Important Formulas of all Chapters of Chemistry Class 12

IMPORTANT FORMULAs of NCERT CHEMISTRY CLASS 12 

UNIT 1: SOLID STATE

1.     Density of the unit cell, 

                         d = ZM/a3NA

       Where,

 Z = No. of atoms per unit cell

M = Molar Mass/Atomic Mass

a = Edge Length of unit cell

N_A = Avogadro Constant

      2. Efficiency of Packing in hcp and ccp structures = 74%

It means 74% of the available volume is occupied by spheres (atoms).

(Note: In FCC unit cell the atoms touch each other along the face diagonal)

Face diagonal,     4r = √2a   ----------- (i)

                                           a = 4r/√2---------- (ii)

                                          r = a/2√2-------- (iii)

where, r = radius of the atom and a = edge length of unit cell.

 3. Efficiency of Packing in bcc structures = 68%

It means 68% of the available volume is occupied by spheres (atoms).

(Note: In BCC unit cell the atoms touch each other along the body diagonal)

Body diagonal,    4r = √3a  ------------ (i)

                                         a = 4r/√3----------- (ii)

                                         r = √3a/4  ---------- (iii)

4. Packing efficiency in simple cubic lattice = 52.4%

It means 52.4% of the available volume is occupied by spheres (atoms).

(Note: In SCC unit cell the atoms touch each other along the edge)

a and r is related as:  

                            a = 2r ---------- (i)

                                        r = a/√2 ---------- (ii)

5. Relationship between the nearest neighbours distance of an element (d) with edge length(a) of the unit cell and radius of the atom (r) :

i) In simple cubic element:  d = a = 2r, r = a/2

ii) In bcc element:  d = 4r = √3, r = √3a/4

iii) In fcc element:  d = 4r = √2a, r = a/2√2 

where, d = distance between nearest neighbours.

 UNIT 2 : SOLUTIONS

1. Mass %  =  (Mass of solute/Mass of solution) x 100

2. Volume %  =  (Volume of solute/Volume of solution) x 100

3. ppm (A)  =  (Mass of component A/Total mass of solution) x 106

4. Molarity (M) = No. of moles of solute / Volume of Solution (in L)

= n_B / V (in L)   =   (w_B x 1000)/(m_B x V {in mL})

Here, n_B is the no. of moles of Solute and w_B is the given mass of solute.

5. Molarity equation (Dilution formula):  M₁V₁  =  M₂V₂

6. Molarity of a mixture:  M_mixture  =  (M₁V₁  +   M₂V₂)/(V₁  +  V₂)

7. Molarity (M)  =  (10 x X x d)/Molecular mass of solute

where, X  =  mass%,  d  =  density of solution

8. Molality (m)  =  No. of moles of solute / Weight of Solvent (in Kg)

 = n_B /w_A (in Kg)  = (n_B x 1000)/w_A (in g)  =  (w_B x 1000)/(m_B x w_A{in g})

Here, n_B is the no. of moles of Solute,  w_B is the given mass of Solute and w_A is the given mass of Solvent

9. Mole fraction (X):

X_A  =  n_A/(n_A + n_B);  X_B  =  n_B/(n_A + n_B) 

{Note:  X_A + X_B = 1)

n_A & n_B are the no. of moles of component A & B respectively

10. Henry’s Law: The partial pressure of the gas in vapour phase (P) is proportional to the mole fraction of the gas (X) in the solution.

 

                         P  =  k_HX

where, k_H  =  Henry’s Law constant.                                        

                                                                                                              

11. Raoult’s Law: i) For a solution of volatile liquids, the partial vapour pressure of each component in the solution is directly proportional to its mole fraction.

For component 1:  P1  α  X1

                                  P₁  =  P10X1

where, P10 =  V.P. of pure component 1.

For component 2:  P2 α  X2

                                  P2  =  P20X2

where, P20 =  V.P. of pure component 2.

 ii) In case of non-volatile solute:  (PA0  -  PA)/ PA0  =  XB                            

12. The total vapour pressure (PTotal) over the solution phase in the container is equal to the sum of partial pressures of the components of the solution. (Dalton’s Law)

i.e.  PTotal  =  P1  +  P2          (where X1  + X2  =  1)

                                                     =  P10X1  + P20X2            

                                          =  P10  +  (P20  -  P10)X2

13. Colligative properties:

i) Relative lowering of vapour pressure:

(PA0  -  PA)/ PA0  =  XB  =  n_B/(n_A + n_B)   {another form of Raoult’s Law).

