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Chapter 4 . <strong>Amino</strong> <strong>Acids</strong><br />
pH = 6.0 + log [His 0 ]<br />
[His 1+ ]<br />
52<br />
or,<br />
[His 0 ]<br />
[His 1+ = 10<br />
]<br />
pH − 6.0 = 10 2.0− 6.0 and,<br />
[His 0 ] = [His 1+ ] × 10 −4 = 1.53 × 10 −5 M<br />
The concentration of negatively charged histidine is calculated using the Henderson-Hasselbalch<br />
equation with pKa = 9.2, pH = 2.0, and [His 0] = 1.53 x 10 -5 M. In this case<br />
pH = 9.2 + log [His1- ]<br />
[His 1- ]<br />
[His 0 ]<br />
[His 0 ]<br />
or,<br />
= 10 pH− 9.2 = 10 2.0−9.2 and,<br />
[His 1- ] = [His 0 ] ×10 −7.2 = 1.53 ×10 −5 ×10 −7.2 = 9.6 ×10 −13 M<br />
At pH = 2.0 we have: [His 2+] = 0.097 M , [His 0] = 1.53 x 10 -5 M,<br />
[His 1+] = 0.153 M, [His 1-] = 9.6 x 10 -13 M.<br />
At pH = 6.4, we can assume that the carboxyl group is fully unprotonated and carries a -1<br />
charge while the α-amino group is fully protonated and carries a +1 charge. Thus, the ionic<br />
species of histidine depends critically on the ionic state of the imidazole side chain. When the<br />
imidazole group is protonated, histidine carries a net +1 charge. When it is unprotonated,<br />
histidine is uncharged.<br />
So, using<br />
pH = 6.0 + log [His 0 ]<br />
[His 1+ ]<br />
and [His 0 ] + [His 1+ ] = 0.25M ,<br />
we find that the ionic species of histidine at pH = 6.4 are :<br />
[His 0 ] = 0.179M and [His 1+ ] = 0.071M<br />
[His 2+] and [His 1-] are calculated using the Henderson-Hasselbalch equation with pH = 6.4, pKa<br />
= 1.8 and 9.2 and [His 1+] = 0.071 M and [His 0] = 0.179 M. We find [His 2+] = 2.8 x 10 -6 M and<br />
[His 1-] = 2.25 x 10 -4 M.<br />
At pH = 6.4 we have: [His 2+] = 1.78 x 10 -6 M , [His 0] = 0.179 M,<br />
[His 1+] = 0.071 M, [His 1-] = 2.84 x 10 -4 M.<br />
At pH = 9.3, the carboxyl group is unprotonated and negatively charged, the imidazole group is<br />
unprotonated and uncharged, and only the protonation state of the α-amino group needs to be<br />
determined. Histidine, at pH = 9.3 will be portioned between the His 0 and His 1- states. From<br />
pH = 9.2 + log [His1- ]<br />
[His 0 ]<br />
and [His 0 ] + [His 1- ] = 0.25M ,<br />
we find that the ionic species of histidine at pH = 9.3 are :<br />
[His 0 ] = 0.111M, [His 1- ] = 0.139M and<br />
[His 2+ ] = 1.75 ×10 -12 M, [His + ] = 5.5 ×10 -5 M<br />
7. Calculate the pH at which the g carboxyl group of glutamic acid is two-thirds<br />
dissociated.<br />
Answer: The pKa of γ carboxyl group of glutamic acid is 4.3.
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