General Biochemistry I
General Biochemistry I BCHM 56100
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This 9 page Class Notes was uploaded by Braden Runolfsson on Saturday September 19, 2015. The Class Notes belongs to BCHM 56100 at Purdue University taught by Harry Charbonneau in Fall. Since its upload, it has received 51 views. For similar materials see /class/207992/bchm-56100-purdue-university in Biochemistry at Purdue University.
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Date Created: 09/19/15
Biochemistry 561 Buffer Capacity Ionic Strength and Tables of pKa The proper functioning of biological systems require control of pH since most metabolic processes are inactivated outside a certain na1row range of concentration of hydrogen ions A buffer is a system containing either a weak acid and its salt or a weak base and its salt which resists changes in pH upon addition of acid or base All pH buffers can be thought of as weak acids in the Bronsted sense The dissociation of a Bronsted general acid proton donor can be represented by the following equation HAZ Qf AZ39l H 1 where z is the ionic charge on HA the acid and AZ391 is the conjugate base Examples of Bronsted acids include NHJr z1 CH COOH 20andHPO392 z2 4 3 4 You will note that ammonium ion NH4 is considered an acid rather than ammonia NH3 as a base since a separate set of equations for treating bases as buffers is then unnecessary The dissociation of the general acid HAZ to its conjugate base and hydrogen ion is a reversible process The Law of Mass Action establishes a relationship between the chemical activities of an acid and its dissociation products at equilibrium aA aH Ka 7 2 aHA where Ka is the dissociation constant and a is the activity of the species indicated by the subscripts The activity and concentration of a chemical species are generally not equal but converge to the same value as the solution becomes more dilute Activities are not convenient units to work with in the laboratory and an analogous equation expressing equilibrium conditions in terms of concentrations of the chemical species can be written Kg A HA aH 3 where A and HA are the molar concentrations of the species indicated and Kay is the apparent dissociation constant Hydrogen ions are still expressed as activity since electrochemical systems such as the pH meter exist which directly measure the activity of hydrogen ion The apparent dissociation constant K81y unlike Ka is not a constant but rather is a function of the quot of the various species in the buffer system Biochemistry 561 A useful relationship can be obtained from equation 3 by taking the logarithm of appropriate terms A HA log Ka log aH log 4 BY DEFINITION pH log aH and pKa log Ka By substitution of these equivalent terms into equation 4 the HendersonHasselbalch equation is obtained A HA pH pKa39 log 5 Examination of this equation shows that since K81V is approximately constant variation with concentration is small the pH will depend primarily on the ratio A HA but will also show a secondary dependence on the total buffer concentration AHA due to variation of K81y with concentration BUFFER CAPACITY Buffer capacity represents the ability of a buffer to resist changes in pH An instantaneous buffer capacity can be de ned as the negative of the rst derivative of the amount of acid added with respect to pH dHJr 1nstantaneous buffer capac1ty 7 de from equation 5 l A de de 7 d In 6 a 2303 HA d l du HINT 7 log u if dx u dx which becomes A HA dPH MdHl 7 l 2303B dH HA since K81y is approximately constant deaV cs 0 Biochemistry 561 A The quantity W can be expanded to d A d H A d HA gtlt HA HA 2 d HI When a mole of acid is added to a buffer it converts a mole of A into HA Therefore dmA dm dH dH Substituting these quantities into equation 7 yields dHJr A HA 2303 0 8 AHHA Buffer Capacity NOTE that at constant buffer concentration the highest buffer capacity is observed when AHA ie when pH pKai A second important conclusion from equation 8 is that at a xed ratio A HA the buffer capacity is proportional to the total buffer concentration IONIC STRENGTH Generally it is more important to specify the ionic strength rather than the concentration of a buffer Ionic strength is de ned by l 1 2 2 212 Ki 9 i where 21 is the charge on the ion 139 present at a