STATES OF MATTER

1. Boyle's Law 
   PV = constant [at constant n , T]     ∴ P₁V₁ = P₂V₂
2. Charle's Law 
   
   VT
    = constant [at constant n , P]     ∴ 
   V₁T₁
    = 
   V₂T₂
   
   V_t = V_o ( 1 + t / 273 )     [T(kelvin = 273 + t(^oC)]
3. Gay-Lussac's Law 
   
   PT
    = constant [at constant n , V]     ∴ 
   P₁T₁
    = 
   P₂T₂
4. Ideal Gas Eqaution 
   
   PVnT
    = R = 0.0821 l . atm . K^-1 . mol^-1
       = 1.987 Cal K^-1 . mol^-1 = 8.314 J K^-1 . mol^-1
   1 atm = 760 mm of Hg = 76 cm of Hg = 101325 pascal ; 1 bar = 0.9863 atm
   Satnadard Temperature and Pressure (STP) or Normal Temperature and Pressure (NTP)
   P = 1 atm , T = 0^oC or 273 K
5. Density and Molar Mass Relation 
   Density (D) = 
   PMRT
6. Dalton's law of Partial Pressure 
   P_Total = P₁ + P₂ + P₃ + .....
   where P₁,P₂,P₃, .... etc are partial pressures of individual gases .
   Partial Pressure = Total pressure x mole function
   Relative humidity = 
   Partial pressure of water in airVapour pressure of water
   
   Vap. Pressure of dry gas = Vap. Pressure of wet gas - Vap. pressure of water vapour (aqu. Tension)
7. Graham's Law (Diffusion and Effusion)
   
   (r_A) Rate of effusion of gas A(r_B) Rate of effusion of gas B
    = 
   √ρ_B√ρ_A
    = 
   √M_B√M_A
    [at constant pressure]
   
   (r_A) Rate of effusion of gas A(r_B) Rate of effusion of gas B
    = 
   P_AP_B
    
   √ρ_B√ρ_A
    = 
   P_AP_B
    
   √M_B√M_A
    [at different pressure]
8. Velocity of Molecules 
   
9. Real Gases , compressibility Factor
   Z = 
   PVnRT
   
   Z measures the extent of non - idealness of an ideal gas .
   Z < 1 , implies that gas is more compressible
   Z > 1 , implies that gas is less compressible
   Z = 1 , implies that gas is ideal
10. Gas Equation (van der Waal's) 
    
11. Nature of Gas Constant R 
    R = 
    PVnT
     = 
    Pressure x VolumeMoles x Degree(K)
     = 
    (Force / Area) x VolumeMoles x Degree(K)
     = 
    Force x LengthMoles x Degree(K)
     = Work Done per degree per mole
12. Units of Gas constant (R)
    R = 0.0821 atm L K^-1 mol^-1 = 0.0821 atm dm³ K^-1 mol^-1
    (Here P = 1atm , V = 22.4 L , T = 273K , 1 L = 1 dm^-1)
    
    If P is expressed in dynes per square centimeter (P = 76 x 981 x 13.6 dyne/cm²)
    V = 22400 dm³ and T = 273 K
    then R = 8.314 x 10⁷ ergs K^-1 mol^-1 = 8.314 JK^-1 mol^-1 and R = 1.987 cal K^-1 mol^-1
    
    1 atm pressure = 0.76 m x 13.6 x 10³ kg m^-3 x9.81 ms^-2 = 101.325 x 10³ Nm^-2 = 101.325 x 10³ Pa
    1 Nm^-2 = 1 Pa
    
    Thus , the gas constant R = 
    (101.325 x 10³ Nm^-2) x (22400 x 10^-6m³)(273K) x (1 mol)
     = 8.314 x NmK^-1 mol^-1 = 5.189 x 10¹⁹ eVK^-1 mol ^-1
    [ 1eV = 1.602 x 10^-19 volts coulomb (Joule) ]
13. Avogadro's Law
    V α n or V α N (at constant T,P)
14. Calculation of Kinectic Energy
    Acoording to gas equation , Pv = 
    13
     Mu² for 1 mole of gas
    or PV = 
    23
    12
     Mu² for 1 mole of gas
    K.E. = 
    12
     = 
    32
    PV = 
    32
    RT
    For molecule , the KE = 
    32
    RTN_o
     = 
    32
    KT
    K(Boltzman constant) = 
    RN_o
15. Average molecular weight of a gaseous mixture 
    M_mix = 
    Σ n_iM_iΣ n_i
     , where n_i is the number of moles and M_i is the molecular weight of the component.
16. Critical Pressure (P_C) = 
    a27b²
17. Critical Temperature (T_C) = 
    8a27Rb
18. Critical Volume (V_C) = 3b
19. Relation between P_C , V_C and T_C : 
    P_CV_CRT_C
     = 
    38
20. Boyle's Temperature (T_B) = 
    abR

