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