Percentage of species 100 50 ph 1 2 3 4 5 6 7 8 9 10

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percentage of species 100 50 pH 1 2 3 4 5 6 7 8 9 10 11 12 cation anion zwitterion isoelectric point At the half neutralization point of an acid, pK a = pH + Log [acid] [conj. base] pK a = pH + Log(1) = pH + 0 thus, pK a = pH pK a = pH pK a = pH H 3 NCHCO 2 + - -H + +H + H 2 NCHCO 2 H 3 NCHCO 2 H -H + +H + + - pK a = 2.3 pK a = 9.7 CH 3 CH 3 CH 3
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Titration Curve of the Alanine Species As hydroxide ion is added to an acidic solution of alanine, the pH of the solution changes as shown in the titration curve below. pH 2 4 6 8 10 12 equivalents of HO - added 0.5 1.0 1.5 2.0 The titration curve is typical for titrating a weak acid with a strong base. K a = [H 3 O + ] [A - ] [HA] Log K a = Log [H 3 O + ] + Log [A - ] [HA] Log [H 3 O + ] = Log K a - Log [A - ] [HA] - Log [H 3 O + ] = - Log K a + Log [A - ] [HA] pH = pK a + Log [A - ] [HA] As HO - is added, the ratio of [A - ]/[HA] increases, and the pH increases. At the half neutralization point, pH = pK a . pH = pK a pI = pK a + pK a 2 pH = pK a H 3 NCHCO 2 + - -H + +H + H 2 NCHCO 2 H 3 NCHCO 2 H -H + +H + + - pK a = 2.3 pK a = 9.7 CH 3 CH 3 CH 3
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Some Other General Observations on Isolectric Points Lysine has two amino and one carboxyl functions. At low pH, it has three acid functions that deprotonate as HO - is added in order of their acid strengths. The isoelectric point of lysine is the average of pK a2 and pK a3 : pI = 9.0 + 10.5 2 = 9.8 At pH = 9.8, the dominant lysine species in solution is the neutral zwitterion. H 3 N(CH 2 ) 4 CHCOOH NH 3 + + HO - H 3 O + dicationic form of lysine (pK a1 = 2.2) H 3 N(CH 2 ) 4 CHCO 2 - NH 3 + + monocation form of lysine (pK a2 = 9.0) HO - H 3 O + H 3 N(CH 2 ) 4 CHCO 2 - NH 2 + zwitterionic form of lysine (pK a3 = 10.5) HO - H 3 O + H 2 N(CH 2 ) 4 CHCO 2 - NH 2 anionic form of lysine
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Aspartic acid has one amino and two carboxyl functions. At low pH, it
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