Download Fractional Composition

Robert G. Michel
Acid-base Titrations
Fractional Composition diagrams
Fractional Composition Equations
• Let C be the (formal) concentration of a weak
acid, then the mass balance:
• C = [HA] + [A-]. or [A-] = C - [HA]
• Substitute into Ka
[H + ](C − [HA])
Ka =
• or
[H + ]C
[HA] = +
[H ] + K a
[HA]
…….. eqn (1)
€
€
Fraction in the form HA
• α HA =
[HA]
[HA]
=
[HA] + [A−]
C
…eqn (2)
• Dividing eqn 1 by C gives the fraction in the
form HA:
€
• α HA =
[HA]
[H + ]
= +
C
[H ] + [K a ]
…eqn (3)
• similarly fraction in form A- is:
•
€
αA − =
[A− ]
[K ]
= + a
C
[H ] + [K a ]
…eqn (4)
€
1
Robert G. Michel
Monoprotic systems
• pKa = 5.00
• below pH 5
HA is dominant
• above pH 5
A- dominates
Note: if conjugate Pair BH+
and B, instead of HA and A• Equation 3 gives the fraction in the form BH+
• Equation 4 gives the fraction in the form B
• Ka is then the acid dissociation constant for
BH+ (which is Kw/Kb)
Diprotic Systems
re-arrange
re-arrange
Express [HA-] in terms of [H2A]
2
Robert G. Michel
Diprotic mass balance
Diprotic alpha equations
• In a similar manner the following can be
derived
Diprotic fractional diagram
• formic acid
• pK1, pK2 not separated by much, so
fraction of HA never close to unity
3
Robert G. Michel
Charge balance
Fraction of titration φ
• equilibrium constant, Henderson-Hasselbalch
use approximations that fail if:
– low concentrations
– equilibrium constants too close
• use fractional composition equations to
calculate titration curves in spreadsheets
• need to calculate mls of titrant (eg NaOH)
• done by use of charge balance and fraction of
titration φ
Charge balance
• solutions are electrically neutral
• sum of positive and negative charges must balance
– accounts for equilibrium concentrations
– molarities must balance on each side of equation
• so for titration of weak acid with strong base
– vol. Va of HA, initial = Ca
– vol. Vb of NaOH initial = Cb
• [H+] + [Na+] = [A-] + [OH-]
– see Harris Ch. 9-1
CV
• from which:
[Na + ] = b b
Va + Vb
• because CbVb moles NaOH diluted to volume of Va+Vb
€
Charge balance (cont.)
• similarly for weak acid:
• check back with eqn 4:
€
• from which:
€
[C HA − ] = [HA] + [A− ] =
αA − =
CaVa
Va + Vb
[A− ]
[K ]
= + a
C
[H ] + [K a ]
[A− ] = α A − C HA = α A −
CaVa
Va + Vb
• substitute in
CV
CaVa
+
+ [OH − ]
charge balance eqn: [H ] + b b = α A −
€
Va + Vb
Va + Vb
- eqn (5)
€
4
Robert G. Michel
Fraction of titration φ
• eqn (5) rearranged gives fraction of titration φ
[H + ] − [OH − ]
CV
Ca
φ= b b =
[H + ] − [OH − ]
CaVa
1−
Cb
αA − −
• bingo! relates volume of titrant to pH
• φ is the fraction of the way to the equivalence point, Ve
• when
€ φ = 1 volume of base added = Ve
• put [H+] on RHS to calculate volume on LHS
• use in spreadsheet
Hwk, due date Mon. March 22
• for acetic acid, oxalic acid, and phosphoric acid
do the calculations for their titration with
NaOH
• plot the fractional composition diagram and
the titration curve
• use a spreadsheet to do the calculations
• assume 0.1M NaOH and titrations with 20 mL
of 0.1 M of the acids
• assume a 5 ml increment
• near the end point assume smaller increments
sufficient to define the curve
• useful web site:
http://chemistry.beloit.edu/Rain/pages/titr.html
5