Some Useful Equations for CHEM 1120

Normality and Titration*footnote1
 
Definition of Normality (N used here): 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 ΔrHө from ΔfHөs : ΔrHө   = νΔfHөproducts −  νΔfHө reactants
Obtaining the ΔrSө from Sө :
 ΔrSө  = νSө products − νSө reactants
(for ions these are ΔSө)
Note the SI symbol to designate one mole of reaction is the subscript r after the Δ so: Δr .  Examples: Δr Hө and ΔrSө .
 
Summary of the criteria for equilibrium and spontaneity
Condition For an Isolated System For a Closed System at Constant Pressure
Spontaneous Process ΔS > 0 ΔG < 0
Equilibrium ΔS = 0 ΔG = 0
Non spontaneous Process Impossible ΔG > 0

Equations on Equilibria:

    The equilibrium constant from thermodynamic data:

K = exp(−ΔGө/RT) (very important)
The van't Hoff plot uses the linearized version of this equation in the form:
ln K =  − (ΔHө/R)(1/T) + ( ΔSө/R) that is,
  y  =   m x   +  b
Where the slope, m, is: m = −(ΔHө/R )    (NOTE NEGATIVE!)
and the intercept, b, is b = (ΔSө/ R)
where x is: x = (1/T)
and y is: y = ln K

 Definitions of some Ks

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

    CaF2  ⇌  Ca2+   +  2F−

    Ksp = [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

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

Kf = 1/Kd

Equations on pH:

p function:   p( ) = −log10( )

    Examples:

                   pH = −log [H3O+]

                   pOH = −log[OH−]

                   pCl = −log[Cl−]

                   pKa = −log Ka

 Types of equilibrium problems encountered (see handout about type I and type II equilibrium problems):
 

pH of a strong acid:

pH = −log(Cacid)

,b>pH of a strong base:

pOH = −log(Cbase)

pH = 14.00 − pOH

pH of a weak acid:

Ka = x2/( Cacid − x)             x underlined can usually be ignored.

solve for x

pH = −log(x)

pH of a weak base:

Kb = x2/( Cbase − x)             x underlined can usually be ignored

solve for x

pOH = −log(x)

pH = 14.00 − pOH

pH of an acid buffer:

Ka = x( Csalt + x) /( Cacid − x)             x underlined can usually be ignored

solve for x:   x = Ka( Cacid ) / ( Csalt )

pH = −log(x)

pH of a base buffer:

Kb = x( Csalt + x)/( Cbase − x)             x underlined can usually be ignored.

solve for x:   x = Kb( Cbase ) / ( Csalt )

pOH = −log(x)

pH = 14.00 − pOH

pH of a salt of a strong acid and weak base:

Ka = x2/( Csalt − x)             x underlined can usually be ignored.

where Ka = Kw/Kb(of the conjugate base)

solve for x

pH = −log(x)

pH of a salt of a strong base and a weak acid:

Kb = x2/( Csalt − x)             x underlined can usually be ignored.

where Kb = Kw/Ka(of the conjugate acid)

solve for x

pOH = −log(x)

pH = 14.00 − pOH

Molar solubility:
Notice that you need to know how to write the equilibrium equation for thedissolution of the salt to get the values for νcationand νanion.

Ksp = ( νcationx )νcation(νanionx )νanion

solve for x

pH for the dissolution of a slightly soluble hydroxide:

Ksp = ( νcationx )νcation(νhydroxidex )νhydroxide

solve for x

pOH = −log( νhydroxidex )

pH = 14.00 − pOH

dissociation of a complex ion:

 Equations on Kinetics:

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

    integrated rate equation:    C =−kt + Co

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

    integrated rate equation:    lnC = − kt + lnCo

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

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

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                & nbsp;       REDUCTION

Standard Potentials, Eө, are reduction potentials

Eөcell = Eөoxidation, anode + Eөcathode

Eөoxidation =   −E ostd

Eөreduction =  + Eө std

For non-standard conditions:

Nernst Equation:

    Ecell = Eө cell − (RT/nF) lnQ    n is the number of electrons transferred

    Ecell = Eө cell − (0.0592/n) lnQ  at 25өC

The relationship between Gibbs' free energy and potential:

    ΔG = − nFE

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