B Sc Chemistry Formulas Molecules and Chemical Arithmetic Part I

B Sc Chemistry Formulas 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. = 1.66×10^-24g
• Atomic Weight = Gram Atomic Weight (GAW)
•  1 Gram Atomic Weight (GAW) of every element contains 6.023×10²³ 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

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                         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 1.66×10^-24g

Methods of Determining Atomic Weight

1.              Diffusion Method:

                                          Applicable only for gases.

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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

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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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B Sc Chemistry Formulas 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 = 6.02×10²³
• No. of atoms in given substance = 6.02×10²³ x Weight/GAW
• No. of atoms in 1 gram of an element = 6.02×10²³/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. = 6.02×10²³ per mol

Mole Concept related Chemical Formulas

• 1 mole contains 6.02×10²³ 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 = 6.02×10²³ molecules
• 1 mole = 1 gram atomic weight
• 1 mole = 6.02×10²³ 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

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B Sc Chemistry Formulas Structure of Atom Part 1

Chemistry Formulas from Rutherford Atomic Model

• Radius of Nucleus, r_n = r₀ × A^1/3

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)

_ZE^A

• Atomic Number (Z) = Number of Protons = Number of Electrons
• Mass Number (A) = Number of Protons + Number of Neutrons
• No. of Neutrons = A – Z

 

hemistry Formulas from Bohr’s Model of Atom

·         Angular momentum of electron in n^th 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 n^th 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 = 6.62×10^-27erg sec,

         m = 9.1×10^-28g,

         e = 4.8×10^-10

     we get,

    r = 0.529 Å

So, radius of first orbit of hydrogen atom is 0.529 Å.

·         Radius of n^th orbits of hydrogen like species

r_n = 0.529n²/Z Å

·         Velocity of electron in n^th 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 n^th orbit (E_n)

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	-21.79×10-19	-13.6	-313.5
2	-5.42×10-19	-3.4	-78.4
3	-2.41×10-19	-1.51	-38.84
4	-1.36×10-19	-0.85	-19.6
5	-0.87×10-19	-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 n^th 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

 

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