# B Sc Chemistry Formulas Molecules and Chemical Arithmetic Part I

B Sc Chemistry Formulas 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

#### 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.

Where,  r1 & r2 is rate of diffusion of gases and M& 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

# 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

# B Sc Chemistry Formulas Structure of Atom Part 1

### 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
1. 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
1. 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
1. 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

### hemistry 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,

#### ·         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.

rn = 0.529n2/Z Å

#### ·         Velocity of electron in nth orbit

On substituting values of the constants

We get,

#### ·         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 -21.79×10-19 -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

### Chemistry Formulas from Photoelectric Effect

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

# B Sc Nuclear Chemistry Radioactivity

Empirical relationship between size of nucleus and its mass number is

R = R0A1/3

Where,

R = radius of nucleus,

A = mass number,

R0 = contestant = 1.4×10-13cm

### 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,

N0 = No. of atoms originally present,

N = No. of atoms present after time t

### Half Life Time (t1/2)

t1/2 = 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 (T1/2)

Where,

K = decay constant

T = Average Life Time

T1/2 = 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 Ra226 = 3.7 x 1010dps

Where,

dps = disintegrations per second

millicurie (mc) = 3.7 x 107dps

microcurie (µc) = 3.7 x 104dps

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

1rd = 106dps

#### Becquerel (Bq)

Becquerel (Bq) is the SI unit of radioactivity.

1Bq = 1 disintegrations per second

1 Bq = 1 dps

A —-à B —-à C

NA/NB = KB/KA = TA/TB

Where,

KA = radioactivity constant for the process A—àB

KB = radioactivity constant for the process B—àC

TA = average life period of A

TB = average life period of B

Radioactive Equilibrium in terms of half-life periods,

NA/NB = (T1/2)A/ (T1/2)B