B.tech. ii engineering chemistry Unit 1 atoms and molecules

1. Course: B.Tech.
Subject: Engineering Chemistry
Unit: I

2.  Imagine a particle strictly confined between two
``walls'' by a potential energy that is shown in
the figure below.
 confines the particle to the region .
1

3.  Mathematically, the potential energy is expressed as
 If the potential is infinite outside the box, then there is
zero probability that the particle will be found there.
 Thus, we require outside the box, and this can
only happen if at the boundaries
 and .

4.  Since outside the box, we only need to
integrate between 0 and L , so that
 Since we already know that outside the box,
we only need to solve the Schrödinger inside the box
where .
 In this case, the Schrödinger looks like the free-particle
equation we already wrote down

5. Rearranging gives
We have already seen that the solutions are sin or cos
functions.
In fact, we can easily show that the solution of this
differential equation must be either

6. Where A and B are arbitrary constants. But since we need , the
only solution that is consistent with the boundary condition is the
sin solution. Thus, we take
It's a simple matter to verify that this function satisfies the differential
equation:

7. At this point, all we have is a general solution to the
equation, but we still do not know the allowed values of E .

8.  But, there is also still one boundary condition we have
not yet enforced. We need . This requires
 In order to satisfy this, we can take any point where the
sin function vanishes. We know that for
any value of n . Thus, our boundary condition is
equivalent to

9.  Solving this equation for E, gives us the allowed
energies:

10.  Angular momentum, moment of momentum, or
rotational momentum is a measure of the amount of
rotation an object has, taking into account its mass,
shape and speed.
 It is a vector quantity that represents the product of a
body's rotational inertia and rotational velocity about a
particular axis.
 The angular momentum of a system of particles (e.g. a
rigid body) is the sum of angular momenta of the
individual particles.

11.  For a rigid body rotating around an axis of symmetry
(e.g. the wings of a ceiling fan)
 The angular momentum can be expressed as the
product of the body's moment of inertia, I,
 (i.e., a measure of an object's resistance to changes in
its rotation velocity) and its angular velocity, ω.

12.  In quantum mechanics, angular momentum is
quantized – that is, it cannot vary continuously, but
only in "quantum leaps" between certain allowed
values.
 For any system, the following restrictions on
measurement results apply, where is the reduced Planck
constant and is any direction vector such as x, y, or z:

13.  The orbital angular momentum is quantized according
to the relationship:
 It is a characteristic of angular momenta in quantum
mechanics that the magnitude of the angular
momentum in terms of the orbital quantum number is
of the form

14.  that the z-component of the angular momentum in
terms of the magnetic quantum number takes the form
 This general form applies to orbital angular
momentum, spin angular momentum, and the total
angular momentum for an atomic system.

15.  The relationship between the magnitude of the angular
momentum and its projection along any direction is
space is often visualized in terms of a vector model.
 The orbital angular momentum of electrons in atoms
associated with a given quantum state is found to be
quantized in the form

16.  This is the result of applying quantum theory to the
orbit of the electron.
 The solution of the Schrodinger equation yields the
angular momentum quantum number. Even in the case
of the classical angular momentum of a particle in
orbit,
 the angular momentum is conserved. The Bohr theory
proposed the quantization of the angular momentum in
the form

17. The spectroscopic notation used for characterizing energy
levels of atomic electrons is based upon the orbital quantum
number.

18.  When the orbital angular momentum and spin angular
momentum are coupled, the total angular momentum is
of the general form for quantized angular momentum
 where the total angular momentum quantum number is

19.  This gives a z-component of angular momentum
 As long as external interactions are not extremely
strong, the total angular momentum of an electron can
be considered to be conserved and j is said to be a
"good quantum number".

20.  Consider the hydrogen atom as a proton fixed at the
origin, orbited by an electron of reduced mass .
The potential due to electrostatic attraction is
 ___________(1)
 in SI units. The kinetic energy term in the Hamiltonian
is
 ____________(2)

21.  so we write out the Schrödinger equation in spherical polar
coordinates as


_(3)
 It happens that we can factor into ,
where are again the spherical harmonics. The
radial part then can be shown to obey the equation


22.  which is called the radial equation for the hydrogen
atom. Its (messy) solutions are
 Where , and is the Bohr radius , The
functions are the associated Laguerre
functions. The hydrogen atom eigenvalues are

23.  Atomic orbitals are (energy) states or wave forms of
electrons in the atom.
 If we insist on the particle nature of electrons, then the
probability of finding an electron in an atomic orbital is
proportional to the square of the wave function.
 The values of the wave function can be either positive
or negative, but the probability is always a positive
value.

24. The 1s, 2s, and 3s orbitals
First Energy Level: ( n = 1 )
Number of Orbitals: n2 = 12 = 1
First Orbital is Designated as " s "
So, First Energy Level is called the "1s" Orbital.

