Chemistry 1st Paper:

Laws and Equations

Sowmitra Dassowmitra.josephite@gmail.com

1. Boyle’s Law:

V ∝ 1

P[T constant]

2. Charle’s Law:V ∝ T [P constant]

3. Gay-Lussac’s Pressure Law:

P ∝ T [V constant]

4. Combined Law of Boyle’s and Charle’s:

V ∝ T

P⇒ PV

T= constant

5. Avogadro’s Law:

V ∝ n [P and T constant]

6. Ideal-Gas Equation:PV = nRT

P=Pressure, V=Volume, n=Mole-Number, T=Temperature, and, R=UniversalGas Constant

(a) Density Form:PM = dRT

d=Density of Gas, M=Molecular Mass of Gas

(b) Concentration Form:P = CRT

C=Concentration of Gas

7. Van-der-Waal’s Equation:

(P +an2

V 2)(V − nb) = nRT

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8. Dalton’s Partial Pressure Law:

P = P1 + P2 + P3 + . . .+ Pn

P=Total Pressure of the mixture of Gases, Pi=Partial Pressure of the i-thGas.

(a) Molar Form:Pi = xiP

xi=Mole-Fraction of the i-th Gas

(b) Volume Form: (In case of transfering gases from one container toanother)

PV = P1V1 + P2V2 + P3V3 + . . .+ PnVn

P=Total Pressure of gases in Final Container, V=Volume of finalContainer, Pi=Pressure of each Gas in Individual Container, Vi=Volumeof Individual Container

9. Clausius’ Kinetic Equation for Ideal Gases:

PV =1

3nMc̄2

n=Mole-Number, M=Molecular Mass, c=Root-mean-square velocity ofgas.

10. Graham’s Law of Diffusion:

r ∝ 1√d∝ 1√

M

r=Rate of Diffusion, d=Density of Gas, M=Molecular Mass of Gas

11. Ritz Combination Principle:

ν̄ = RH(1

n21

− 1

n22

)

ν̄=Wave Number, n1=Quantum No. of Ground-State Orbit, n2=QuantumNo. of Excited-State Orbit, RH=Rhydberg Constant

12. De-Broglie’s Equation:

(mv)× (λ) = h

mv=Momentum of Particle, λ=Wavelength of Particle, h=Planck’s Con-stant.

13. Mole-Ratio Equivalence:

MAVA/MBVB = a/b; MoxVox/MredVred = x/y

MA=Concentration of Acid, VA=Volume of Acid, a=Mole-number of Acid,etc.

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14. Ostwald’s Dilution Law:

Ka = α2C

Ka=Equilibrium Constant of Acid, α=Dissociation Constant of Acid,C=Concentration of Acid.

15. Henderson-Hasselbach Equation:

pH = pKa + log[Salt]

[Acid]; pOH = pKb + log

[Salt]

[Base]

[x] means Concentration of ’x’.

16. Faraday’s Equation:

W =M

nF× It

W=Amount of Element deposited, M=Atomic Mass of Element, n=Chargeon Ion, I=Current, t=time, F = 96500 Coulomb.

17. Nernst Equation:

(a) For Half Cell:Cell Reaction: Mn+ + ne− ⇀↽M

EMn+|M = E0Mn+|M +

RT

nFln [Mn+]

(b) For Full Cell:Cell Reaction: xAy+ + yB ⇀↽ xA+ yBx+

Ecell = E0cell +

RT

nFln

[Ay+]x

[Bx+]y

n = xy =No. of electrons transfered.

18. Law of Mass Action:Reaction: α1R1 + α2R2 + α3R3 + . . . = β1P1 + β2P2 + β3P3 + . . .

Kc =[P1]α1 [P2]α2 [P3]α3 . . .

[R1]α1 [R2]α2 [R3]α3 . . .

Ri=Reactant, Pi=Product, etc.

19. Kp,Kc Equivalence:Kp = Kc(RT )∆n

∆n=Difference in Mole-Number of Reactants and Products

20. Vant Hoff’s Equation:

lnKp = −∆H

RT+ c

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21. Arrhenius’ Equation:

k = p · Z · e−EaRT ⇒ ln k = lnA− Ea

RT

k=Rate Constant, p=Steric Factor, Z=Collision Rate, A = p×Z=ArrheniusFactor, Ea=Activation Energy of Reactant.

22. Rate Constant Equation:

(a) Zero Order:c = c0 − kt; x = kt

c0=Initial Concentration of Reactant, c=Concentration of Reactantafter time t, x=Concentration of Product.

(b) First Order:

lnc

c0= −kt; ln

a

a− x= kt

c0 = a =Initial Concentration of Reactant

(c) Second Order:

i. Reaction: A(Reactant)→ B(Product)

x

a(a− x)= kt

ii. Reaction: A(Reactant-1) +B(Reactant-2)→ C(Product)

1

(a− b)ln

(b

a· a− xb− x

)= kt

a=Initial Concentration of 1st Reactant,b=Initial Concentration of 2nd Reactant.

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