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Quantum Mechanical Model of Atom :: Principle Quantum Number ‘n’ , Azimuthal Quantum Number ‘p’ , Magnetic Orbital Quantum Number ‘mi’ , and Electron Spin Quantum Number (ms)

Quantum Mechanical Model of Atom

Branches of science which explain duel behavior of Metter is called quantum mechanics .
ð Quantum mechanics independently developed by Werner Heisenberg and Erwin Schrodinger (1926)
Fundamental equation developed by Schrodinger (won Nobel Prize 1933)
Equation for a system (atom or molecules was energy does not change with time)

Principle Quantum Number ‘n’

·        It is a positive Integer with value of n = 1,2,3......
·        It determine size and energy of orbital
·        It also identifies the shell with increase in an , number of allowed orbital increase. And given by n2
N      =1,    2,    3,    4........
Shell = k,    l,    m,    l......
·        Size of orbital increase with increase in an  n.

             Azimuthal Quantum Number ‘p’

·        It is also known as orbital angular momentum or subsidiary quantum no.
·        It defined 3d shape of orbital of orbital
·        For given value of n possible value of  
        L= 0,1,2,3,4,5,----------(n-1) ,
                    Ex :- if   n=1   then   l=0
                             if   n=2   then   l=0,1
                             if   n=5   then   l=0,2,3,4
·        Each shell consists of one or more sub-shells or sub-shells.
·        No of sub-shells = value of  n
If  n= 1  then  1 sub-shell =  (l=0)
If  n= 2  then  2 sub-shell =  (l=0,1)
If  n= 3  then  3 sub-shell =  (l=0,1,2)
·                      Value of    l =  0,  1,  2,  3,  4,  5  ----------
     Notation for sub-shell= s, p, d,   f,   g, h--------------
·        Sub-shell notation
n
l
Sub-shell   notation
1
0
1s
2
0
2s
2
1
2p
3
0
3s
3
1
3p
3
2
3d
4
0
4s
4
1
4p
4
2
4d
4
3
4f

 Magnetic Orbital Quantum Number ‘mi

·        This quantum no (mi) gives information about orientation of  the  orbital .
·        Ml = (2l+1) i.e. if value of   l  is  1 then value of  ml = 2×1+1=3=(-1,0,1)
Value of p
0
1
2
3
4
5
Sub-shell notation
S
P
D
F
G
H
No of orbital’s
1
3
5
7
9
11

Electron Spin Quantum Number (ms)

·        Proposed by G. Uhlen beck & S. Goodsmit (1925)
·        Electrons spins around its own axis
·        Ms have two value +1/2 & -1/2
·        Ms gives information about orientation of the spin of   the electron.

Dual Behaviour of Matter and Heisenberg’s Uncertainty Principle

Dual Behaviour of Matter

=>  Explain by de Broglie (1924)
=>  He explain that matter also behave like radiation and exhibit dual behavior means both like particle and wave like properties .
=> Relation
dual behavior of matter
   Where  l =  wavelength.
             m = mass of particle ,
             v = velocity of particle,
              p = momentum

Heisenberg’s Uncertainty Principle

 Given by Werner Heisenberg (1927)
He explain that it is impossible to determine simultaneously the exact positive and exact momentum (or velocity) of an electron
Mathematical explanation
Heisenberg uncertainty principle
                                     
     Where,  Dx= uncertainty  in position
                   
                   DVx  = uncertainty in velocity or momentum

Bohr’s model for hydrogen atom and Limitation of Bohr’s model

Bohr’s model for hydrogen atom

=>  Explain by nails Bohr (1913).
=>  Postulates for Bohr’s modal are,
1.     Electron in hydrogen atom move around nucleus in circular path of fixed radius and energy. these paths are called orbits
2.     Energy of e does not change with time.
However, when electron move from lower to higher stationary state it absorbed sub amount of energy and energy release when it comes back.
3.     Frequency of radiations emitted or absorbed when transition of e occur is given by
bohr model
Where, e1 & e2 is lower & higher energy state.
4.     Angular momentum of n electron in given stationary state is given by
bohr model
[Where n =1,2,3.....]