25. •Second Energy Level: ( n = 2 )
•Number of Orbitals: n2 = 22 = 4 ;[ 2s, 2px, 2py, 2pz ]
• "p" Orbitals shapes look like "dumbbells" which lie along each axis (x,y,z)
An Orbital DOES NOT describe a "house" in which an electron roams about. The orbital is
a description of an electron wave.
The 2p orbitals

27. The 3d orbitals
•Third Energy Level: ( n = 3 )
•Number of Orbitals: n2 = 32 = 9 ; [ 3s, 3px, 3py, 3pz, & 5 - 3d ] (there are five "3d" orbitals)

29. The 4fxyz orbital, one of the seven 4f orbitals
3
•Fourth Energy Level: ( n = 4 )
•Number of Orbitals: n2 = 42 = 16 ; [ 4s, 4px, 4py, 4pz, 5 - 4d, 7 - 4f ]
3

30.  Electron density is the measure of the probability of
an electron being present at a specific location.
 In molecules, regions of electron density are usually
found around the atom, and its bonds. In de-localized
or conjugated systems, such as phenol, benzene and
compounds such as hemoglobin and chlorophyll, the
electron density covers an entire region, i.e., in benzene
they are found above and below the planar ring.

31.  This is sometimes shown diagrammatically as a series
of alternating single and double bonds. In the case of
phenol and benzene, a circle inside a hexagon shows
the de-localized nature of the compound.
 In quantum chemical calculations, the electron density,
ρ(r), is a function of the coordinates r, defined so
ρ(r)dr is the number of electrons in a small volume dr.

32.  For closed-shell molecules, can be written in terms of a
sum of products of basis functions, φ:

33.  A molecular orbital diagram, or MO diagram, is a
qualitative descriptive tool explaining chemical
bonding in molecules in terms of molecular orbital
theory in general and the linear combination of atomic
orbitals (LCAO) molecular orbital method in particular.
 A fundamental principle of these theories is that as
atoms bond to form molecules, a certain number of
atomic orbitals combine to form the same number of
molecular orbitals, although the electrons involved may
be redistributed among the orbitals.

34.  Molecular orbital diagrams are diagrams of molecular orbital (MO)
energy levels, shown as short horizontal lines in the center, flanked
by constituent atomic orbital (AO) energy levels for comparison,
with the energy levels increasing from the bottom to the top.
 Lines, often dashed diagonal lines, connect MO levels with their
constituent AO levels. Degenerate energy levels are commonly
shown side by side. Appropriate AO and MO levels are filled with
electrons symbolized by small vertical arrows, whose directions
indicate the electron spins.
 For a diatomic molecule, an MO diagram effectively shows the
energetics of the bond between the two atoms, whose AO unbonded
energies are shown on the sides.
 For simple polyatomic molecules with a "central atom" such as
methane (CH4) or carbon dioxide (CO2), a MO diagram may show
one of the identical bonds to the central atom.

36.  The smallest molecule, hydrogen gas exists as
dihydrogen (H-H) with a single covalent bond between
two hydrogen atoms.
 As each hydrogen atom has a single 1s atomic orbital
for its electron, the bond forms by overlap of these two
atomic orbitals.
 In above figure the two atomic orbitals are depicted on
the left and on the right.
 The vertical axis always represents the orbital energies.

37. 2

38.  Molecular orbitals of Hydrogen Fluoride are mostly
derived from the Fluorine 2s and 2p atomic orbitals
respectively.
 Qualitatively, the high fluorine character of these
orbitals is a consequence of the high electronegativity
of fluorine as compared to hydrogen.
 The 1 π orbitals are non-bonding and Fluorine 2p in
character. Finally, the anti-bonding "3-sigma" orbital is
primarily H 1s in character. The use of nodes to give a
general idea of the energy ordering still works. "1-
sigma" has no nodes, "2-sigma" and "1 π" have one
node, and "3-sigma" has two nodes.

40. The type of chemical bond developed between the two
combining atoms depends upon the way these atoms
acquire a stable noble gas configuration.
Elements may combine through any one of the following
ways to form stable compounds.
i. By the transfer of electrons from the atom of an
element to the atom or atoms of another. This gives
rise to an ionic (or electrovalent) bond.
ii. By mutually sharing the electrons. This gives rise to a
covalent bond.
iii. By one-sided sharing of electrons. This gives rise to a
coordinate bond.

41. This type of bond is established by transfer of
an electron from one atom to another.
In an ionic bond, one atom loses an electron
to another atom, forming a cation and anion,
respectively. And, they attract towards each
other ,by electrostatic attraction they combined
togather.
An IONIC BOND is an electrostatic interaction
that holds together a positively charged ion (cation)
and a negatively charged ion (anion).

42. A has one electron in excess and B has one electron short than the stable
octet.
Therefore, A transfers an electron to B and in this transaction both atoms
acquire stable electronic configuration.
And they held togather by electrostatic attraction.

44. In table salt, for example, a valence electron from a sodium
atom is transferred to a chlorine atom, forming Na+ and Cl-.
Because the ions have opposite charges, they are attracted
to each other. The loss of a valence electron and the
attraction to the atom that took it happen simultaneously.
4

45. A covalent bond is formed between two atoms (similar
or dissimilar) by a mutual sharing of electrons. The
shared pairs of electrons are counted towards the stability
of both the participating atoms.
A covalent bond is defined as the force of attraction
arising due to mutual sharing of electrons between
the two atoms.
The combining atoms may share one, two or three pairs
of electrons.