molar concentration Xi Points to remember in calculating ionic strength Uncharged species do not contribute to ionic strength 2 If a solution contains more than one type of salt or buffering species the ionic strength contributions of each salt must be summed 3 The calculation of ionic strengths in solutions containing multiply charged ions can be simpli ed by recognizing that each class of salts has a corresponding integer ratio of ionic strength to molaritywm This integer relationship holds only if one of the ions has a charge of1 or 1 Biochemistry 561 for NaCH3C00 a 11 salt 1 12 lZNa 12CH3COO39 1211M111M1M thus yM l for NaZHPO4 a 21 salt 1 12 12Na 22HPO439 1212Ml4lMl3M thus EM 3 for Na3PO4 a 31 salt 1 12 12Na 32PO439 1213M9M6M thus yM 6 Theory and experimental results indicate that I is a more valid measure than concentration of the effects ionic species have on other components of a solution Ionic species interact with one another and behavior of ionic solutions even at great dilution is far from ideal IONIC STRENGTH and pKa Activim and activity coe zcients When a solute dissolves in water or another solvent the crystal structure is destroyed and there is generally an accompanying temperature change The solute may go into solution as molecules ion pairs or as ions The solute molecules or ions become solvated by interacting with solvent Such interaction between solute and solvent or between different moleculesions of solute results in nonideal behavior ie the effective concentration of the solute species is often quite different from its real known concentration The effective concentration is called the activity of the species and may be less than equal to or greater than the molar or formal concentration of the species The activity of a species can be related to its concentration by the expression 31 Cl 10 where al is the activity of substance z39 91 is the activity coefficient of substance 139 and C1 is the molar or formal concentration Equation 10 holds for solute species which do not dissociate If the solute dissociates however the expression for activity is more complex Generally speaking the activity coefficients for nonionic solutes are approximately 1 except in concentrated solution In the case of ionic substances however the activity coefficient approaches 1 only in very dilute solution The differences between concentration and activity arise because of ionic interaction For electrolytes activity coefficients may easily be as small as 01 and deviations from ideal behavior can be significant at concentrations as low as 001 M Biochemistry 561 The DebyeHuckel theory postulates that all deviations from ideal behavior by ionic solutions arise from electrostatic interactions between ions For example a positive ion in solution will attract and therefore quotseequot more negative ions than positive ions Each ion is thought of as surrounded by an ion atmosphere of opposite charge When approximations to very dilute solutions are made the DebyeHuckel Limiting Law is obtained 12 e3z2 2 7 N 1 1n 7 7 7 21mm 1000 where Y activity coefficient of 139 e electronic charge Zi number of charges on 139 8 dielectric constant of medium k Boltzman constant 13805 x 103912 erg deg391 T Kelvin temperature N Avagadro39s number 6022 x 1023 l ionic strength of solution Substituting values for the constants and converting logarithms to base 10 gives the Debye Huckel limiting law at 25 C log Y 0509 Z xl However because we cannot study ions of a single charge only the mean activity coefficient can be directly measured Thus for the reaction HA H AZ log Vi 0509 IZH ZA N at 25 0C The DebyeHuckel equation simply states that the activity coefficient of any ion depends on the ionic strength of the solution This equation also predicts that K81y apparent dissociation constant will also depend on ionic strength 1 but not on the nature of the salts contributing to 1 Thus pKay will also depend on ionic strength It is common practice to use pKa values when calculating pH and buffer problems instead of pKay values appropriate to the buffer concentration The pKay values are known as a function of buffer concentration for only a few common buffers but it is possible to calculate approximate pKay from pKa values for a given ionic strength Use of pKay allows more accurate prediction