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Transcript
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