What is the charge of the amino acid lysine at pH 2?


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> What is the charge of the amino acid lysine at $\mathrm{pH}=2$? $\mathrm{p}K\_\mathrm{a}$'s are carboxylic: 2.18; amino: 8.95; side chain: 10.79.
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The side chain of lysine is an amine group, so I assume that when fully protonated it has positive charge ($\ce{NH3+}$).


At $\mathrm{pH} = 2$, everything will be protonated because their $\mathrm{p}K\_\mathrm{a} > \mathrm{pH}$.


This gives a net 0 (carboxy) + 1 (amino) + 1 (side chain) = +2 charge. Why do sites such as [this](https://www.mtholyoke.edu/courses/sdecatur/chem333/problems/ps1key.html) say that at $\mathrm{pH} = 2$, lysine's charge is only +1, not +2?


There's probably something really simple I don't know. If anyone can help point it out, that would be great.




At $\mathrm{pH}=2$, the charge will be: 


(charge near neutral pH, 2 groups positive, one negative) + (the fraction of the pKa = 2.18 group that is protonated) 


=1 + (the fraction of the $\mathrm{p}K\_\mathrm{a} = 2.18$ group that is protonated) 


$=1 + 1/(1 + 10^{\mathrm{pH}-\mathrm{pK}}) =1 + 1/(1 + 10^{2-2.18})=1.60$ 


So the charge is +1.60, which is closer to 2 than 1, as you are saying. 


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> [OP] This gives a net 0 (carboxy) + 1 (amino) + 1 (side chain) = +2 charge.
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This is approximately correct. See DavePhD's answer for a more accurate treatment.



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> [OP] Why do sites such as [this](https://www.mtholyoke.edu/courses/sdecatur/chem333/problems/ps1key.html) say that at $\mathrm{pH} = 2$, lysine's charge is only +1, not +2?
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The table you cite is for proteins. When lysine gets incorporated into a protein, it forms peptide bonds with its carboxylate and its main chain amino function groups. Therefor, these groups no longer exist and don't get protonated or deprotonated (unless the lysine is the C-terminus or the N-terminus, in which case the table gives the wrong value). In short, the table is about the charge state of the side chain, not the original free amino acid.



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> [question cited] What is the charge of the amino acid lysine at $\mathrm{pH}=2$? $\mathrm{p}K\_\mathrm{a}$'s are carboxylic: 2.18; amino: 8.95; side chain: 10.79.
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The $\mathrm{p}K\_\mathrm{a}$ values given are correct for lysine in water. In a protein, they might differ depending on the chemical environment of the specific lysine residue you are looking at. They would also depend on ionic strength and on cosolvents, if any.


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