#164 How many chiral centers are present in each of the

How many chiral centers are present in each of the - Organic Chemistry

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Free Chegg Question

How many chiral centers are present in each of the following molecular structures?

a. 
b. 
c. 
d. 

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Free Chegg Answer

The chiral center is the point or carbon atom which possesses all the four different groups attached to it. A chiral center is commonly denoted by an asterisk (*).
(a)
The structure of the given molecule is as follows:

Now we can find the carbon atom is chiral or not as described as follows:

Carbon number 1 and 4 consists of one Cl (chlorine) atom and one H (hydrogen) atom attached to them. But both these carbons consist of the same groups (CH₂-CH₂-CH-Br) at their left and right side. Thus, C-1 and C-4 carbon atoms are not chiral centers.
Carbon number 2, 3, 5, and 6 consists of two same groups (hydrogen atoms). From the definition, it gets clear that a chiral carbon is the one that has all the four different groups attached to it. No two groups can be similar. Thus, C-2, C-3, C-5, and C-6 carbon are not chiral centers.
Hence, the given structure does not show any chiral centers.

(b)
The structure of the given molecule is as follows:

Now we can find the carbon atom is chiral or not as described as follows:

Carbon number 1 consists of four different groups attached to it. It consists of one hydrogen atom, one hydroxyl (OH) group, CH₂-CH₂-CH₂ (propyl) group on its one side and CHCH₃-CH₂-CH₂ (1-methyl propyl) group on its other side. Thus, all the four groups are different, thus, the C-1 carbon is a chiral center.
Carbon number 2 consists of four different groups attached to it. It consists of one hydrogen atom, one methyl group, CH₂-CH₂-CH₂ (propyl) group on one side and CHOH-CH₂-CH₂ (1-hydroxy propyl) group on the other side. Thus, all the four groups are different, thus, the C-2 carbon is a chiral center.
Hence, the given structure shows two chiral centers.

(c)
The structure of the given molecule is as follows:

Now we can find the carbon atom is chiral or not as described as follows:

All the carbon atoms consist of double bonds. According to the definition, a chiral center should have four different groups attached to it. Since the double bonded carbon atoms consists of only three groups, thus, the structure has no chiral center. Thus, all the carbons are not chiral centers irrespective of any substituent attached to it.
Hence, the given structure does not show any chiral centers.

(d)
The structure of the given molecule is as follows:

Now we can find the carbon atom is chiral or not as described as follows:

All the carbon atoms consist of double bonds. According to the definition, a chiral center should have four different groups attached to it. Since the double-bonded carbon atoms consist of only three groups, thus, the structure has no chiral center. Thus, all the carbons are not chiral centers irrespective of any substituent attached to it.

Characteristics of Covalent Bonds

Characteristics of Covalent Bonds - Organic Chemistry

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The following important charactersitic properties of covalent bonds give us valuable information specially when we compare them in different molecules.

Bond Lengths

The critical distance between the nuclei of two bonded atoms is known as the bond length or bond distance. This distance ensures maximum stability of the covalent bond because at this distance the internuclear and interelectronic repulsions are completely balanced by the stabilizing effect of overlapping atomic orbitals. The unit which is usually used to express bond lengths is angstrom (Å is the symbol for angstrom, 1 Å = 10^-8 cm). The most important method for measuring bond lengths are X-ray diffraction (only for crystals), electron diffraction (only for gases) and spectroscopic methods. Since molecules are always vibrating the distance between atoms of a bond is not constant. Therefore, the measurements obtained are average values and different methods give different values. Bond lengths of some important covalent bonds are given in Table 1.2.