of buffer pH The following table gives values for pKay pKa as a function of ionic strength 1 and temperature for various values of Z charge on HA as defined in equation 1 Biochemistry 561 Values of pKa39 pKa I Temp zl 20 z1 z2 0 C 004 004 013 021 001M 20 C 004 004 013 022 37 C 005 005 014 023 0 C 008 008 024 040 005M 20 C 008 008 025 042 37 C 009 009 026 043 0 C 010 010 031 051 010M 20 C 011 011 032 053 37 C 011 011 033 055 Example What is the pKay for acetic acid at 37 C in a 01 1 buffer The pKa at 37 C is 477 At 37 C and 01 land for z 0 the correction factor pKay pKa is 011 pKaV pKa pKay pKa 477 011 466 The Debey Huckel prediction that Ka depends on ionic strength 1 but not on the nature of the salts contributing to 1 has been veri ed experimentally at low ionic strengths For example the Ka of acetic acid is the same function of l for l S 02 regardless of whether the solution contains NaCl LiCl or BaClz For I 2 02 Ka depends on the nature of the salt added Solvent Corrections for buffer calculations The solvent of interest in most biochemical systems is water which itself is a weak acid Bronstead sense a proton donor and dissociates H20 H OH We already have de ned Kw39 Hl OH39l At 25 C the numerical value of KW is approximately 1039 For the purposes of buffer calculations pKW is assumed to be 14 Normally water is ignored in setting up the equations to calculate pH of a buffer However when the pH is extreme outside the usual pH range of 3 to 11 or the buffer is suf ciently dilute the H and OH39 contributed by the dissociation of H20 Biochemistry 561 have a signi cant effect on the buffer equilibrium and their effects on the pH must be taken into account If neither H4r nor OH39 appear explicitly in the dissociation reactions of buffers a reaction of the buffer species with water should be written to show for the purposes of calculation the origin of the H and OH39 ions When titrations are carried out to the pH extremes a signi cant amount of titrant is consumed in changing the pH of the solvent H20 In these instances corrections are made by titrating and equal volume of water alone solvent blank correction Biochemistry 561 pKa FOR BUFFERS Buffer g 0 C 20 C 37 C Oxalic acid 0 127 25 OC EDTA 0 17 Maleic acid 0 192 25 OC Aspartic acid 1 213 202 195 Phosphoric acid 0 206 213 221 Asparagine 1 21 25 OC Glycine 1 244 236 233 PyruVic acid 0 249 25 0C 242 EDTA 1 26 Pyrophosphoric acid 1 264 25 OC Malonic acid 0 286 25 OC Tartaric acid 0 312 304 302 Citric acid 0 322 314 311 Balanine 1 365 357 352 Formic acid 0 379 375 376 Lactic acid 0 389 386 387 Aspartic acid 0 401 392 388 y Aminobutyric 1 409 404 403 Succinic acid 0 428 422 419 Oxalic acid 1 420 425 432 Tartaric acid 1 443 437 437 eAminocaproic acid 1 442 438 438 Acetic acid 0 478 476 477 Citric acid 1 484 4 77 475 Propionic acid 0 490 487 489 Pyridine 1 517 25 OC Succinic acid 1 568 564 565 Malonic acid 1 567 568 574 MES 0 64 615 60 Maleic acid 1 623 25 OC Cacodylic acid 0 624 624 EDTA 2 63 Carbonic acid 0 658 638 630 Citric acid 2 639 639 643 BISTRIS 1 646 25 OC Pyrophosphoric acid 2 676 25 OC 0 73 69 66 Imidazole 1 69 25 OC pKa FOR BUFFERS Biochemistry 561 Buffer g 0 C 20 C 37 C MOPS 0 74 72 70 Phosphoric acid 1 731 722 718 246Collidine 1 74 23 0C 732 TES 0 80 755 72 N Ethylmorpholine 1 765 25 OC Triethanolamine 1 8 29 7 86 7 53 55Diethylbarbituric acid 0 840 806 782 Tricine 0 86 815 78 Glycinamide 1 88 82 77 Tris 1 885 821 775 Bicine 0 87 84 83 Morpholine 1 86 25 OC Asparagine 0 88 25 OC Diethanolamine 1 955 901 859 Boric acid 0 950 928 915 Ammonia 1 1008 940 889 Pyrophosphoric acid 3 942 25 OC Ethanolamine 1 1031 965 915 Glycine 0 1050 991 948 Aspartic acid 1 1063 1012 975 BAlanine 0 1100 1038 991 Carbonic acid 1 1063 1038 1024 EDTA 3 106 y Aminobutyric 0 1137 1071 1021 Triethylamine 1 1118 1078 1040 Ethylamine 1 1131 1079 1035 eAminocaproic acid 0 1171 1098 1042 Piperidine 1 1196 1128 1075 Abbreviations MES 2Nmorpholino enthanesulfonic acid MOPS 2Nmorpholino propanesulfonic acid BISTRIS m 2hydroxyethy1 iminotr hydroxymethyl methane ACES N 2acetamido 2aminoethanesulfonic acid TES Nm hydroxymethyl methyl2 aminoethanesulfonic acid Tricine N tr hydroxymethyl methylglycine Tris 2 hydroxymethyl2amino13propanediol Bicine N N 2hydroxyethyl glycine
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