                                                    OR

(PA0  -  PA)/ PA0  =  X_B  =  n_B/n_A  =  (w_B x M_A)/(M_B x w_A)

Here w_A & w_B are the given mass of component A & B, M_A & M_B are the molar mass of component A & B.

ii) Elevation of Boiling point (∆T_b):

∆T_b  =  k_bm  ………(i) { m  =  (n_B x 1000)/w_A }

∆T_b  =  (k_b x w_B x 1000)/(M_B x w_A)  ………(ii)

M_B  =  (k_b x w_B x 1000)/(∆T_b x w_A)  ………(iii)

∆T_b  =  T_b  -  T_b0  ………(iv)

T_b  =  ∆T_b  +  T_b0  ………(v)

k_b  =  [R x M_A x (T_b0)²]/[1000 x ∆_fusH]  ………(vi)

where, ∆_fusH = enthalpy of fusion of solvent; M_B = Molar mass of solute; w_A = Mass of solvent; w_B = Mass of solute; k_B = Boiling point elevation constant (Ebullioscopic constant).

iii) Depression of Freezing point (∆T_f):

 ∆T_f  =  k_fm

∆T_f  =  (k_f x w_B x 1000)/(M_B x w_A)

M_B  =  (k_f x w_B x 1000)/(∆T_f x w_A)

∆T_f  =  T_f0  -  T_f

T_f  =  T_f0  +  ∆T_f 

k_f  =  [R x M_A x (T_f0)²]/[1000 x ∆_vapH]

where, R = gas constant; T_f0 = Freezing point of pure solvent; T_f = Freezing point of solution;

k_f = Freezing point depression constant or cryoscopic constant; ∆_vapH = enthalpy of vapourisation.

iv) Osmotic pressure (π):

πV  =  n_BRT

π  =  n_BRT/V  =  CRT  =  MRT  (where C = M {Molarity of solution})

π  =  (w_BRT)/(m_B x V)

14. Van’t Hoff factor (i):

i  =  Normal molar mass/Abnormal molar mass

i  =  Observed colligative property/Calculated colligative property

i  =  (Total no. of moles of particles after association or dissociation)/(No. of moles of particles before association or dissociation)

15. α  =  (i  -  1)/(n  -  1)

where, α = degree of dissociation; i = Van’t Hoff factor; n = no. of ions  produced per formula of the compound.

16. α  =  [i  -  1]/[(1/n)   -  1]

where, α = degree of association [(1/n) < 1]

17. If  i  =  1;  Solute behaves normally ( neither association or dissociation)

i  =  ½;  Solute is dimer

i  =  ¼;  Solute is tetratomic (eg. P₄)

i  =  1/8;  Solute is octa atomic (eg. S₈)

i  >  1;  Solute undergoes dissociation

i  <  1;  Solute undergoes association

18. Modified equations for Colligative properties:

(PA0  -  P_A)/ PA0  =  iX_B 

∆T_b  =  ik_bm

∆T_f  =  ik_fm

π  =  in_BRT/V

 UNIT 3 : ELECTROCHEMISTRY

1. Electrical resistance (R) of electrolytic solution:  R  =  ρl/A

2. Resistivity  (ρ)  =  RA/l

3. Conductance (G)  =  1/R  =  A/ρl  =  kA/l

4. Conductivity (κ)  =  1/ρ  =  l/RA  =  Gl/A;  (1/R = G)

where, A = Cross sectional area of cell; l = length of cell

κ  =  (l/A) x (1/R)  =  Cell constant x Conductance

5. Cell constant of the conductivity cell (G*) =  l/A  =  Conductivity/Conductance

6. κ  =  Cell constant/R  =  G*/R

7. G*  =  κ x R

8. Molar conductivity (Ʌ_m) =  κ/C  =  1000 x κ/M

9. Kohlrausch law of independent migration of ions:

Ʌ_m0  =  ν₊λ₊0  +  ν_-λ_-0

where, Ʌ_m0 = limiting molar conductivity; λ₊0 and λ_-0 are the limiting molar conductivities of cation and anion respectively; ν₊ = no. of cations; ν_- = no. of anions.

10.   =  Ʌ_mc/Ʌ_m0 

where, Ʌ_mc = molar conductivity at concentration ‘C’.

