resemble aliphatic compounds in their properties are classified as alicyclic compounds. \\ Therefore,cyclohexene is an alicyclic compound.

(B) heteroatom is any atom other than carbon or hydrogen in an organic molecule.
$1$. Furan: Contains oxygen as a heteroatom.
$2$. Thiophene: Contains sulphur as a heteroatom.
$3$. Pyridine: Contains nitrogen as a heteroatom.
$4$. Pyrrole: Contains nitrogen as a heteroatom.
$5$. Cysteine: Contains sulphur as a heteroatom.
$6$. Tyrosine: Does not contain sulphur.
The compounds containing sulphur as a heteroatom are Thiophene and Cysteine.
Therefore,the total number of such compounds is $2$.

(D) To determine which molecule does not contain nitrogen,let us examine the chemical structures of each:
$1$. Pyrrole $(C_4H_5N)$: Contains a nitrogen atom in a five-membered ring.
$2$. Piperidine $(C_5H_{11}N)$: Contains a nitrogen atom in a six-membered saturated ring.
$3$. Pyridine $(C_5H_5N)$: Contains a nitrogen atom in a six-membered aromatic ring.
$4$. Pyran $(C_5H_6O)$: Contains an oxygen atom in a six-membered ring,but no nitrogen atom.
Therefore,Pyran is the molecule that does not contain nitrogen.

(D) heteroatom is any atom other than carbon or hydrogen in an organic molecule.
$Furan$ $(C_4H_4O)$ contains an oxygen atom in its ring.
$THF$ (Tetrahydrofuran,$C_4H_8O$) contains an oxygen atom in its ring.
$4H$-Pyran $(C_5H_6O)$ contains an oxygen atom in its ring.
$Pyrrole$ $(C_4H_5N)$ contains a nitrogen atom as the heteroatom,not oxygen.
Therefore,the correct answer is $D$.

(A) The chemical formulas for the given compounds are as follows:
$1$. Thiophene: $C_4H_4S$ (contains sulfur,no nitrogen).
$2$. Pyridine: $C_5H_5N$ (contains nitrogen).
$3$. Pyrrole: $C_4H_5N$ (contains nitrogen).
$4$. Piperidine: $C_5H_{11}N$ (contains nitrogen).
Therefore,Thiophene is the compound that does not contain nitrogen.

(B) homologous series is a group of organic compounds having the same functional group and similar chemical properties,where each successive member differs by a $CH_2$ group.
The molar mass of a $CH_2$ group is calculated as:
$M(CH_2) = M(C) + 2 \times M(H) = 12 \ g/mol + 2 \times 1 \ g/mol = 14 \ g/mol$.
Therefore,the difference in molar masses of two neighbouring members of a homologous series is $14 \ g$.

(A) homologous series is a group of organic compounds having the same functional group and similar chemical properties,where each successive member differs by a $-CH_2$ (methylene) group.
Since the atomic mass of $C$ is $12$ and $H$ is $1$,the molar mass of a $-CH_2$ group is $12 + (2 \times 1) = 14 \ g/mol$.
Therefore,the numerical difference in the molar masses of any two successive members (such as the second and third members) is $14$.

(A) homologous series is a group of organic compounds having the same functional group and similar chemical properties,in which all members can be represented by the same general formula.
Each successive member of a homologous series differs from the previous one by a $CH_2$ group,which corresponds to one carbon atom and two hydrogen atoms.
Option $A$ states that members differ by two carbon atoms,which is incorrect.
Therefore,the statement in option $A$ is not true.

(A) Neighboring members of a homologous series differ by a $CH_2$ group.
The molar mass of $C$ is $12 \ g/mol$ and $H$ is $1 \ g/mol$.
Therefore,the difference in molar mass is $12 + (2 \times 1) = 14 \ g/mol$.

(A) heteroatom is an atom other than carbon or hydrogen in an organic ring structure.
$1$. Furan contains an oxygen atom $(O)$ in its five-membered ring.
$2$. Pyridine contains a nitrogen atom $(N)$ in its six-membered ring.
$3$. Thiophene contains a sulfur atom $(S)$ in its five-membered ring.
$4$. Piperidine contains a nitrogen atom $(N)$ in its six-membered ring.
Therefore,Furan is the compound that contains oxygen as a heteroatom.

(C) carbocyclic compound is one in which the ring is made up of only carbon atoms.
$Benzene$,$Naphthalene$,and $Cyclopentane$ are all carbocyclic compounds because their rings consist solely of carbon atoms.
$Pyridine$ contains a nitrogen atom within its ring structure,making it a heterocyclic compound.

(D) Tetrahydrofuran $(THF)$ is a cyclic ether with the formula $(CH_2)_4O$.
It contains an oxygen atom within the ring,making it a heterocyclic compound.
It does not satisfy $H$ückel's rule for aromaticity (it lacks a continuous system of $p$-orbitals and is not planar),therefore it is non-aromatic.
Thus,it is a heterocyclic non-aromatic compound.

(B) The structures of the given molecules are as follows:
$1$. Furan: $A$ five-membered heterocyclic ring containing an oxygen atom $(O)$.
$2$. Pyrrole: $A$ five-membered heterocyclic ring containing a nitrogen atom $(N)$.
$3$. Thiophene: $A$ five-membered heterocyclic ring containing a sulfur atom $(S)$.
$4$. Piperidine: $A$ six-membered saturated heterocyclic ring containing a nitrogen atom $(N)$.
Comparing these with the given options:
- Option $A$: Furan-$S$ (Incorrect,Furan contains $O$)
- Option $B$: Pyrrole-$N$ (Correct)
- Option $C$: Thiophene-$O$ (Incorrect,Thiophene contains $S$)
- Option $D$: Piperidine-$S$ (Incorrect,Piperidine contains $N$)
Therefore,the correct pair is Pyrrole-$N$.

(B) The given compound is bicyclo[$2.2$.$1$]heptane.
$A$ primary $(1^{\circ})$ carbon atom is a carbon atom bonded to only one other carbon atom.
In this cyclic structure,every carbon atom is bonded to at least two other carbon atoms.
Specifically,the bridgehead carbons are tertiary $(3^{\circ})$ and the other carbons are secondary $(2^{\circ})$.
Therefore,there are zero primary carbon atoms present in the compound.

(D) homologous series is a group of organic compounds having the same functional group and similar chemical properties,where each successive member differs by a $CH_2$ unit.
For the given formula $C_5H_8O_2N$,the next member in the series is obtained by adding a $CH_2$ group.
$C_5H_8O_2N + CH_2 = C_6H_{10}O_2N$.
Therefore,$C_6H_{10}O_2N$ belongs to the same homologous series.