Lecture 11. Buffers

Lecture 11. Buffers - What is the pH of a weak acid...

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Unformatted text preview: What is the pH of a weak acid solution? What Correct solution of the cubic equation and the [H+]>>[OH-] approximation: approximation: [H+] Cubic equation • No approximations No • Correct in full pH range Correct Quadratic equation • Approximation: [H+]>>[OH-] Approximation: • Incorrect for pH > 6 Incorrect • Good enough for almost every practical application every cHAtotal = FHAtotal HAtotal What is the pH of a weak acid solution: Correct solution of the What cubic equation: cubic What is the pH of a weak acid solution: Quadratic solution after [H+] >> [OH-] approximation [H What is the pH of a weak acid solution? What Correct solution of the cubic equation and the [H+]>>[OH-] approximation: approximation: [H+] Cubic equation • No approximations No • Correct in full pH range Correct Quadratic equation • Approximation: [H+]>>[OH-] Approximation: • Incorrect for pH > 6 Incorrect • Good enough for almost every practical application every cHAtotal = FHAtotal HAtotal http://www.chem.ualberta.ca/~iip/chem211irc/TitrationVideo.html EDTA Calcium Titration with EDTA Calcium n Ca+ + (n+m) EDTA4- + m [MgIn]+ n [CaEDTA]2- + m [MgEDTA]2- + m In- n >> m ? n << m ? n=m? In- (Eriochrome T) [Ca2+] in a 3.0 mM EDTA Solution [Ca pCa2+ in a 3.0 mM EDTA solution (pH 7.0) pCa - pCa2+ = -5 Log[Ca2+] Log[Ca -6 -7 -8 -9 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 cCaTotal/ mM pCa2+ in a 3.0 mM EDTA solution (pH 7.0) pCa - pCa2+ = Log[Ca2+] Log[Ca -4 -6 -8 0.001 0.002 0.003 0.004 cCaTotal/ mM The Exact Ca2+ Equivalent of the “HendersonExact Hasselbalch” Equation cCaTotal - [Ca 2 + ] 1 Ca 2 + ] = ' ´ [ K f c EDTAtotal - cCaTotal - [Ca 2 + ] or pCa 2 + æ ö cCaTotal - [Ca 2 + ] ÷ = log(K 'f ) - logç 2+ ÷ çc è EDTAtotal - cCaTotal - [Ca ] ø 2+ EDTA + Ca2+ EDTA EDTA.Ca2+ EDTA The Exact H+ Equivalent of the “HendersonExact Hasselbalch” Equation c HATotal - [H + ] + [OH - ] + [H ] = K a ´ c Atotal + [H + ] - [OH - ] or + -ö æc HATotal - [H ] + [OH ] ÷ pH = pK a - logç + -÷ çc è Atotal + [H ] - [OH ] ø A- + H+ HA HA Ca2+ versus H+ Ca c HATotal - [H + ] + [OH - ] + [H ] = K a ´ c Atotal + [H + ] - [OH - ] cCaTotal - [Ca 2 + ] 1 2+ [Ca ] = ' ´ K f c EDTAtotal - cCaTotal - [Ca 2 + ] Why is there on free ion term for Ca2+ but two for H+ ? two The Exact H+ Equivalent of the “HendersonExact Hasselbalch” Equation Derived from: • Acid dissociation Acid • Mass balance [H+] = Ka [HA] / [A-] [HA] + [A-] = cHAtotal + cAtotal [HA] • Water autoprotolysis H2O <==> H+ + OHOH • Charge balance [M+] + [H+] = [A-] + [OH-] [M [OH the acid as HA} the with [M+] = cAtotal with {if we assume that the base was used as a M+ salt and {if => See pdf file for actual derivation. The Exact H+ Equivalent of the “HendersonExact Hasselbalch” Equation c HATotal - [H + ] + [OH - ] + [H ] = K a ´ c Atotal + [H + ] - [OH - ] or + -ö æc HATotal - [H ] + [OH ] ÷ pH = pK a - logç + -÷ çc è Atotal + [H ] - [OH ] ø A- + H+ HA HA Can this be simplified for pH<<6? Can this be simplified for pH>>8? The Exact H+ Equivalent of the “HendersonExact Hasselbalch” Equation c HATotal - [H + ] + [OH - ] + [H ] = K a ´ c Atotal + [H + ] - [OH - ] or + -ö æc HATotal - [H ] + [OH ] ÷ pH = pK a - logç + -÷ çc è Atotal + [H ] - [OH ] ø A- + H+ HA HA Can this be simplified for cHA, cA >> [H+], [HO-]? (Simplified) Henderson-Hasselbalch Equation (Simplified) For Acids: For æ c Atotal ö pH = pK a + logç ÷ è c HAtotal ø A- + H+ For Bases: HA HA æ c BTtotal ö pH = pK a + logç ÷ c BHTtotal ø è B + H+ BH+ BH Which statement is always true? Which æ[A - ] ö pH = pK a + logç ÷ è[HA] ø æ c Atotal ö pH = pK a + logç ÷ è c HAtotal ø [A-]/[HA], pH and pKa When [A-] = [HA], pH = pKa When [A - ] pH = pK a + log [HA] = pK a + log(1) = pK a If [A-]/[HA] changes by 10 pH changes by 1 Daniel C. Harris, Exploring Chemical Analysis, 2nd ed., W.H. Freeman and Company, New York, 2001. Freeman pCa2+ in a 3.0 mM EDTA solution (pH 7.0) pCa Buffer Capacity - pCa2+ = -5 Log[Ca2+] Log[Ca -6 -7 -8 -9 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 cCaTotal/ mM Buffer Capacity (β ) Buffer A buffer works best when the pH = pKa Commonly Used Buffers Used Daniel C. Harris, Exploring Chemical Analysis, 2nd ed., W.H. Freeman and Company, New York, 2001. Freeman Preparing a Buffer in the Lab Preparing Daniel C. Harris, Exploring Chemical Analysis, 2nd ed., W.H. Freeman and Company, New York, 2001. Freeman Other Considerations Other 1) Buffer pH depends on the temperature. Why? Why? 2) Buffer pH depends on the ionic strength Buffer ...
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This note was uploaded on 04/06/2011 for the course CHEM 2011 taught by Professor Buhlman during the Spring '10 term at Minnesota.

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