REDOX REACTIONS AND ELECTROCHEMISTRY

1. E_cell = E^o_cell - log
   [Products][Reactant]
   
   - Δ G = nFE_cell ; - Δ G^o = nFE^o_cell
   E^o_cell = 
   2.303 RTn F
    log K_eq = 
   0.591n
    log K_eq [at 25⁰C]
   Δ G^o = - 2.303 RT logK
2. Gibb's Helmholtz Equation
   
3. Faraday's First Law
   w = Z i t , 1 faraday is the quantity of charge carried by 1 mole of electrons.
   Z = 
   equivalent mass96500
    ; Z = weight deposited when 1A passed for 1 sec.
4. Faraday's second Law
   
   m₁m₂
    = 
   E₁E₂
   
   m₁ , m₂ are masses deposited and E₁ and E₂ are their equivalent weights ; for same amount of passed charge .
   %current efficieny = 
   Actual CurrentAmmeter current
    x 100
   Ohm's Law = I = E/R
   Ions are always discharged / produced in equivalent amounts whatever their speeds of deposition are ,
   Specific conductance = κ = 1 / ρ , ρ = specific resistance
   ρ = 
   la
    x C      
   la
    = constant , C = conductance = 
   1R
   
   Conductivity = cell constant x observed conductance
   π_eq = 
   kC_eq
    = 
   K x 1000 cm³ L^-1Normality
5. Equivalent conductance , (Λ)
   Λ = κ x V
   V = volume in mL containing 1g equivalent of the electrolyte.
   Molar conductance (μ) = [Equivalent conductance]
   (μ) = nΛ
   n = 
   Molecular MassEquivalent Mass
   
   μ = κ x V      V(mL) containing 1g mole of an electrolyte.
   At infinite dilution , Λ_o = λ_a + λ_c
   λ_c = ku_c
   λ_a = ku_a
   λ_a and λ_c , ionic conductance of anion and cation
   k = 96500C
   u_a = mobility of anion
   u_a = mobility of cations
   degree of dissociation = Λ / Λ_∞
   α = ( K / C)^1/2 = 
   λ_e^Cλ_e^∞
    = 
   λ_m^Cλ_μ^∞
   
   λ_e^C , λ_m^C = equivalent and molar conductance
6. Ostwald's Equation
   K = 
   C( λ_m^C )²λ_m^∞ (λ_m^∞ - λ_m^C)
7. Cell Notation
   
   Transport Number
   Transport Number = 
   Current carried by ionToatl current carried
   
   n_c + n_a = 1

ATOMIC STRUCTURE

1. Planck's Quantum Theory
   E = hν = 
   hcλ
   
   where h = Planck's Constant (6.023 x 10^-34 Js) , ν = Frequency of radiation , c = Velocity of Light , λ = Wavelength of radiation
   c = νλ and wave number = 
   1λ
2. Moseley's Equation
   √ν = a (z - b)
3. Heisenberg's uncertainity Equation
   Δp . Δx ≥ 
   h4π
    and ΔE . Δt ≥ 
   h4π
   
   Kinetic Energy of electron in the nth quantum state = 
   12
    
   Zke²r_n
   
   Potential Energy of electron in the nth quantum state = - 
   Zke²r_n
   
   Total energy (E) = - 
   Zke²2r_n
    = - 
   (13.6)Z²n²
   eV per atom
                = - 
   313.6n²
    kcal / mol = - 
   1312n²
    kJ / mol
                = - 21.8 x 10^-19
   Z²n²
    J / atom
4. Radius of nth quantum state = 
   n²h²4π²mkZe²
    = 
   n²a_oZ
   (a_o = 0.529 A)
5. Velocity of electron (v_n) = 
   2ρZke²nh
    = 
   Zn
    x 2.188 x 10⁶ m/s
   No. of revolutions per second in r.p.s. = 
   v_n2πr_n
    = 
   Zv_n2πn²a_o
   