Limitation of Bohr’s model

1.     Bohr model fail to explain finer detail of hydrogen atom spectrum observed by spectroscopic, techniques.
2.     It fails to explain spectrum of other atom except hydrogen atom.
3.     It fails to explain splitting of the spectral lines in presence of electric (stark effect) or magnetic field ( Zeeman effect )
4.     Fell to explain formation of molecules from atoms by chemical bonding.

Photo electric effect

Photo Electric Effect

=>  given by H. Hertz(1887)
=>  When a beam of light strike a metal surface then electrons were ejected. This phenomena is known as photo electric effect.
1.     Electrons ejected from metal surface when beam of  light strike the metal surface
2.     Number of electron ejected is directly proportional to intensity (or brightness) of light
3.     There is characteristic minimum frequency (n0 threshold frequency) below which photoelectric effect is not observed.
4.     If n > n0 then electrons comes out with kinetic energy which increases with increase in frequency of light.
Kinetic energy of ejected electrons is given by-
h n = h n0+ ½(meV2)

Wave nature of electromagnetic radiations and Particle nature of electromagnetic radiation

Wave nature of electromagnetic radiations: -

First explanation gives by James Maxwell (1870)
1)    Oscillating magnetic & electric fields produced by the oscillating charged particles are perpendicular to each other and both also perpendicular to the wave direction of propagation.
2)    These waves do not require medium i.e. electromagnetic wave can travel in vacuum.
3)    Electromagnetic radiation differs from one another in frequency or wavelength gives electromagnetic spectrum.
4)    Different units are used to represent electromagnetic radiation.
                                 n = frequency, 
                                l = wavelength.

Particle nature of electromagnetic radiation :-   

                                                                        Also known as Planck’s  Quantum theory
=> Planck suggested that the atoms and molecules can absorb or emit energy in discrete quantities nit in continuous manner. Planck gives it name as quantum. Energy (E) of  quantum of  radiation is directly proportional to its frequency(n)
 i.e.            E=hn
Where,      h = planks constant = 6.626× 10-34 js

11 Class Chapter 5- States Of Matter

States Of Matter

·       Water exists in three state i.e. solid (ice), liquid (portable water), gas (steam, vapors).
·       In these three states water has different physical properties but same chemical composition i.e. H2O
·       Also characteristics of these states of water depend on the molecular energy and how molecules aggregate.
·       As molecules change its physical state (from liquid to gas, gas to liquid, solid to gas etc.) there is no change in chemical properties of the substance but some changes may occur in rate of chemical reaction.

Intermolecular Forces:

                             These are forces of attraction and/or repulsion between the interacting particles i.e. atom or molecules.
Dutch Scientist J. Van der Waals (1837-1923) explains deviation of the real gases from ideal behavior with intermolecular forces, so intermolecular forces are also called as van der waals forces.
Example: Hydrogen bonding which is strong dipole-dipole interaction.

Dispersion Forces

                             If an atom gets instantaneous dipole (i.e. Atom has more electron density in right or left hand side) then its nearby atom become induced dipole, so these two temporary dipole attract each other. This attraction force is known as dispersion forces.
·       As these forces were first proposed by F. London so these forces are also known as London forces.

Dipole-Dipole Forces

                                    This type of force act between the molecules which have permanent dipole. Dipole of these molecule possess some partial charges (denoted by delta that is delta positive or delta negative)
Example: HCl molecule, where H possess delta positive and Cl possess delta negative.

Dipole-Induced Dipole Forces

                                             These attractive forces act between polar and non-polar molecules where polar molecules have permanent dipole, which induced the dipole and non-polar molecule by deforming electronic cloud of non-polar molecule.
·       As polarisability increases, strength of the attractive interaction also increases.

Hydrogen-Bond:  

                           It is a type of dipole-dipole interaction present in molecules with high polar N-H, O-H and H-F bonds.

Thermal Energy

                           It is the energy of the body arise due to the motion of its atoms and molecules.
·       Thermal energy is directly proportional to temperature of the substances.