46. When the two atoms combine by mutual sharing of electrons,
then each of the atoms acquires stable configuration of the nearest
noble gas. The compounds formed due to covalent bonding are
called covalent compounds.
Covalency
The number of electrons which an atom contributes towards
mutual sharing during the formation of a chemical bond is called
its covalency in that compound.
Thus, the covalency of hydrogen in H2 (H - H) is one; that of
oxygen in O2 is two (O = O), and that of nitrogen in N2 is three (N
 N).

47. 4

48. If a hydrogen atom is bonded to a highly electronegative
element such as fluorine, oxygen, nitrogen, then the shared
pair of electrons lies more towards the electronegative
element. This leads to a polarity in the bond in such a way
that a slight positive charge gets developed on H-atom, viz.,
H+ d : O- d H+ d : F- d H+ d : N- d
This positive charge on hydrogen can exert electrostatic
attraction on the negatively charged electronegative atom of
the same or the other molecule forming a bridge-like structure
such as
Xd - - Hd+ × × × × × × Yd- - Hd+
where X and Y are the atoms of strongly electronegative
elements.
The bond between the hydrogen atom of one molecule and
a more electronegative atom of the same or another
molecule is called hydrogen bond.

49. Hydrogen fluoride (HF).
Water (H2O).

50. The relatively weak attractive forces that act on neutral atoms
and that arise because of the electric polarization induced in
each of the particles by the presence of other particles.
Inter molecular: between molecules (not a bond)
Intra molecular: bonds within molecules(stronger)

51. 1) dipole-dipole
2) dipole-induced dipole
3) dispersion

52. -Two polar molecules align so that d+ and d- are
matched (electrostatic attraction)
Ex: ethane (C2H6) vs. fluromethane (CH3F)

53. Fluoromethane (CH3F)
H H
H C F H C F
H H
d-
d-d+ d+
Ethane (C2H6)
H H H H
H C C H H C C H
H H H H
Dipole-Dipole
NOT Dipole-Dipole

54. A dipole can a temporary dipole to
form in a non-polar molecule
The molecules then line up to match
d+ and d- charges.

55. H Cld+ d- Are-
e-
e-
e-
e-
e-
e-
e- e-
e-
e- e-
e-
e-
e-
e-
e-
e-
A DIPOLE
(it’s polar)
non-polar
INDUCED
DIPOLE
d-d+
Dipole – Induced Dipole
(weak and short-lived)

56. A temporary dipole forms in a
non-polar molecule…
which leads to…
a temporary dipole to form in ANOTHER
non-polar molecule
Dispersion is the ONLY intermolecular
attraction that occurs between non-polar
molecules

57. Cl-Cle-
e-
e-
e-
e-
e-
e- e-
e-
e-
e-
e-
e-
e-e-
e-
e-
e-
non-polarINDUCED
DIPOLE
d-d+
TEMPORARY
DIPOLE
non-polar
Cl-Cle-
e-
e-
e-
e-
e-e- e-
e-
e-
e-
e-
e-
e-
e-
e- e-
d-d+
Dispersion
(weakest and very short-lived)
5

58.  Electronegativity is a measure of the tendency of an
atom to attract a bonding pair of electrons.
 Electronegativity, symbol χ, is a chemical property
that describes the tendency of an atom or a functional
group to attract electrons (or electron density) towards
itself.

59.  An atom's electronegativity is affected by both its
atomic number and the distance at which its valence
electrons reside from the charged nucleus.
 The higher the associated electronegativity number, the
more an element or compound attracts electrons
towards it.

60.  2 bonded pairs
 0 lone pairs
 Bond angle of 180
 Examples:
 BeCl2,
 CO2,
 HCN,
 C2H2

62.  3 bonding pairs
 0lone pairs
 Bond angle of 120
 Examples:
 BF3
 SO3
 NO3-
 CO32-

64.  4 bonding pairs
 0 lone pairs
 Bond angle of 109.5
 Examples
 NH4
+
 SO4
2-
 PO4
3-
 Ni(CO)4
 CH4

66.  3 bonding pairs
 1 lone pair
 Bond angle of 107
 Examples
 CO3
 PH3
 SO3
2-
 NH3

67. 6

68.  6 bonding pairs
 0 lone pair
 Bond angle of 90
 Example
 SF6

70. 7

71. 1.http://www.chemguide.co.uk/atoms/properties/atomorbs.ht
ml
2.http://www.chem.latech.edu/~upali/chem281/notes/Ch2-
MO-Theory.pdf
3. http://www.avon-chemistry.com/electron_lecture.html
4.http://www.wpclipart.com/energy/atom/atomic_structure.pn
g.html
5.Essentials of Physical chemistry by Bahl & Tuli
6.http://chemwiki.ucdavis.edu/Inorganic_Chemistry/Molecula
r_Geometry
7.http://www.elmhurst.edu/~chm/vchembook/222octahedral.h
tml