   Wave number of spectral line ,
   
6. de Broglie Equation 
   Azimuthal (or angular) Quantum number (l) ; 0 ≤ l ≤ n - 1
   Orbital angular momentum , L = √l ( l + 1 )
   h2π
   
   Magnetic quantum number (m); - l ≤ m ≤ l , total (2l + 1)
   Magnetic Moment , μ_L = 
   eh4πmc
   √l ( l + 1 )
   Spin angular momentum = √s( s + 1 )
   h2π
7. Aufbau Principle 
   Subshell qith lowest (n + l) , value is filled first , if two subshells have same (n + l) value , lower value of 'n' is filled up first .
8. Photoelectric Effect 
   Maximum kinectic energy of ejected electron
   
   12
    mv²_max = hν - hν_o
   Stopping Potential , eV = hν - hν_o
   
   Binding Energy = Mass Effect x 931 MeV
   
   
   • Radius of Nucleus (r_n) = r_o x A^1/3 , where A is the mass number and r_o is proportionality constant whose value is 1.4 x 10^-13 cm
   • Although energy of electron increases with the increase in the value of n (orbit) , yet the difference of energy between successive orbits decreases .
     Thus , E₂ - E₁ > E₃ - E₂ > E₄ - E₃ > E₅ - E₄....etc.
   • No. of spectral lines when electron comes from n^th level to ground level = n (n + 1)/2
   • No. of sub-shells in a main energy level = n
   • No. of orbitals in a main energy level = n²
   • No .of orbitals in a sub shell = (2l+1)
   • No. of electron in each orbit = 2
   • Maximum no. of electron in a sub shell = 2 (2l+1)
   • Maximum no. of electron in a main shell = 2n²

CHEMICAL AND IONIC EQUILIBRIUM

1. Equilibrium in Water : 
   
   • Equilibrium Constant , K = 
     [C]^c[D]^d[A]^a[B]^b
      = 
     k_forwardk_backward
      = K_C
   • In terms of partial pressure
     Equilibrium Constant , K_p = 
     p_C^c p_D^dp_A^a p_B^b
      = K_c (RT)^Δn_g       [Δn_g = n_p - n_r]
2. Van't Hoff Equation : 
   
3. Gibb's Free Energy 
   ΔG = Δ - TΔS
   ΔG_o = - 2.303 RT log₁₀K
4. Buffer : 
   pH = pK_a + log 
   [conjugate base][acid]
   
   pOH = pK_b + log 
   [conjugate acid][base]
   
   Mixture of weak acids = ( k₁c₁ +k₂c₂ )^1/2
   α = 
   % conjugation100
   
   
   ∴ K_sp = [A^y+] ^x [B^x-] ^y
5. Arrhenius Concept : 
   Substance which give H⁺ ions when dissolved in water are called acids , while gives OH^- ions are called bases.
6. Bronsted Lowry Concept : 
   Acid donates proton , base accepts ptoton.
7. Ostwald's Dilution Law : 
   α = ( K / C)^1/2
   K = dissociation constant of weak electrolyte
   C = Concerntatation
   α = degree of dissociation
   K_W = [H⁺ ][OH^- ]
8. Hydrolysis Constant : 
   K_h = 
   h²C1 - h
   
   h = 
   amount of salt hydrolysedTotal salt taken
9. 
   

THERMODYNAMICS

1. Mechanical Work
   W = - P_ext (ΔV) [during expansion]
2. First Law of Thermodynamics
   ΔE = q + W
   ΔE = q - PΔV
3. Adiabatic Change
   
4. Isochoric Change
   ΔV = 0
   W = PΔV = 0
   ΔE = q + W = q
5. Cyclic Change (reversible)
   ΔE = 0
   q = -W = PΔV
   q = -W_max = P∫dV
6. Isothermal reversible Expansion
   ΔH = ΔE = 0 (internal energy is a function of temperature)
   q = -W_max = 2.303 nRT log( V₂ / V₁) = 2.303 nRT log( P₁ / P₂)
   ΔH = ΔE + Δn_gRT
7. Joule - Thompson coefficient 
   