Intermolecular forces v/s Thermal interactions

·       Intermolecular forces make molecules of the substance keep together.
·       While thermal energy of the substance make molecules keep apart.
·       These two (thermal energy and intermolecular forces) decides collectively the states of matter.
·       If intermolecular forces predominance then
                                      Gas->Liquid->Solid
·       If thermal energy predominance then
                                      Solid->Liquid->Gas

What is Troposphere

                                   It is the lowest layer of the atmosphere held to surface of the earth by gravitational forces where we live. It contains O2, CO2, N2 and water vapors etc.

Gaseous State

                     Only 11 elements ( H, O, N, F, Cl, He ,Ne, Ar, Kr, Xe, Rn exists in gaseous state under normal conditions.

Characteristic Physical Properties Of Gases

·       Gases are highly compressible.
·       Gases exert the equal pressure in all direction.
·       As compared to solid and liquids, gases have much lower density.
·       Gases don’t have definite (fix) shape and volume.
·       Gases mix completely and evenly in all proportions.

Gas Laws

Boyle’s law

                   It is also known as Pressure Volume relationship.
As per Boyle’s law, ”At constant temperature and fixed amount of gases in no. of moles, its pressure varies inversely with its volume.”
Mathematically, at constant T and n,
P1/V ……………..1
P = k1 x 1/V   =   k1/V ………..2
Where, P = Pressure, V = Volume and k = proportionality constant and value of k1 depends upon Pressure P and Volume V.
Also,    K1 = PV ………..3
According to above relation, product of pressure P and volume V remains constant, if we fixed the amount of gas at constant temperature. You read these first class chemistry notes for classes 11 at online classes by www.ChemistryNotesInfo.com.
So,  P1V1 = P2V2 = Constant  ………4
Then,   P1/ P2 = V2/V1   ……………..5
As we know, Density is equal to mass divided by volume i.e. d=m/V
So, V = m/d …………6
From equation 2 & 6,
P = k1d/m
·       d = (m/k1)/P = k’P ……………7
Where, k’ = m/k1

Charle’s Law

               This is also known as Temperature and Volume relationship.
As per Charle’s law, “At constant pressure and fixed mass of gas, Volume is directly proportional to Absolute temperature.”
Mathematically, at constant P and n,
                             V  online classes T
Also, V=k2T
Where, K2 is a constant.

Thermodynamic Scale:  

                                       Kelvin scale of the Temperature is known as the Thermodynamic Scale which is utilized in many scientific works.

Kelvin Scale

                   To obtain temperature in Kelvin scale we add 273.15 (generally 273) in Celsius temperature.
i.e. K= 273.15 + °C (degree  Celsius)

Gay Lussac’s Law

                         This law is also known as Pressure and Temperature relationship.
According to Gay Lussac’s Law “At constant Volume and fixed amount of gas, pressure is directly proportional to temperature.”
Mathematically, at constant V and n,
                             P  online classes T
Also, P=k3T
Where, K3 is a constant.

Avogadro’s Law

                        This law is also known as Volume and amount relationship.
According to Avogadro’s law “Equal volume of all the gases under same condition of pressure and Temperature contain equal no. of molecules.”
V  universities n ………….1
V=k4n ……………2
Where, V is volume, k4 is a constant and n is no. of moles of gas.

Avogadro’s Constant

One mole has 6.022x1023 no. of molecules which is called as Avogadro’s constant. As we know, mole is equal to mass divided by molar mass.
So n = m/M  ……………..3
Then from equation 2 & 3
V = k4(m/M)
M = k4. m/V
M = k4.d    {here . represents multiplication}
Where M is molar mass, m is mass and V is volume, K4 is constant and d is density.

Ideal Gas Equation

                              Combination of 3 laws (Boyles Law, Charles Law and Avogadro law) gives a single equation (PV=nRT) called as Ideal gas equation.
Mathematically,
According to Boyle’s Law; at constant T and n,
V 1/P ……….1
According to Charles Law; at constant P and n,
V T ……….2
According to Avogadro Law; at constant T and n,
V n  ……….3
From equation 1, 2 and 3; we get,
V nT/P ……….4
Or, V =R nT/P ……….5
Also, PV = nRT  …………..6
Then, R = PV/nT  ………..7
Where, R is a gas constant which is same for all gases and known as Universal Gas Constant and equation 6, PV = nRT is known as Ideal Gas Equation.

