Normality and Titration*^footnote1
 

Definition of Normality:	NA = [#H+, #OH- or #e - ] CA
Use for Titration:	N1V1 = N2 V 2

Equations on thermodynamics:
 
 

Definition of molar heat capacity:	q = Cn ΔT
First Law of Thermodynamics:	ΔE = q + w
Definition of enthalpy:	ΔH = ΔE + PΔV
Definition of Gibbs' free energy :	ΔG = ΔH - TΔS
Obtaining the ΔrHo from ΔHof :	ΔrHo   = νΔH of products -  νΔHof reactants
Obtaining the ΔrSo from So :	ΔrSo  = νSo products - νSo reactants (for ions these are ΔSo)

    The equilibrium constant from thermodynamic data:

        K = e^{-Δ Go/RT}                     (very important)

 The van't Hoff plot uses the linearized version of this equation in the form:

ln K =  - (ΔH^o/R)(1/T) + ( ΔS^o/R)

 i.e

  y  =   m x   +  b

Where the slope, m, is:   m = -(ΔH^o/R )    (NOTE NEGATIVE!)
and the intercept, b, is:    b = (ΔS^o/ R)
where x is:                      x = (1/T)
and y is:                          y = ln K

 Definitions of some Ks

K_sp is the equilibrium constant between a slightly soluble ionic compound (reactant) and its ions in solution (product).  Example:

    CaF₂  <-->  Ca²⁺   +  2F^-

    K_sp = [Ca²⁺][F^- ]²

Kd is the equilibrium constant of a complex ion (in a Lewis acid-base reaction) with its dissociated simple ion and ligands.  Example:

    Co(NH₃)₆²⁺  <-->  Co²⁺  +  6NH₃

    K_d =   [Co²⁺ ] [NH₃]⁶
                [Co(NH₃)₆²⁺]

p function:   p( ) = -log₁₀( )
    Examples:
                    pH = -log [H₃O⁺]
                    pOH = -log[OH^-]
                    pCl = -log[Cl^-]
                    pK_a = -log K_a

 Equations on Kinetics:

Zero order kinetics:
    rate equation:                    -ΔC/Δt = k

    integrated rate equation:    C = -kt + C_o

First order kinetics:
    rate equation:                    - ΔC/Δt = kC

    integrated rate equation:    lnC = - kt + lnC_o

Second order kinetics:
    rate equation:                    - ΔC/Δt = kC²

    integrated rate equation:    1/C = kt + 1/C_o

Arrhenius equation:            k = A e^-ΔH*/RT
                                                     where ΔH* is the "activation energy" or "enthalpy of activation"

Equations on Electrochemistry:

In the stoichiometry of the electrochemical cell, one can convert from coulombs to moles of electrons using the Faraday constant, F.  F = 96 487 C mol^-1

Cell diagram:

Anode | Anolyte | (salt bridge) | Catholyte | Cathode
   OXIDATION                        REDUCTION

Standard Potentials, E^o, are reduction potentials

E^o_cell = E^o_{oxidation, anode} + E^o_cathode

E^o_oxidation =   -E ^o_std

E^o_reduction =  + E^o _std

For non-standard conditions:

Nernst Equation:

    E_cell = E^o _cell - (RT/nF) lnQ                     n is the number of electrons transferred

    E_cell = E^o _cell - (0.0592/n) lnQ  at 25^oC

The relationship between Gibbs' free energy and potential:

    ΔG = - nFE

*footnote 1:  SIO and IUPAC have recommended elimination of normality.  Thus, the algebraic symbol, N, and the unit symbol, N, are not standard SI.  I disagree with this decision which was was based upon the understanding the normality is a convenience and not a necessity.  The real reason for the use of normality is if one has a totally unknown substance when doing a titration, in which case the answer can be reported only in normality (or something equivalent.)  The convenience of the equation: N₁V₁ = N ₂V₂  is only a side issue.