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Bond Strengths (Bond Energies) 

There are two measures of bond strengths :
(i) Bond dissociation energy (D) and
(ii) Average bond energy (E)
(i) Bond dissociation energy (D): The energy required to break a particular bond (in the gaseous phase) to give free radicals (in the gaseous phase) is called the dissociation energy, D. For example, D for H₂0(g) ~ "OH(g) + "H(g) is 118 kcal/mole. It should be noted that the same amount of energy is released during the formation of the particular bond. It is characteristic of a particular bond. The greater the bond dissociation energy, the stronger is the bond.
(ii) Average bond energy (E): It is often simply called as bond energy (E). In poly atomic molecules, bond dissociation energies (D) are not identical even where apparently equivaJent bonds dissociate. For example, when the four equivalent C-H bonds in methane dissociate successively, they have different values of D, viz., 102 kcal/mole for CH₃-H, 105 for CH₂-H, 108 for CH-H and 83 kcal/mole for C-H. Thus, the average value of the C-H bond energy in methane would be 1/4 (102 + 105 + 108 + 83) = 99.5 kcal/mole. The dissociation of a bond also depends on various factors like resonance, hyperconjugation, hybridisation, angle strain, steric effects, etc. Usually average of all the D values of equivalent bonds is taken, and this average value is called the bond energy (E). Bond energy (E) may be measured from heat of atomization, but the more usual practice is to calculate it from the heat of combustion. Bond energies (E) for some important bonds are given in Table 1.3.

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Bond energies are measures of bond strengths. Shorter bonds are stronger bonds (cf. Table 1.3) due to stronger- attraction between nuclei and electrons. Double bonds are both shorter and stronger than cr bonds, but not twice strong, because 1t overlapping is lesser than σ overlapping.

Bond Angles

All atomic orbitals (except s orbital) have directional preferences, hence covalent bonds formed by their overlapping are also directional and have an angle between them. The angle between the directions of two covalent bonds is known as the bond angle. Since s-orbital is spherical, it has no directional preference, but the three p-orbitals have different directions. They are directed at right angles to each other. Similarly, different hybrid orbitals, e.g., sp, sp² and sp³ also have directional preference. The most important methods for determining bond angles are X-ray diffraction (only for crystals), electron diffraction (only for gases) and spectroscopic methods. Due to continuous atomic vibrations in molecules, the measured bond angles are average bond angles.
Bond angles give an idea of the geometries and shapes of molecules, as they depend on bond angles. As we shall see while dealing with hybridisation (Section 1.1.12), the methane molecule has HCH bond angle of 109° 28' (the tetrahedral angle), hence it has tetrahedral shape. Similarly, ammonia and water molecules have bond angles of 107° and 104.5°, respectively, showing that they have distorted tetrahedral shapes being pyramidal in ammonia and "V" shaped in water. This suggests that nitrogen and oxygen in these compounds are in the sp3 hybrid state. Since the four pairs of electrons in ammonia and water are not equivalent, the bond angles are slightly deviated from the ideal value of 109.5°.

These deviations are understandable in the light of the following order of repulsions between electron pairs in the valence shell :
lone pair-lone pair> lone pair-bond pair> bond pair-bond pair.
This order can be explained on the basis that the lone pair is under the influence of only one nucleus, hence its electron cloud will spread out in space to a greater extent than that of a bond pair, which is under the influence of two nuclei. This greater spread over of electron cloud in space results in a greater repulsion between a lone pair and another lone pair than that between a lone pair and a bond pair, and there is least repulsion between a bond pair and another bond pair of electrons.
In methane there are four bond pairs with equal repulsive forces which completely balance each other, thus tetrahedral valency angle HCH of 109.5° is maintained.
In ammonia, there are three bond pairs and one lone pair, and since the latt.::r has a greater repulsive force, the bond pairs are forced closer together resulting in the HNH bond angle of 107°.
Similarly. in water molecule, because of two lone pairs there is greater repulsion than that in ammonia molecule, and thus forcing the bond pairs still closer together resulting in the HOH bond angle of 104.5°.