Equation Of State

                            Ideal gas equation is also known as equation of state because it gives relationship between 4 variables i.e. P, V, n and T. which describes state of any gas.
Let  if pressure, volume and temperature of fixed amount of ideal gas changes from P1, V1, T1 to P2, V2, T2  then,
P1V1/T1 = nR …………..8
P2V2/T2 = nR …………..9
So, from equation 8 & 9, we get
P1V1/T1 = P1V1/T1 ………..10
This above equation (eq. 10) is called Combined Gas Law.
Density And Molar Mass Of Gaseous Substances:
As per Ideal Gas Equation,
PV=nRT
Then, n/V = P/RT
On replacing n by m/M (as mole n= mass m/ molar mass M); we obtain,
m/MV=P/RT
On replacing m/V by density d; we obtain,
d/M=P/RT
Also, on rearrangement,
M = dRT/P
Where, M is molar mass, d is density, R is gas constant, T is temperature and P is pressure.

Dalton Law Of Partial Pressure:

According to Dalton law of partial pressure, “Total exerted pressure by mixture of all non-reactive gases is equal to the sum of partial pressure of all individual gases.”
At constant temperature T and Volume V
                             Ptotal = p1 +p2 +p3…………..
Where, Ptolal = total exerted pressure of mixture of all gases.
p1, p2, p3 etc. is pressure exerted by individual gases known as partial pressure.

Aqueous Tension

                           It is exerted by the saturated water vapors.
Pdrygas = Ptotal – Aqueous Tension

Partial Pressure In Terms Of Mole Fraction

                                                    Let at T temperature, 3 gases of Volume V exert the partial pressure p1, p2, p3. Then as per ideal gas equation,
p1=n1RT/V
p2=n2RT/V
p3=n3RT/V
Where, n1, n2, n3 are no. of moles.
 Also, according to Daltons law of partial pressure
Ptotal = p1 +p2 +p3
Or, Ptotal = n1RT/V + n2RT/V + n3RT/V = (n1+n2+n3)RT/V
And, on dividing p1 by PTotal , we obtain
P1/ PTotal={n1/(n1+n2+n3)}{RTV/RTV}
P1/ PTotal=n1/(n1+n2+n3) = n1/n = x1
Where, n= n1+n2+n3 and x1 is mole fraction of first gas.
So, p1=x1PTotal
Similarly, p2=x2PTotal
P3=x3PTotal
Then, general equation is written as-
Pi=xiPTotal
Where, pi is partial pressure of ith gas.
xi is mole fraction of ith gas.

Kinetic Molecular Theory Of Gases

                                                     The postulates or assumption of Kinetic molecular theory of the gases are as follows:

  • ·       Gases contain atoms or molecules, as large no. of identical particles. These atoms or molecules are at large distances from each other, so that volume of gases is very high as compared to actual Volume of all molecules of gases. ‘Great compressibility of the gases is explained by these assumptions’.

  • ·       Gases occupy all available space by expansion because at ordinary pressure and temperature there are no attractive forces between gas particles.

  • ·       Gas particles always move in random and at constant motion because if gas particles are at rest and they occupy fixed positions then gas would have fixed shape, which is not observed at all.

  • ·       Gas particles move in straight lines in all the possible directions. During random motion these particles collide with each other and also collide with the walls of the container of the gas. As a result of this collision of gas particles with wall of the gas container pressure is exerted by gas.

  • ·       Collision between the gas molecules is perfectly elastic. It means total energy of the molecules don’t change that is It remains same before and after collision. Individual energy of the molecules may change due to exchange of energy between the colliding molecules, but sum of energies of all molecules remains same.

  • ·       Molecules of the gas move with the different speeds and their individual speed goes on changing due to collision of molecules but at particular temperature, distribution of speeds of molecules remains constant.

  • ·       Kinetic energy of molecules (of the gas) is directly proportional to absolute temperature because on heating gas at fixed volume, its pressure increases. As on heating molecules moves with more speed and strike with walls of the container more rapidly, so exerts more pressure.

