Chemistry of solutions equations (NYB)

Properties of Solutions
Concentrations

  • The solute (called A):
    is the compound dissolved in the solvent.
  • The solvent:
    is the compound dissolving the solute A
  • The solution:
    is the combination of both A and the solvent.
molarity (M) =   mole of solute  = mol/L
liter of solution
normality (N) =   equivalent of solute  = Eq/L       (mostly used for acid-base or redox reaction)
liter of solution





Normality could be ambiguous. The equivalence unit (Eq) depends both on the reactant and the type of reaction present.
If H2SO4 is used in an acid-base reaction (neutralization); then 1 mole of H2SO4 = 2 equivalents of H+. Therefore, 1 M H2SO4 = 2 N H+ (correctly, it should be written H3O+).
However, if H2SO4 is used in a precipitation reaction with Ba2+ then 1 mol H2SO4 reacts with 1 mol Ba2+ then 1 M H2SO4 = 1 N H2SO4
IUPAC and NIST discourage the use of normality.
molality (m) =   mole of solute  = mol/kg
kg of solvent
mass percent (A%) =   mass of A  x 100%   = %
total mass of solution
mole fraction (χA) =   mole of A          no unit.
total mole of the solution
%dissociation =   mole of solute ionized  x 100% = %
mole of formula unit added
Solubility of gases
Henry's lawCgas = kgas Pgas

where Cgas : gas solubility (mol/L),   kgas : Henry's constant for the solubility of the gas (M/atm)
Dalton's law of partial pressure Ptotal = PA + PB + PC + ... + Pn
χA(gas phase) =   PA
PTot
Colligative properties
Raoult's law (vapor pressure of two volatile chemicals)Ptotal = χA⋅P°A  +  χB⋅P°B
Raoult's law (solvent + non volatile solute)Psolution = χsolvent ⋅ P°solvent
Boiling point elevationΔTb = Kb⋅msolute       (for an electrolyte: ΔTb = i Kb⋅msolute)
Freezing point depressionΔTf = Kf⋅msolute       (for an electrolyte: ΔTf = i Kf⋅msolute)
Osmotic pressureΠ = M R T       (for an electrolyte: Π = i M R T)
van't Hoff factor
i =   mole of particle in solution        no unit.
mole of formula unit added
Equilibrium
Equilibrium constant
  • For the equilibrium: aA + bB   ⇌   cC + dD
K =   [C]c [D]d 
[A]a [B]b


        note: K = Kc (based on molarity)
Reaction quotient (Q)
Q =   [C]oc [D]od 
[A]oa [B]ob


        note: [ ]o = initial concentration (not at equilibrium)
Relation between Kc and Kp
  • Kp: pressures in atmosphere
  • Δn: difference between ngas product - ngas reactant
  • R: 0.08206 L.atm.K-1mol-1
Kp = Kc(RT)Δn
Acid-base and pH
acid strength
% dissociation =   number of mole dissociated at equilibrium x 100%
number of mole initially added
pH measurement pH = -log[H+]      ,       [H+] = 10-pH

pOH = -log[OH-]  ,      [OH-] = 10-pOH

pH + pOH = 14.00 at 25°C

Kw = [H+][OH-] = 1.0x10-14 at 25°C
Henderson - Hasselbach equation
pH = pKa + log ( [A-])  for the conjugate system HA ⇌ H+ + A-
[HA]
Solubility
solubility product MX3(s) ⇌ M3+(aq) + 3X+(aq)       then       Ksp = [M3+] [X+]3
Kinetic
Rate of a reaction
  • Consider the reaction: aA → bB
Rate =   change of concentration 
change in time
  =   -Δ[A] 
a Δtime
  =   +Δ[B]  = M/s
b Δtime
Rate law
  • k: rate constant (variable units)
  • n , m: order of the reactant
  • n + m = overall order of the reaction
Rate = k [A]n   single reactant.

Rate = k [A]n [B]m ...   multiple reactants.    
Integrated rate law
 Order
 zeroonetwo
Rate lawRate = kRate = k[A]Rate = k[A]2
Integrated rate law [A] = [A]o - kt  Ln[A] = Ln[A]o - kt 
  1 =  
[A]
1 + kt 
[A]o
Plot axes to get a line [A] vs. tLn[A] vs. t
1 vs. t 
[A]
Rate constant unitsM.s-1s-1M-1.s-1
Half-life (t1/2)
t1/2 =  [A]o 
2k
t1/2 =  Ln 2 
k
t1/2 =  1 
k[A]o
Arrhenius equation
  • A = frequency factor (M.s-1)
  • R = 8.314 J.K-1.mol-1
  • T = temperature in Kelvin
  • Ea = activation energy (J.mol-1)
k = A e -Ea/RT
Arrhenius equation (linearized form)
Lnk = LnA -  Ea × 
R
1      The plot Lnk of 1/T should give a straight line with a slope of -Ea/R.
T
Arrhenius equation (for two temperatures)
Ln  k2 = 
k1
-Ea
R
 (  1
T2
 -  1 ) 
T1
Thermodynamic
Difference between two states (Δ) Δ = Final state - Initial state
First law of thermodynamic: conservation of the energy ΔE = q + w           where E: potential energy,   q: heat,   w: work

ΔE = ΔH - PΔV      where H: enthalpy,   P: pressure (kPa),   V: volume (L)
Entropy ΔSUniverse = ΔSsystem + ΔSsurrounding

Ssolid < Sliquid << Sgas
ΔS =   qreversible 
T



Second law of thermodynamic: spontaneity ΔG° = ΔH° - TΔS°     where G = free energy (kJ.mol-1),   T: temperature (K),
                                      S: Entropy (J.K-1mol-1)
Available free energy (system not at equilibrium) ΔG = RT ln (Q/K)           where R = 8.314 J.K.mol,   T: temperature (K)

ΔG = ΔG° + RT ln Q      where: ΔG° = - R T ln K

The symbol degree on ΔG° indicate "standard state conditions"
Standard state conditions
Gas:  P° = 1 atm
Concentration:  [c]° = 1 mol/L
State of matter:  The one at P = 1 atm and T = 25°C
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