Chemistry 232

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Chemistry 232

• Electrolyte Solutions

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Thermodynamics of Ions in Solutions

• Electrolyte solutions deviations from ideal
  behaviour occur at molalities as low as 0.01
  mole/kg.
• How do we obtain thermodynamic properties of
  ionic species in solution?

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Thermodynamics (II)

• For the H(aq) ion, we define
• ?fH? 0 kJ/mole at all temperatures
• S? 0 J/(K mole) at all temperatures
• ?fG? 0 kJ/mole at all temperatures

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Activities in Electrolyte Solutions

• For the following discussion
• Solvent s
• Cation
• Anion -
• Consider 1 mole of an electrolyte dissociating
  into ? cations and ?- anions
• G ns ?s n ?
• ns ?s n ? n- ?-
• Note since ? ? ?- ? ? ? ? ?- ?-

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The Mean Ionic Chemical Potential

• We define
• ? ? ? / ?
• We now proceed to define the activities
• ? ?? RT ln a
• ? ?? RT ln a
• ?- ?-? RT ln a-
• ?? ??? RT ln a?

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The Relationship Between a and a?

• Since ? ? ? / ?
• ? ?? RT ln a ? (??? RT ln a?)
• Since ??? ?? / ?
• This gives us the relationship between the
  electrolyte activity and the mean activity
• (a?)? a

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The Relationship Between a? , a- and a

• We note that ? ? ? ?- ?-
• and ? ? ? / ?
• This gives us the following relationship
• (??? RT ln a?) n (?? RT ln a)
• ?- ( ?-? RT ln a-)
• Since ? ??? ? ?? ?- ?-?
• (a?)? (a)? (a-)?-

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Activities in Electrolyte Solutions

• The activities of various components in an
  electrolyte solution are defined as follows
• a ? m
• a- ?- m-
• a ? m
• As with the activities
• (??)? (?)? (?-)?-
• (m?)? (m)? (m-)?-

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The Chemical Potential Expression

• This can be factored into two parts

Deviations from ideal behaviour
The ideal part
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Activity Coefficients As a Function of Molality

• Data obtained from
• Glasstone et al., Introduction to
  Electrochemistry, Van Nostrand (1942).
• CRC Handbook of Chemistry and Physics, 63rd ed.
  R.C. Weast Ed. CRC Press, Boca Raton, Fl
  (1982).

CaCl2
HCl
LaCl3
KCl
H2SO4
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Determination of Activity Coefficients in Solution

• Two ways
• Use the Gibbs-Duhem equation and ? for the
  solvent to estimate ? for the solute.
• Determination of osmotic coefficients from
• colligative properties
• vapour pressure measurements

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Estimates of Activity Coefficients in Electrolyte
Solutions

• A few have been proposed to allow the theoretical
  estimation of the mean activity coefficients of
  an electrolyte.
• Each has a limited range of applicability.

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The Debye Huckel Limiting Law

• This is valid in the up to a concentration of
  0.010 molal!

Z charge of cation z- charge of anion
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Debye Huckel Extended Law

• This equation can reliably estimate the activity
  coefficients up to a concentration of 0.10
  mole/kg.

B 1.00 (kg/mole)1/2
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The Davies Equation

• This equation can reliably estimate the activity
  coefficients up to a concentration of 1.00
  mole/kg.

k 0.30 (kg/mole)
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The Equilibrium Constant

• For a nonideal system, the nonstandard Gibbs
  energy of reaction is written

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The Equilibrium Condition

• If we apply the equilibrium conditions to the
  above equation

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The Autoionization of Water

• Water autoionizes (self-dissociates) to a small
  extent
• 2H2O(l) ? H3O(aq) OH-(aq)
• H2O(l) ? H(aq) OH-(aq)
• These are both equivalent definitions of the
  autoionization reaction.
• Water is amphoteric.

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The Autoionization Equilibrium

• From the equilibrium chapter

• But we know a(H2O) is 1.00!

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The Defination of Kw

• Kw a(H) a(OH-)
• Ion product constant for water, Kw, is the
  product of the activities of the H and OH- ions
  in pure water at a temperature of 298.15 K
• Kw a(H) a(OH-) 1.0x10-14 at 298.2 K

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The pH scale

• Attributed to Sørenson in 1909
• We should define the pH of the solution in terms
  of the hydrogen ion activity in solution
• pH -log a(H)
• Single ion activities and activity coefficients
  cant be measured

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Determination of pH

• What are we really measuring when we measure the
  pH?
• pH -log a?(H)
• a? (H) is the best approximation to the hydrogen
  ion activity in solution.
• How do we measure a?(H)?