Hybridisation

The chemical properties of an element depend on the electronic configuration of the outermost shell. Carbon has four electrons in its outermost shell.
₆C = 1s²2s²2p² 

The valency of an element is usually defined as the number of half-filled orbitals present in the outermost shell of its atom. Thus, according to the ground state electronic configuration of carbon, it should be divalent, but actually it is tetracovalent in most of its compounds.
Carbon's tetravalency is explained by promoting one, 2s, electron to a 2pz orbital. Some energy must be supplied to the system in order to effect this promotion. Th~s promotion requires energy about 96 kcal/mole, but this energy is more than regained by the concurrent formation of chemical bonds.

The promotion of an electron from 2s orbital to one of the vacant 2p orbitals explains the observed valencies of this element. But there is one difficulty that three of the electrons have p-orbitals and the fourth one has s-orbital. It means we would expect to obtain three bonds of one kind and the fourth bond of a different kind; as well as the mutual angles as calculated for p-p bonds and s-p bonds ~lle 90° and 125.4°, respectively. But the bond angle is equal to 109.5° in methane and all four bonds are equivalent. In order to explain these results, the, valence bond theory has been supplemented by the concept of hybridisation. This is a hypothetical concept and has been introduced by Pauling and Slater.
According to this concept all the four orbitals of carbon (one s and three p) are mixed together and their energies redistributed in order to get the resultant orbitals having greatest directional character, because such an orbital will form strongest covalent bonds. The result of this mixing and energy redistribution is that one gets four new orbitals each having equal energy, and each being directed towards the comer of a regular tetrahedron because in this geometry, the orbitals each having one electron, are farthest apart.
This mixing and redistribution of energy is called hybridisation and the resultant orbitals are called hybrid orbitals. Because in this hybridisation there are one s-orbital and three p-orbitals, hence it is called as sp3-hybridisation and hybrid orbitals are known as sp3-hybrid orbitals.
A schematic representation of sp³ -hybridisation is shown below :

Hybridisation Rules

(1) The orbitals of similar energies take part in hybridisation.
(2) Number of hybrid orbitals formed is always equal to the number of atomic orbitals which have taken part in the hybridisation.
(3) Generally, all the hybrid orbitals are similar but they are not necessarily identical in shape. They may differ from one another mainly in shape.
(4) Hybrid orbitals form only sigma bonds.
Examples of sp, sp² and sp³ Hybridis~tion :
(1) sp or Digonal Hybridisation : In this type of hybridisation one s and one p-orbital of the valence shell of central atom of the given molecule combine to form two sp hybrid orbitals as follows:

Combination of Atomic Orbitals to Form Molecular Orbitals

Combination of Atomic Orbitals to Form Molecular Orbitals and Comparison between VB and MO theories - Organic Chemistry

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(i) Combination of s-orbitals :

Combin~tion of p-orbitals :

(i) Combination of two p-orbitals 

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(ii) Combination of two pz-atomic orbitals

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Comparison between VB and MO theories

(A) Similarities between VB and MO theories:

(i) They account for the directional nature of the bond.
(ii) Bond results by the overlapping of two orbitals of minimum energy.
(iii) Electronic charge persists in between two atomic nuclei in bond formation.
(iv) Atomic orbitals should be of same energy, should overlap and should have same symmetry.

(B) Dissimilarities between VB and MO theories :

Molecular Orbital Theory Localized Chemical Bonding

Molecular Orbital Theory in Localized Chemical Bonding - Organic Chemistry

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Molecular Orbital

The molecular orbital (MO) theory of bonding is mainly based on the work of Hund, Lennard-Jones, HUckel, and Mulliken. According to this theory the molecule is regarded as being formed by the overlap of all atomic orbitals (n) of the bonded atoms. When two atoms are brought closer to one another, their all atomic orbitals combine to give a set of new molecular orbitals (wave functions) in equivalent number (n) that encompass the entire molecule. Thus, every molecule is supposed to have orbitals associated with it in much the same way as a single isolated atom has. The Pauli's exclusion principle is applied to the MO's in the same way as it is applied to the atomic orbitals. MO's also follow Aufbau principle and Hund's rule.