   (i) For cooling , u > 0 (-ve sign)
   (ii)For heating , u < 0 (+ve sign)
8. Second Law of Thermodynamics 
   Efficiency of the Carnot engine = η = 
   q₂ - q₁q₂
    = 
   T₂ - T₁T₂
    = 1 - 
   T₁T₂
   
   q₂ = heat absorbed by engine
   q₁ = heat lost to sink
9. Entropy Change 
   ΔS_total = ΔS_system + ΔS_surrounding
   ΔS_fusion = 
   ΔH_fusionT_fusion
    ; ΔS_vapour = 
   ΔH_vapourT_vapour
10. Gibb's Free Energy (G)
    ΔG = G₂ - G₁
    ΔG = ΔH - TΔS (Gibb's Helmholtz equation)
    ΔG < 0 (means spontaneous process)
    ΔG > 0 (means non-spontaneous process)
    ΔG = 0 (means system is at equilibrium)
11. Kirchoff's Equation
    
    ΔH₂ - ΔH₁T₂ - T₁
     = ΔC_p and 
    ΔE₂ - ΔE₁T₂ - T₁
     = ΔC_v
    where , ΔC_p = ∑C_p(products) - ∑C_p(reactants) and ΔC_v = ∑C_v(products) - ∑C_v(reactants)
12. Degree of Dissociation (x)
    x = 
    D - dd
     = 
    M_t - M_oM_o
    
    where , D = theoretical V.D. and d = observed V.D.
13. pH of a solution
    pH = -log[H₃O⁺]
    pOH = -log[OH^-]
    pH + pOH = pK_W = 14
14. Isothermal (reversible)
    ΔS = 2.303 nR log (V₂ / V₁)
    at constant pressure ,
    ΔS = 2.303 C_p log₁₀ (T₂ / T₁)
    For vaporization ,
    ΔS = 
    ΔH_vapT_bp
    
    ΔG^o = - nFE⁰_cell
15. Sign Convention
    
    • If work is done on the system , W is +ve.
    • If work is done by the system , W is -ve.
    • If heat is absorbed by the system , or ΔH is +ve.
    • If heat is given out by the system , q or ΔH is -ve.
    • If energy is absorbed by the system , i.e. internal energy increases , ΔE is +ve.
    • If energy is released i.e., internal energy of the system decreases , ΔE is -ve.
16. Heat Capacity
    (i) Heat capacity at constant volume , C_V = [ ∂E / ∂T ]_V
    (ii) Heat capacity at constant pressure , C_p = [ ∂H / ∂T ]_p
    For an ideal gas , C_p - C_v = R
17. Heat of Reaction
    ΔH = ∑ H_(p) - ∑ H_(R)
    For exothermic reaction : ∑ H_(p) < ∑ H_(R) (∴ Δ is -ve)
    For endothermic reaction : ∑ H_(p) > ∑ H_(R) (∴ Δ is +ve)
    Heat change at constant pressure = q_p = ΔH
    Heat change at constant volume = q_v = ΔH
    ΔH = ΔU + PΔV
    ΔH = ΔU + Δn_(g)RT
    If,
    Δn_(g) = 0 , ΔH = ΔU
    Δn_(g) > 0 , ΔH > ΔU
    Δn_(g) < 0 , ΔH < ΔU
18. Clausis - Clapeyron Equation
    
    where ΔH_v = molar heat of vapourisation
    
    • Calorific Value is the amount of heat evolved when one gram of fuel as food is burnt in the presence of air or excess of oxygen.
    • Joule's Relationship between work done (w) and heat produced (H)
      W α H or W = JH
      where J = mechanical equivalent of heat ; J = 4.184 JCal^-1
    • S₁ and S₂ are solubility at temperature T₁ and T₂ respectively