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• For the dissociation of HCl in water
• HCl (aq) ? Cl-(aq) H(aq)
• We measure the mean activity of the acid
• a(HCl) a(H) a(Cl-)
• a(H) a(Cl-) (a?(HCl))2

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• Under the assumption
• a(H) a(Cl-)
• We obtain
• a(H) (a(HCl))1/2 a?(HCl)

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Equilibria in Aqueous Solutions of Weak Acids/
Weak Bases

• By definition, a weak acid or a weak base does
  not ionize completely in water (? ltlt100).
• How would we calculate the pH of a solution of a
  weak acid or a weak base in water?

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Equilibria of Weak Acids in Water The Ka Value

• Define the acid dissociation constant Ka
• For a general weak acid reaction
• HA (aq) ? H (aq) A- (aq)

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Equilibria of Weak Acids in Water

• For the dissolution of HF(aq) in water.
• HF (aq) ? H (aq) F- (aq)

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The Nonelectrolyte Activity

• HF (aq) ? H (aq) F- (aq)
• The undissociated HF is a nonelectrolyte
• ? a(HF) ?(HF) mHF ? mHF
• ?(HF) ? 1

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Equilibria of Weak Bases in Water

• Calculate the percentage dissociation of a weak
  base in water (and the pH of the solutions)
• CH3NH2 (aq) H2O ? CH3NH3(aq) OH- (aq)

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The Kb Value

• Define the base dissociation constant Kb
• For a general weak base reaction with water
• B (aq) H2O (aq) ? B (aq) OH- (aq)

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Calculating the pH of Solutions of Strong Acids

• For the dissolution of HCl, HI, or any of the
  other seven strong acids in water
• HCl (aq) ? H (aq) Cl- (aq)
• The pH of these solutions can be estimated from
  the molality and the mean activity coefficient of
  the dissolved acid
• pH -log (?? (acid) mH)

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Calculating the pH of Solution of Strong Bases

• For the dissolution of NaOH, Ba(OH)2, or any of
  the other strong bases in water
• NaOH (aq) ? Na (aq) OH- (aq)
• pOH -log (?? (base) mOH-)

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Calculating the pH of a Weak Acid Solution

• The pH of a weak acid solution is obtained via an
  iterative procedure.
• We begin by making the assumption that the mean
  activity coefficient of the dissociated acid is
  1.00.
• We correct the value of ?(H) by calculating
  the mean activity coefficient of the dissociated
  acid.
• Repeat the procedure until ?(H) converges.

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The Definition of a Buffer

• Buffer ? a reasonably concentrated solution of a
  weak acid and its conjugate base
• Buffers resist pH changes when an additional
  amount of strong acid or strong base is added to
  the solutions.

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• How would we calculate the pH of a buffer
  solution?

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note pH -log a(H)
Define pKa -log (Ka )
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The Buffer Equation

• Substituting and rearranging

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The Generalized Buffer Equation

• The pH of the solution determined by the ratio of
  the weak acid to the conjugate base.
• Henderson-Hasselbalch equation often used for
  buffer calculations!

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• Buffer ? CH3COONa (aq) and CH3COOH (aq))
• CH3COOH (aq) ? CH3COO- (aq) H (aq)
• The Equilibrium Data Table

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• The pH of the solution will be almost entirely
  due to the original molalities of acid and base!!

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Solubility Equilibria

• Examine the following systems
• AgCl (s) ? Ag (aq) Cl- (aq)
• BaF2 (s) ? Ba2 (aq) 2 F- (aq)
• Using the principles of chemical equilibrium, we
  write the equilibrium constant expressions as
  follows

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The Common Ion Effect

• What about the solubility of AgCl in solution
  containing NaCl (aq)?
• AgCl (s) ? Ag (aq) Cl- (aq)
• NaCl (aq) ? Na (aq) Cl- (aq)
• AgCl (s) ? Ag (aq) Cl- (aq)

Equilibrium is displaced to the left by
LeChateliers principle (an example of the common
ion effect).
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Solubility in the Presence of an Inert Electrolyte

• What happens when we try to dissolve a solid like
  AgCl in solutions of an inert electrolyte (e.g.,
  KNO3 (aq))?
• We must now take into account of the effect of
  the ionic strength on the mean activity
  coefficient!

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The Salting-In Effect

• AgCl (s) ? Ag (aq) Cl- (aq).
• Designate the solubility of the salt in the
  absence of the inert electrolyte as so m(Ag)
  m(Cl-) at equilibrium.

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• For a dilute solution

• Designate s as the solubility of the salt in the
  presence of varying concentrations of inert
  electrolyte.

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Reaction Equilibria in Nonideal Gaseous Systems

• For a nonideal system gaseous, the nonstandard
  Gibbs energy of reaction is written

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The Equilibrium Condition

• Calculate the equilibrium composition from the
  fugacity coefficients from compression factor
  data

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Temperature and Pressure Dependence of Ko

• As a function of temperature

• As a function of pressure