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Chemistry Formula for Atomic Structure Part 2

Chemistry Formulas for Atomic Structure

Chemistry Formulas from Bohr’s Model of Atom

·         Angular momentum of electron in nth orbit


Where, m = Mass of the electron,
            v = velocity of electron,
            r = radius of the orbit,
            h = Planck’s constant,
            n = no. of orbit in which electron is present,

·         Energy of electron in nth orbit

            
           Where, Z = Atomic No. of Electron,

·         Energy absorbed or released in an electron jump ( E)

 

·         Radius of orbits of hydrogen like species

              
         For hydrogen atom Z = 1, for first orbit n = 1,
         On substituting values of the constants
         h = 6.62x10-27erg sec,
         m = 9.1x10-28g,
         e = 4.8x10-10
     we get,
    r = 0.529 Å
So, radius of first orbit of hydrogen atom is 0.529 Å.

·         Radius of nth orbits of hydrogen like species

rn = 0.529n2/Z Å

·         Velocity of electron in nth orbit

          
      On substituting values of the constants
      We get,

·         No. of revolution per second made by an electron around the nucleus of atom

·         Energy of electron in nth orbit (En)

       
        On substituting values of the constants
        We get,          
            
         In general,
                          

·         Energy of electron in a Hydrogen Atom in different energy levels

Energy Level
E (Joules/atom)
E (eV/atom)
E (kcal/mol)
1
-21.79x10-19
-13.6
-313.5
2
-5.42x10-19
-3.4
-78.4
3
-2.41x10-19
-1.51
-38.84
4
-1.36x10-19
-0.85
-19.6
5
-0.87x10-19
-0.544
-12.5
Infinite
0
0
0

·         Frequency or wave length of emitted radiation

          
            Where, λ = wavelength of emitted radiations
                        R = Rydberg constant for Hydrogen atom

·         Number of spectral lines produced when an electron drops from nth level to ground level

          

Chemistry Formulas from Photoelectric Effect

·         Planck’s Relationship,

E = hv

·         Total energy,

Total Energy = (mv2/2) + w
Where, w = energy required to remove the electron.

Chemistry Formulas from Wave Mechanical Concept of Atom

·         De Broglie’s Equation,

            
          Where, m = mass of particle,
                        v = velocity of the particle,
                        h = Planck’s Constant,
or,       
          

Chemistry Formulas from Heisenberg’s Uncertainty Principle

·        Heisenberg’s Uncertainty Principle,

            
           Where,   = uncertainty in the position of the particle,
                        = uncertainty in the momentum of the particle,
Also,
           
 

Chemistry Formulas from Quantum Numbers

·         Principle Quantum Number (n),

Maximum no. of electrons in n principle quantum number = 2n2

·         Azimuthal Quantum Number (l),

For the given value of principle quantum number (n), azimuthal quantum number (l), may have all integral values from 0 to (n-1)

·         Magnetic Quantum Number (m),

No. of orbitals in a sub-shell = 2 l +1

·         Spin Quantum Number (s),

For spinning of electron about its own axis

Chemistry Formulas for Structure of Atom Part 1

Chemistry Formulas of Structure of Atom

Chemistry Formulas from Rutherford Atomic Model

·         Radius of Nucleus, rn = r0 × A1/3
Where, A = Mass Number,
               r0 = Proportionality Constant = 1.4 × 10-13 cm
·         Volume of the nucleus = Approx. 10-39 cm3
·         Volume of the atom = Approx. 10-24 cm3
·         Density of the nucleus = 1014 g cm-3
Or,

Important Characteristics of Three Fundamental Particles
1.      Electron
·         Charge on an Electron = -1.602×10-19 coulombs.
·         Mass of an Electron = 9.11×10-28 g
·         Specific Charge (e/m ratio) of electrons (cathode rays) = 1.76×108 coulombs/gram
·         Radius of the electron = 10-15 cm
·         Density of the electron = 2.17×1017g/cc
·         Mass of one mole of the electrons = Approx. 0.55mg
·         Charge on one mole of the electrons = 96500 Coulombs = 1 Faraday
2.      Proton
·         Mass of Proton = 1.672×10-24g
·         Charge on Proton = 1.602×10-19 Coulombs
·         Specific Charge of Proton = 9.58×104 Coulombs/gram
·         Mass of one mole of proton = 1.007 gram
·         Charge on one mole of proton = 96500 Coulombs = 1 Faraday
·         Volume of Proton = Approx. 1.5×10-38cm3
3.      Neutron
·         Mass of Neutron = 1.675×10-24g
·         Specific Charge on Neutron = 0
·         Density of Neutron = 1.5×1014g/cc
·         Mass of one mole of neutron = 1.008g
4.      Other Sub-Atomic Particles of Atom
·         Positrons
·         Neutrions
·         Mesons
Chemistry Formulas of Atomic Number (Z) and Mass Number (A)
·         General Symbol for an Atom of Element (E) indicating its Atomic Number (Z) and Mass Number (A)
ZEA
·         Atomic Number (Z) = Number of Protons = Number of Electrons
·         Mass Number (A) = Number of Protons + Number of Neutrons
·         No. of Neutrons = A – Z