Behavior Of Real Gases

Deviation From Ideal Gas Behavior

                                                   When we do different experiments, we find that real gases don’t follow PV=nRT Equation of ideal gases. So real gases don’t follow Boyle’s law means, if we plot graph between PV and P then we don’t get parallel straight line at all pressures with X-axis.
Graph

Real gases in above graph show some significant deviation from ideal gas behavior. As we see-
1) Dihydrogen and helium shows positive deviation means PV value increases with increase in pressure.
2) Methane and Carbon monoxide shows negative deviation and positive deviation means first with increase in pressure, PV value decreases and reaches the minimum then starts increasing with increasing pressure.

  • ·       Real gases don’t follow Boyle’s law, Charles law and Avogadro’s law perfectly under the all conditions, So real gases liquefy when they cooled and compressed.

  • ·       Under very high pressure attraction forces start operating between molecules of gases so pressure exerted by real gases is lower than that of ideal gas, because in ideal gas there is no attraction force exists at high pressure.

Pideal=Preal+(an2/V2) …………..1
Preal = observed pressure
an2 /V2 = correction term
Where ‘a’ is constant

  • ·       Under very high pressure gas molecule don’t move freely but restricted to (V-nb) Volume, Where nb is actual Volume occupied by the gas molecules themselves. So we can write gas equation for real gases as :

{P+(an2/V2)}(V-nb)=nRT …………2
Equation 2 is known as van der walls equation.
Where n is no. of moles of the gas.
a and b is vander walls constant and value depends on gas characteristics.

  • ·       Deviation from ideal behavior from real gases is measured with compressibility factor z.

Compressibility factor,
 z = PV/nRT  …………3
If z =1 gas is ideal gas because PV = nRT
If z > 1 or z<1, gas is real gas and If z > 1 then it is more difficult to compress gas.

  • ·       Boyle’s temperature or Boyle’s point is a temperature at which real gas behaves like ideal gas under appreciable range of pressure.

  • ·       Compressibility factor is also defined as ratio between actual molar volume and calculated molar volume

                             i.e. z = Vreal / Videal
As per above discussion we say that gases behave ideally -

  • 1.   At low temperature and high pressure.

  • 2.   or, If volume occupied by the gas is very large therefore volume occupied by gas molecule can be neglected in comparison to it.

Liquification Of Gases

·       The process of converting gas into liquid is known as liquification of gas
·       The highest temperature at which gas start liquefying is known as critical temperature (Tc)
·       Volume of one mole of the gas at this critical temperature is known as critical volume (Vc)
·       Pressure at this critical temperature is known as critical pressure (Pc)
·       Gases are cooled below their critical temperature for the liquefication of gases
·       When we apply cooling as well as compression, gases liquefy easily

Liquid State

Intermolecular forces in liquids are stronger than in gases. Liquid have definite (fix) volume and they can flow and take the shape of the container in which these liquids are stored. These online education classes degree notes are published by ChemistryNotesInfo.com and hosted at ChemistryNotesInfo.blogspot.com Vapour pressure, viscosity, surface tension are some physical properties of liquids which are described below-

Vapor Pressure

                    Pressure exerted by the vapors on the walls of the container containing liquid is known as vapour pressure.
·       Vaporization depends on temperature
·   Vapour pressure at which equilibrium is achieved between liquid phase and vapor phase is known as Saturated Vapour Pressure or Equilibrium Vapour Pressure
·      Boiling is a condition of free vaporization means vapor extends freely into the surroundings.
·       Boiling temp. at 1 atm pressure is known as Normal Boiling Point
·       Boiling temp. at 1 bar pressure is known as Standard Boiling Point
·       Temp. at which clear boundary between liquid and vapors disappear is known as Critical Temperature

Surface Tension

                         Liquids tends to minimize their surface area because molecules of the liquid on the surface experience net attractive force towards the interior of the liquid, this characteristic property of the liquid is known as Surface Tension.
Example: Mercury do not form thin film and capillary action

Viscosity

              It is a measure of resistance to flow that arise due to internal friction between the layers of liquid (or fluid), when they slip over one another, during the flow of liquid or fluid.
·       Force required to maintain flow of liquid layers is-
                             F=online classesAdu/dz
Where, A is area of contact,
du/dz is velocity gradient,
is coefficient of viscosity.
SI unit of is “Newton second per square meter (Nsm-2)”
cgs unit of is “poise”
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