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