11. k_a  =  Cα2/(1  -  α)

k_a  =  Cα2  (α << 1)

where, α = Degree of dissociation; k_a = Dissociation constant of weak acid like acetic acid.

12. Quantity of electricity passed (Q)  =  It

13. Q  =  nF

where, I = Current in amperes; t = Time in sec; Q = no. of coulombs required; n = no. of moles of e^-s involved; F = Faraday’s constant = 96,487 Cmol^-1 ~ 96,500 Cmol^-1.

14. Nernst Equation:

Nernst Equation for the electrode at 298K:

E_Mⁿ⁺_/M  =  E0_Mⁿ⁺_/M   +  (0.059/n)log[Mⁿ⁺]

Cell potential for the cell (emf of the cell):

E_cell  =  E0_cell  +   (0.059/n)log [reduced form]/[Oxidised form]

where, E0_cell =  E0_cathode  -  E0_anode

E_cell   =  E0_cell  -  (0.059/n)log[products]/[reactants]

15. At Equilibrium, E_cell = 0,

therefore E0_cell  =  (0.059/n)log k_c

E0_cell  =  (2.303 RT/nF) log k_c

16. ∆_rG0  =  -2.303 RT log k_c

17. ∆_rG0  =  -nFE^ө_cell

18. If E_cell is positive, ∆G = negative; ie cell will work (spontaneously)

If E_cell is negative, ∆G = positive; ie cell will not work (non-spontaneously)

If E_cell  =  0;  Cell is at equilibrium.

 

UNIT 4 : CHEMICAL KINETICS

 

1. r_avg  =  - ∆[R]/∆t  =  ∆[P]/∆t

where, r_avg = average rate of reaction

2. r_inst  =  -d[R]/dt  =  d[P]/dt

where, r_inst = instantaneous rate of a reaction

3. Rate of reaction  =  -(1/ν_R)d[R]/dt  =  (1/ν_P)d[P]/dt

            Where v_R and v_P are the stoichiometric coefficient of reactant and product,

4. Units for Rate of Reaction = molL-1s-1

5. Units for rate constant (k)  =  (molL-1)1-ns-1

1^st order reaction n = 1; k = s-1

2^nd order reaction n = 2; k = mol-1Ls-1

0 order reaction n = 0; k = molL-1s-1

6. For a reaction aA + bB + cC -----à Product

 Rate = k [A]x[B]y[C]z

Overall order of a reaction = x + y + z. (x, y and z may same as a, b and c)

7. Integrated rate equation for zero order reaction:

k  =  ([R]₀  -  [R])/t

 

k  =  - slope (m = - k)

[R]  =  -kt  +  [R]₀                                                     

     y  =  mx  +  c

          

8. Integrated rate equation for first order reaction:

 k  =  (1/t) ln [R]₀/[R]

 k  =  (2.303/t) log [R]₀/[R]     OR  =  (2.303/t) log(a/a – x)

 ln[R]  =  - kt  +  ln[R]₀

  k  =  - slope  =  - m

                    

      

    log [R]₀/R  =  kt/2.303 

     y  =  mx

 

 

                                                   

                                 [R]  =  [R]₀e^-kt

9. Half-life of a reaction:

a) t_1/2 for zero order reaction:

t_1/2  =  [R]₀/2k

t_1/2  α  R₀;  t_1/2  α  1/k

b) t_1/2 for first order reactions:

t_1/2  =  0.693/k

First order reaction:

i)t_1/2 is independent of [R]

ii) t_1/2   α  1/k

9. Arrhenius equation:

k  =  Ae-Ea/RT

lnk  =  -E_a/RT  +  lnA

lnk₁  =  -E_a/RT₁  +  lnA; at temperature T₁

lnk₂  =  -E_a/RT₂  +  lnA; at temperature T₂

ln (k₂/k₁)  =  E_a/R[(1/T₁)  -  (1/T₂)]

log (k₂/k₁)  =  E_a/2.303R[(1/T₁)  -  (1/T₂)]

                 

where, t_1/2 = Half Life; [R]₀ = Initial concentration of the reactant; [R] = concentration of the reactant at t; K = Rate constant; E_a = Activation energy; A = Arhennius factor; T = Absolute temperature; R = Gas constant.

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By: Mr. S. K. Nigam

PGT Chemistry