24. Part A
i) pH=1:
At pH 1, His has 1 posively charged side chain, 1 posively charged amine group and a uncharged carboxyl group (COOH). So the net charge = 1+1+0 = +2
ii) ph=4.50:
Since pK1 is 1.82, His loses a proton from the carboxyl group at pH 1.82.
At pH 4.50, His has 1 posively charged side chain, 1 positiely charged amine group and a negatively charged carboxyl group (COOH). So the net charge = 1+1-1 = +1
iii)pH=7.59:
Since pKR is 6.0, His loses a proton at pH 6.0.
At pH 7.59, His has uncharged side chain, 1 positively charged amine group and a negatively charged carboxyl group (COOH). So the net charge = 0+1-1 = 0. It exists as a zwitter ion.
iv)pH=9.50:
Since pK2 is 9.17, His loses a proton from the amine group at pH 9.17.
At pH 9.50, His has uncharged side chain, 1 uncharged amine group and a negatively charged carboxyl group (COOH). So the net charge = 0+0-1 = -1
Part B:
pH= 7; pKa= 6.0;
[His]+[His-]=500nM
[His]=500-[His-]-------------1
According to Henderson–Hasselbalch equation pH=pKa + log([His-]/[His])
7=6+log([His-]/[His])
log([His-]/[His])=7-6
log([His-]/[His])=1
([His-]/[His])=101
([His-]/[His])=10
Using 1,
[His-]/(500-[His-])=10
[His-]=10*(500-[His-])
[His-]=5000-10[His-]
[His-]+10[His-]=5000
11[His-]=5000
[His-]=5000/11
[His-]=454.5mM
Moarity of protonated R-group at pH=454.5mM
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