Chemistry formulas for Atoms, Molecules and Chemical Arithmetic Part II

Chemistry formulas for Atoms, Molecules and Chemical Arithmetic Part II

Gram Atomic Weight (GAW) related Chemical Formulas

·         No. of Gram Atoms or Mole Atoms = Weight of an Element/GAW
·         Weight of an Element in gram = No. of Gram Atoms x GAW
·         No. of atoms in 1 GAW = 6.02x1023
·         No. of atoms in given substance = 6.02x1023 x Weight/GAW
·         No. of atoms in 1 gram of an element = 6.02x1023/Atomic Weight

Gram Molecular Weight (GMW) related Chemical Formulas

·         No. of Gram molecules or Mole Molecules = Weight of Substance/GMW
·         Weight of Substance in gram = No. of Gram Molecules x GMW
·         Avogadro’s No. = 6.02x1023 per mol

Mole Concept related Chemical Formulas

·         1 mole contains 6.02x1023 particles
·         1 mole of an atom = 1 GAW of it
·         1 mole of a compound = 1 GMW of it
·         Examples, 1 mole of Na = 23 g
·         1 mole of H2O = 18 g
·         1 mole of OH- ions = 17 g
·         1 mole = 1 gram molecules
·         1 mole = 1 gram molecular weight
·         1 mole = 22.4 litres at NTP
·         1 mole = 6.02x1023 molecules
·         1 mole = 1 gram atomic weight
·         1 mole = 6.02x1023 atoms
·         No. of Moles = Weight of Substance in Gram/Gram Molecular Weight
·         No. of Moles = No. of Unitary Particles/Avogadro’s No.
·         No. of Moles = Volume in Litres at NTP/22.4 Litres

Gram Molecular Volume related Chemical Formulas

·         1 Gram Molar Volume = 22.4 Litres
·         Example, Volume of 16 gram (1 mole) of CH4 at STP= 22.4 Litres
·         Volume of 2 gram (1 mole) of H2 at STP = 22.4 Litres
·         Weight of 11.2 litres of any Gas at STP = VD (Vapour Density) of that Gas in Gram
·         Density of Gas at NTP = Molar Weight in Gram/22400 mL

Chemistry formulas





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Chemistry formulas for Atoms, Molecules and Chemical Arithmetic Part I

Chemistry formulas for Atoms, Molecules and Chemical Arithmetic Part I

Atomic Weight related Chemical Formulas

·         Atomic Weight of an Element = Weight of an average Atom of that Element/ (1/12)x Mass of an element of C12
·         1 a.m.u. = 1.66x10-24g
·         Atomic Weight = Gram Atomic Weight (GAW)
·          1 Gram Atomic Weight (GAW) of every element contains 6.023x1023 atoms of that element.
·         No. of gram of an element = weight of element in gram/ Gram Atomic Weight (GAW) of that element

Methods of Determining Atomic Weight

                         i.     Dulong and Pettits Method: 

                                                                  Applicable only for solid elements except Be, B, C, Si.
·      Atomic Weight  x Specific Heat = 6.4 (app.)
·      Atomic Weight  (app.) = 6.4/ Specific Heat (in Calories)
·      Exact Atomic Weight = Equivalent Weight x Valency
·      Valency = App. Atomic Weight / Equivalent Weight

                        ii.     Vapour Density Method: 

                                                              Applicable only for those elements whose chlorides are volatile.
·         Valency of the Element = Molecular Weight of Chloride / Equivalent Weight of Chloride
·         Valency of the Element = (2 x V.D. of Chloride) / (Equivalent Weight of Metal + 35.5)
Where, V.D. = Vapour Density
·         Atomic Weight = Equivalent Weight of Metal x Valency

                      iii.     Specific Heat Method: 

                                                          Applicable only for Gases.
·         Cp/Cv for monoatomic gases = 1.66
·         Cp/Cv for diatomic gases = 1.40
·         Cp/Cv for triatomic gases = 1.33
·         Atomic Weight of Gaseous Element = Molecular Weight/ Atomicity
Where, Atomicity is number of atoms present in a molecule of a gaseous element. For example atomicity of Inert Gas is 1, atomicity of Ozone is 3, atomicity of H2 N2 O2 X2 is 2, and atomicity of Sulphur is 8.

