Normality and Titration*^{footnote1}
Definition of Normality (N used here): | N_{A} = [#H^{+}, #OH^{−} or #e^{ −} ] C_{A} |
Use for Titration: | N_{1}V_{1} = N_{2} V_{ 2} |
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 Δ_{r}H^{ө} from Δ_{f}H^{ө}s : | Δ_{r}H^{ө} = νΔ_{f}H^{ө}products − νΔ_{f}H^{ө} reactants |
Obtaining the Δ_{r}S^{ө} from S^{ө}
: |
Δ_{r}S^{ө} = νS^{ө} products −
νS^{ө} reactants (for ions these are ΔS^{ө}) |
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 |
Definitions of some Ks
K_{sp} is the equilibrium constant between a slightly soluble ionic compound (reactant) and its ions in solution (product). Example:
CaF_{2} ⇌ Ca^{2+} + 2F^{−}
K_{sp} = [Ca^{2+}][F^{−}]^{2}
K_{d} is the equilibrium constant of a complex ion (in a Lewis acid-base reaction)with its dissociated simple ion and ligands. Example:
Co(NH_{3})_{6}^{2+} ⇌ Co^{2+} + 6NH_{3}
K_{d} = [Co^{2+}
] [NH_{3}] ^{6}
[Co(NH_{3})_{6}^{2+}]
K_{f} = 1/K_{d}
p function: p( ) = −log_{10}( )
Examples:
pH = −log [H_{3}O^{+}]
pOH = −log[OH^{−}]
pCl = −log[Cl^{−}]
pK_{a} = −log K_{a}
Types of equilibrium problems encountered (see handout about type I and type II
equilibrium problems):
pH of a strong acid:
pH = −log(C_{acid})
,b>pH of a strong base:
pOH = −log(C_{base})
pH = 14.00 − pOH
pH of a weak acid:
K_{a} = x^{2}/( C_{acid} − x) x underlined can usually be ignored.
solve for x
pH = −log(x)
pH of a weak base:
K_{b} = x^{2}/( C_{base} −
x) x underlined can usually be ignored
solve for x
pOH = −log(x)
pH = 14.00 − pOH
pH of an acid buffer:
K_{a} = x( C_{salt} + x) /( C_{acid} − x) x underlined can usually be ignored
solve for x: x = K_{a}( C_{acid }) / ( C_{salt} )
pH = −log(x)
pH of a base buffer:
K_{b} = x(
C_{salt} + x)/( C_{base} − x)
x underlined can usually be ignored.
solve for x: x = K_{b}( C_{base }) / ( C_{salt} )
pOH = −log(x)
pH = 14.00 − pOH
pH of a salt of a strong acid and weak base:
K_{a} = x^{2}/( C_{salt} − x) x underlined can usually be ignored.
where K_{a} = K_{w}/K_{b}(of the conjugate base)
solve for x
pH = −log(x)
pH of a salt of a strong base and a weak acid:
K_{b} = x^{2}/( C_{salt} − x) x underlined can usually be ignored.
where K_{b} = K_{w}/K_{a}(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
ν_{cation}and ν_{anion}.
K_{sp} = ( ν_{cation}x )^{νcation}(ν_{anion}x )^{νanion}
solve for x
pH for the dissolution of a slightly soluble hydroxide:
K_{sp} = ( ν_{cation}x )^{νcation}(ν_{hydroxide}x )^{νhydroxide}
solve for x
pOH = −log( ν_{hydroxide}x )
pH = 14.00 − pOH
dissociation of a complex ion:
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 = kC^{2}
integrated rate equation: 1/C = kt + 1/C_{o}
Arrhenius equation:
k = A e^{−Δ}^{H*/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, E^{ө}, are reduction potentials
E^{ө}_{cell} = E^{ө}_{oxidation, anode} + E^{ө}_{cathode}
E^{ө}_{oxidation} = −E^{ o}_{std}
E^{ө}_{reduction} = + E^{ө}_{ std}
For non-standard conditions:
Nernst Equation:
E_{cell} = E^{ө}_{ cell} − (RT/nF) lnQ n is the number of electrons transferred
E_{cell} = E^{ө}_{ cell} − (0.0592/n) lnQ at 25^{ө}C
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: N_{1}V_{1} = N_{ 2}V_{2} is only a side issue.