Lecture of 15 January 2020Outline of today's lecture

Office hours - Monday 7:30-8:30 SFL 220 (correct room!)• except office hours on Monday Jan 20 (MLK Day) are moved to •Tuesday Jan 21 - same time and placePublic Service Announcement: attend seminars!•Polyprotic acids•Relationships between Ka's and cooperativity•

Titration of glycine - the hydrogen atom of polyprotic acids:

What does the titration curve of glycine look likeExpect it to look similar to the superpositions of thetitration curves of acetic acid pka4.75 andNity pKa9.25

Let's start with fully protonated glycineexpected titration sequence based on acidlbaseproperties

Ht HtChu Chu g ch

HI cozH Hsiu coz HaN cosAkan4.25 expected

i pKa 9.25strongeracid 2

note this analysis is thermodynamically exact but thestructural depictions omit the minor presenceof

ittEdsall Wyman 1958 µzN WzHpKa 2.35pKa 9.78

Cb

T AdesdpHi

measured pKa 2.35

pKa 9.78

pKa is 250 x stronger acid than acetic aciddue to favorable electrostatic interactions with

NHot group John G Kirkwood analysis

pKa that if NHyt

glycine has the best buffering capacitynear pKa and Kaz Derivative ofthis titration curve gives bufferindex P ddpHglycine is a poor buffer between pKa please

As a starting point to study the

titration curve of glycine lets evaluate

the titration behavior of a weak acid aceticacid with a strong base

Introduce Tn average numberofprotons lost per acetic acidfor any one molecule 4 0 or I but over the

ensemble of all acetic acid molecules h will

be non integer Ka CataCH cozH

tiCCHscoi

CHScoz It tCCHzC0j

CkHt

Htconc ofstrongbase

In titrant

craft a

9introducedpreviously totalconc aceticacid

isence P fifty 2303 dd yhtt

can derive the buffer index introduced last lecture

Titration curve of glycine starting with

fully protonated form titrate with strongbase

b average number 1 protons lost1 prot lost 2 protons lostt d

f N'HzUtz Cosi t 2 Ha CauCosiFVHz ChucozH t IvHzcuzcoz xCNHrCHz 65

total cone ofglycine Sum of all Spectre's

Casio can coil Effy Hs't ch witggfgmaymin terms ofAdv Citi Coi Kya Hsiu CHL cont CHIN Utucont

f FIT 2 KAKI importantHtresult

1 t Kai KaikanHt t Ht 2

Ka's are aciddissociation constants units_M butcan deriveequivalent equations in terms ofthe reciprocalassociationconstNote the denominator is proportional tothe total conc of

acetic aciddenom I t t Kotka each term isHt

T T q proportional to fractiondissociated Ht

What is the pH when glycine has2 CHLZero net charge yo yo isoelectric point

At the isoelectric pointIn Ht M 6.06

Ka Ka 10

How does the titration of a dibasicCd'iprotic acid compare to the titration of amixture of two different mono protic acids

Define the acid dissocconstant of monobasic groupswith lower case ka with

molecule 1 ha j molecule 2 ha

The titration curve is the sum of the two cumsbar

a FEItheft It k

Htka has 2ha katitration of

2 different Ht tmy

moleculeseachwite1 titmice I Chaitt Laikagroup Ht t C yr

recall the It K ZKacKayTh fora Httitration curveof a diproticacid L t fifty Kaikan

Htt

The two equations inKa kait has the red boxes are

Ka haiku equivalent giving thesekaitkaa relationships between

Kds and ka'sTwo limiting carers

the two sites are very different ha Karteen Ka Kai makes sense

Kaz Kaz

Two sites are identical independentso that Isa haze ka

in this Ka a 2kgcare

ka k

Kafka 4 identical independent

Remarkably Ka Kaz when the two

sites are identical independent Thereason for this reflects the statistics ofbinding to and dissociation firm multiplesitesNumerical factors Kalka 4 are statistical

factors

Exa Wssingle site CHA Ht Ai

haCHt

HA

kaa

CHAlet p probability of protonatedL p deprotonated

kaEtty

Ip

Zsile problem dental independentsites

HaA HA AIpm 2pct p l p5

LEFT YII 4pct 21pm2kHt

Kae CA'TCH'T It LI 7 zttf IFT

giving for 2 equivalentand independentsites Ka 2 Ka

Kae hahKaiKa 4

Another way to explore these effects is toremember that the terms in the Tn denomentor are

proportional to the fractions of the different species's

denominator It k4 Kaikan

Ht 2

Equivalently It FEI It 7,5generalizeto n sites

indenominator Itchy

but it also equals It 1 t t n

Equating terms again gives the relationshipbetween Ka's and ka

f on n 2 Ka Z kaKau hah

for the general case of n usingthe binomial expansion

Hx It 1 x t 1 2 2n

one derivesKa n ka

k.az Iz kai

The deviation of Ka's from there values

reflects the interactions between sites

and can be used to establishcooperativ2ty between ionizing groups

to be continued