                     iv.     Volatile Chloride Formation Method:

·         Atomic Weight of the Element = Equivalent Weight (Z) x Valency (x)

                       v.     Isomorphism Method: 

                                                        This method based on law of Isomorphism. According to law of Isomorphism, “Compounds having identical crystal structure have similar constitution and chemical formula”
·         Atomic Weight = Equivalent Weight x Valency
·         Weight of Element A that combines with certain weight of other elements/Weight of Element B that combines with the same weight of other elements = Atomic Weight of A / Atomic Weight of B

Molecular Weight related Chemical Formulas

·         Molecular Weight = Weight of 1 Molecule of the Substance/ (1/12)x Weight of 1 atom of C12
·         Actual Weight of 1 Molecule = Molecular Weight x 1.66x10-24g

Methods of Determining Atomic Weight

1.              Diffusion Method: 

                                          Applicable only for gases.
 ·         


Where,  r1 & r2 is rate of diffusion of gases and M1 & M2 is Molecular Weight.

2.              Vapour Density Method: 

                                                    Applicable only for gases.
·         Molecular Weight = 2 x Vapour Density

3.              Victor Mayer Method:  

                                                 Applicable only for volatile liquids and solids.
·         Molecular Weight of a substance = 22400 ml of vapour of a substance at STP

Equivalent Weight related Chemical Formulas

·         No. of Gram Equivalent Weight = Weight of the substance in gram/ Gram Equivalent Weight of the substance
·         Equivalent Weight of an Element = Atomic Weight/ Valency
·         Equivalent Weight of an Acid = Molecular Weight/ Basicity
·         Equivalent Weight of an Base = Molecular Weight/ Acidity
·         Equivalent Weight of a Salt = Formula Weight/ Total Positive or Negative Charge
·         Equivalent Weight of a Reducing Agent = Formula Weight/ No. of electrons lost per molecule or Total change in Oxidation Number
·         Equivalent Weight of an Oxidising Agent = Formula Weight/ No. of electrons gained per molecule or Total change in Oxidation Number
·         Equivalent Weight of Radicals = Formula Weight of Radical/ No. of units of Charge

Methods of Determining Equivalent Weight

1.              Hydrogen Displacement Method: 

                                                                   Applicable for metals which can displace or combine with hydrogen.
·         Equivalent Weight of Metal = (Weight of metal x 1.008)/ Weight of Hydrogen Displaced
·         Equivalent Weight of Metal = (Weight of metal x 11200)/ Volume in ml of H2 displaced at STP

2.              Oxide Formation Method:

·         Equivalent Weight of Metal = (Weight of metal x 8)/ Weight of Oxygen
·         Equivalent Weight of Metal = (Weight of metal x 5600)/ Volume in ml of Oxygen at STP

3.              Chloride Formation Method:

·         Equivalent Weight of Metal = (Weight of metal x 35.5)/ Weight of Chlorine
·         Equivalent Weight of Metal = (Weight of metal x 11200)/ Volume in ml of Chlorine at STP

4.              Neutralization Method:

·         Equivalent Weight of Acid or Base = Weight of  acid or base in gram/ (Volume of base or acid in litre required for neutralization x Normality of base or acid)

5.              Metal Displacement Method:

·         Weight of Metal Added W1/ Weight of Metal Displaced W2 = Equivalent Weight of Metal Added E1/ Equivalent Weight of Metal Displaced E2

6.              Electrolytic Method:

·         Gram Equivalent Weight = Electrochemical Equivalent x 96500
·         Weight of X deposited/ Weight of Y deposited = Equivalent Weight of X/ Equivalent Weight of Y

7.              Double Decomposition Method:

·         Weight of Salt taken (W1)/ Weight of ppt. obtained (W2) = Equivalent Weight of Salt (E1)/ Equivalent Weight of Salt in ppt. (E2)

8.              Conversion Method:

·         Weight of Compound A (W1)/ Weight of Compound B (W2) = (Equivalent Weight of Metal + Equivalent Weight of Anion of Compound A)/ (Equivalent Weight of Metal + Equivalent Weight of Anion of Compound B)

9.              Volatile Chloride Method:

·         Equivalent Weight = {(2 x Vapour Density of Chloride)/ Valency} – 35.5

10.          Silver Salt Method: 

                                           Applicable for organic acids
·         Equivalent Weight of Acid = Molecular Weight of Acid/ Basicity


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