# 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 related Chemical Formulas__

- Atomic Weight of an Element = Weight of an average Atom of that Element/ (1/12)x Mass of an element of C
^{12} - 1 a.m.u. = 1.66×10
^{-24}g - Atomic Weight = Gram Atomic Weight (GAW)
- 1 Gram Atomic Weight (GAW) of every element contains 6.023×10
^{23}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 H_{2} N_{2} O_{2} X_{2} 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 Related Chemical Formulas__

- Molecular Weight = Weight of 1 Molecule of the Substance/ (1/12)x Weight of 1 atom of C
^{12} - Actual Weight of 1 Molecule = Molecular Weight x 1.66×10
^{-24}g

**Methods of Determining Atomic Weight**

**1. ****Diffusion Method:**

Applicable only for gases.

Where, r_{1} & r_{2} is rate of diffusion of gases and M_{1 }& M_{2} 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__

__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 H
_{2}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 W
_{1}/ Weight of Metal Displaced W_{2}= Equivalent Weight of Metal Added E_{1}/ Equivalent Weight of Metal Displaced E_{2}

**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 (W
_{1})/ Weight of ppt. obtained (W_{2}) = Equivalent Weight of Salt (E_{1})/ Equivalent Weight of Salt in ppt. (E_{2})

**8. ****Conversion Method:**

- Weight of Compound A (W
_{1})/ Weight of Compound B (W_{2}) = (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

# B Sc Chemistry Formulas Molecules and Chemical Arithmetic Part II

__Gram Atomic Weight (GAW) related Chemical Formulas__

__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 = 6.02×10
^{23} - No. of atoms in given substance = 6.02×10
^{23}x Weight/GAW - No. of atoms in 1 gram of an element = 6.02×10
^{23}/Atomic Weight

__Gram Molecular Weight (GMW) related Chemical Formulas__

__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. = 6.02×10
^{23}per mol

__Mole Concept related Chemical Formulas__

__Mole Concept related Chemical Formulas__

- 1 mole contains 6.02×10
^{23}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 H
_{2}O = 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 = 6.02×10
^{23}molecules - 1 mole = 1 gram atomic weight
- 1 mole = 6.02×10
^{23}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__

__Gram Molecular Volume related Chemical Formulas__

- 1 Gram Molar Volume = 22.4 Litres
- Example, Volume of 16 gram (1 mole) of CH
_{4}at STP= 22.4 Litres - Volume of 2 gram (1 mole) of H
_{2}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

# B Sc Chemistry Formulas Structure of Atom Part 1

**Chemistry Formulas from Rutherford Atomic Model**

- Radius of Nucleus, r
_{n}= r_{0}× A^{1/3}

Where, A = Mass Number,

r_{0} = Proportionality Constant = 1.4 × 10^{-13} cm

- Volume of the nucleus = Approx. 10
^{-39}cm^{3} - Volume of the atom = Approx. 10
^{-24}cm^{3} - Density of the nucleus = 10
^{14 }g cm^{-3}

Or,

**Important Characteristics of Three Fundamental Particles**

- 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) = 1.76×10
^{8}coulombs/gram - Radius of the electron = 10
^{-15}cm - Density of the electron = 2.17×10
^{17}g/cc - Mass of one mole of the electrons = Approx. 0.55mg
- Charge on one mole of the electrons = 96500 Coulombs = 1 Faraday

- Proton

- Mass of Proton = 1.672×10
^{-24}g - Charge on Proton = 1.602×10
^{-19}Coulombs - Specific Charge of Proton = 9.58×10
^{4}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
^{-38}cm^{3}

- Neutron

- Mass of Neutron = 1.675×10
^{-24}g - Specific Charge on Neutron = 0
- Density of Neutron = 1.5×10
^{14}g/cc - Mass of one mole of neutron = 1.008g

- 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)

_{Z}E^{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^{-27}erg sec,

m = 9.1×10^{-28}g,

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} = 0.529n^{2}/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 = h*v*

#### · Total energy,

Total Energy = (mv^{2}/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 = 2n^{2}

#### · 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

**B Sc Nuclear Chemistry Radioactivity **

Empirical relationship between size of nucleus and its mass number is

R = R_{0}A^{1/3}

Where,

R = radius of nucleus,

A = mass number,

R_{0} = contestant = 1.4×10^{-13}cm

### Rate of Decayof radioactive substance

Where,

K = decay constant,

N = No. of atoms,

t = time of decay,

dN = small fraction of N,

dt = small fraction of t

### Value of Decay Constant

Where,

N_{0} = No. of atoms originally present,

N = No. of atoms present after time t

### Half Life Time (t_{1/2})

t_{1/2} = 0.693/K

Where,

K = decay constant

### Average Life Time (T)

Average life time (T) =Sum of the lives of the nuclei/ Total number of nuclei

T = 1/K

Also,

Average life time (T) = 1.44 x Half-life (T_{1/2})

Where,

K = decay constant

T = Average Life Time

T_{1/2 }= Half Life

### Specific Activity

Specific Activity = Rate of decay/m

= KN/m

= K x Avogadro Number/ Atomic Mass in gram

Where,

N = Number of Radioactive nuclei that undergoes disintegration

### Units of Radioactivity

Standard unit of radioactivity is** curie (c)**.

1c = Activity of 1gram Ra^{226} = 3.7 x 10^{10}dps

Where,

dps = disintegrations per second

millicurie (mc) = 3.7 x 10^{7}dps

microcurie (µc) = 3.7 x 10^{4}dps

Other units of radioactivity are Rutherford (rd) and Becquerel (Bq).

#### Rutherford (rd)

1rd = 10^{6}dps

#### Becquerel (Bq)

Becquerel (Bq) is the SI unit of radioactivity.

1Bq = 1 disintegrations per second

1 Bq = 1 dps

### Radioactive Equilibrium

A —-à B —-à C

At steady state,

N_{A}/N_{B} = K_{B}/K_{A} = T_{A}/T_{B}

Where,

K_{A} = radioactivity constant for the process A—àB

K_{B} = radioactivity constant for the process B—àC

T_{A} = average life period of A

T_{B} = average life period of B

Radioactive Equilibrium in terms of half-life periods,

N_{A}/N_{B} = (T_{1/2})A/ (T_{1/2})B

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