SOLUTIONS

1. Solubility
   ΔH_solution = ΔH_lattice - ΔH_hydration
   If hydration energy > lattice energy , the solute goes into solution and ΔH_solution comes out to be -ve value i.e., the process is exothermic.
2. Henry's Law
   Mass of the gas dissolved per unit volume (n) α pressure (P)
3. Parts per million
   ppm (A) = 
   Mass of ATotal mass of the solution
    x 10⁶
   Weigth % = wt. of solute per 100gm of solution
   Volume % = wt. of solute per 100ml Of solution or Volume of solute per 100ml of solution
   Mole % = 
   Mass of soluteMoles of solute + Moles of solvent
    x 100
4. Relationship between Molality(m) of a solution and Mole fraction of the solute (X₂)
   X₂ = 
   m M₁1 + m M₁
    , where M₁ is the molecular mass of the solvent
5. Relationship between Molality(m) , Molarity (M) and Density of a solution (d)
   Molality , m = 
   M1000d - MM₂
    x 1000 , where M₂ is the molar mass of the solute .
6. Relationship between Mole fraction of the solute (x₂) and Molarity (M) of the solution
   X₂ = 
   MM₁M(M₁ - M₂) + d
   
   where M₁ & M₂ are the molecular masses of solvent and solute respectively . Density of solution is d. For isotonic or iso-osmotic solutions .
7. Raoult's Law (Vapour - Pressure lowering of solution)
   p_s = p_o.X_solvent
   
   p_o - p_sp_s
    = 
   nN
   
   p_o = pressure of pure solvent ; p_s = pressure of solvent
   α , during dissociation ,
   α = 
   i - 1n - 1
    , n = no. of ions after dissociation
   α , during association ,
   α = 
   1 - i1 - (1/n)
   
   Variation of vapour pressure with temperature
   
   Variation of vapour pressure with external pressure
   
8. Osmotic Pressure
   π = i 
   n_iV
   RT = hdg (due to association or dissociation)
9. Van't Hoff Factor
   i = 
   P_observedP_normal
    = 
   (Δp)_observed(Δp)_normal
    = 
   (ΔT_b)_observed(ΔT_b)_normal
    = 
   (ΔT_f)_observed(ΔT_f)_normal
    = 
   Normal molecular massObserved molecular mass
   
   For solution showing dissociation , the Van't Hoff factor i > 1
   For solution showing association , the Van't Hoff factor i < 1
   For solution showing no dissociation or association, the Van't Hoff factor i = 1
10. Raoult's Law
    P = P_A + P_B = P_A⁰ X_A + P_B⁰ X_B = ( 1 - X )P_A⁰ + P_B⁰ X_B
11. Ideal Solutions
    They obey Raoult's law for all range of concerntatation and temperature. ΔH_mix = 0 and ΔV_mix = 0
    eg. Hexane + Heptane ; Ethyl bromide + Ethyl chlroride ; Chlorobenzene + Bromobenzene , etc..
12. Non - Ideal Solutions
    The non-ideal solution do not obey Raoult's law for all concerntatation.
    ΔH_mix ≠ 0 and ΔV_mix ≠ 0
    If ΔH_mix > 0 and ΔV_mix > 0 , then non-ideal solutions show +ve deviations.
    If ΔH_mix < 0 and ΔV_mix < 0 , then non-ideal solutions show +ve deviations.
    e.g. Acetone + ethyl alcohol , water + ethyl alcohol , CCl₄ + CHCl₃ , etc.
13. Types of Azeotropic Mixtures
    (i) Minimum Boiling Azeotropic
    eg:- Ethanol (95.5%) + water(4.5%) mixture boiling .
    (ii) Maximum Boiling Azeotropic
    eg:- HNO₃ (68%) + water(32%) mixture boiling at 393.5K .
14. Elevation in boiling Point
    ΔT_b = T_b - T_o = K_b m = 
    K_B x W_B x 1000M_B x W_A
    
    W_A = mass of solvent (g) ; W_B = mass of solute (g)
15. Molal depression Constant (K_f)
    K_f = 
    RT_f²1000L_f
     [L_f = latent heat of fusion]
    Note :- Above equation are valid only when K_f and K_b are expressed in Kelvin m^-1

chemistry ncert study material

10th ncert

classification of elements

Carbon and Its Compounds

Metals and Non-metals

Acid Base And Salt

Chemical Reactions and Equations

9th ncert

Metals And Non-metals

Coal And Petroleum

Structure of Atom

Atoms and Molecules

Matter In Our Surroundings

8th ncert

Combustion and Flame

Materials: Metals and Non-Metals

Synthetic Fibres and Plastics

Coal and Petroleum

7th ncert

Physical and Chemical Changes

Soil

Acid, Base and Salt

Fiber To Fabric.

6th ncert

air around us

changes around us

Seperationof substances

Sorting Materials into Groups

Fibre to Fabric