According to molecular orbital theory, the atomic orbitals combine (overlap) and form a resultant orbital known as the molecular orbital in which the identity of both atomic orbitals is lost. All the electrons pertaining to, both the atoms are considered to be moving along the entire molecule under the influence of all the nuclei.
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Basic Principles of Molecular Orbital Theory 

1. When nuclei of two atoms come close to each other, their atomic orbitals interact resulting in the formation of molecular orbitals (MO). In molecule atomic orbitals of atoms lose their identity after the formation of molecular orbitals.
2. Each molecular orbital may be described by the wave function Ψ, which is known as MO, wave function, Ψ² represents the electron density.
3. Each MO wave function (Ψ) is associated with a set of quantum numbers which represent energy and shape of the occupied MO.
4. Each MO wave function (Ψ) is associated with a definite energy value. The total energy of the molecule is the sum of the energies of the occupied MO.
5. Molecular orbitals follow Pauli's exclusion principle, Hund's rule and Aufbau principle.
6. Each electron in a molecular orbital belongs to all the nuclei present in the molecule.
7. Each electron moving in the molecular orbital is having clockwise or counter-clock wise

8. Number of molecular orbitals are always equal to the number of atomic orbitals. The molecular orbitals can be obtained by the method of Linear combination of atomic orbitals (LCA,O). Let two atoms A and B form AB molecule which is hetero diatomic molecule. Their atomic orbitals are represented by Ψ_A and Ψ_B, respectively. There are following two way~ of their combination:
(i) Additive Overlap: Additive overlap is also known as positive overlap or ++ overlap. In this type of linear combination the positive lobe (i.e., the lobe having positive sign) of Ψ_A overlaps with the positiv~ lobe of Ψ_B, thus a molecular orbital is formed. This molecular orbital has lower energy than that of atomic orbitals of atom A and B due to attraction between the nuclei of A and B. Such type of molecular orbitals are known as bonding molecular orbitals (BMO) and represented as Ψ_b
(ii) Subtractive Overlap: Subtractive overlap is also known as negative overlap or +– overlap. In this type of the linear combination the positive lobe of Ψ_A overlaps with the negative lobe of Ψ_B thus a moleGular orbital is formed. This molecular orbital has higher energy than that of atomic orbitals of atom A and B due to repulsion between nuclei of A and B. Such type of molecular orbitals are known as anti-bonding molecular orbitals (ABMO) and represented as Ψ_a or Ψ
On the basis of above discussion, the formation of BMO and ABMO by the LCAO of Ψ_A and Ψ_B may be represented as :

When we show the contribution made by Ψ_A and Ψ_B in Ψ^a and Ψ^b molecular orbitals, the above equations may be written as :

The relative order of the energy of Ψ_A, Ψ_B. Ψ^b and Ψ^a is shown in Fig. 1.3.

It is to be noted that in the case of a bonding molecular orbital electron density is concentrated between two nuclei of the two atoms (Fig. 1.4), while in the case of anti-bonding molecular orbital nuclei of the two atoms come close to each other due to same charge and absence of the electron density, the nuclei repel each other (Fig. 1.5). We know that the square of the wave function (Ψ²) is known as probability of finding the electrons hence :

It is clear from the equation (5) that the value of Ψ^b₂is greater than the sum of Ψ²_A and Ψ²_B. It means that the probability of finding the electrons in the molecular orbitals obtained by the LCAO in accordance with equation 1 is greater than that in either of the AO's Ψ_A and Ψ_B In other words, the energy of Ψ_b is lower than either of ΨA and ΨB. Hence this orbital forms a stable chemical bond and named as bonding molecular orbital.
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In the same way we can say that from equation (6) that the value of Ψ²_a  is lesser than Ψ²_A  + Ψ²_B It means that the probability of finding the electron in the MO's obtained by the LCAO in accordance with equation (2) is lesser than that in either of the AO's Ψ_A and Ψ_B In other words, the energy of Ψ_a is higher than either of Ψ_A and Ψ_A Hence, this orbital catlnot form a stable chemical bond and is named as anti-bonding molecular orbital.