Question

For biochemistry, it asks "At what optimal pH can you separate an amino acid mixture of lysine, arginine, and cysteine" and the answer is 9.5

Then it asks for the net charge of arginine at the chosen pH. The answer came out as 0.24, which I have no idea how it got there. My question is how do you do this? This is the info i have:

pKa of COOH = 2.2

pKa of NH3+ = 9.0

pKa of R group = 12.5

Answer 1

You'd start by drawing the structure onto a piece of paper. You might even add the pKa values next to the pertinent groups.

Then you can use this table

Amino Acid	charge at pH 2	charge at pH 7	charge at pH 12
Glutamtic acid	0	-1	-1
Aspartic acid	0	-1	-1
Lysine	+1	+1	0
Arginine	+1	+1	+1 (50%)
Histidine	+1	+1 (25%)	0
Tyrosine	0	0	-1
Cysteine	0	0	-1

The net charge of arginini will depend on the pH due the values of the pKa, When you have a pH value between two pkaas it will mean that the group o the groups that have less value of pKa than the pH you are studying are DEprotonated.

To determine the net charge on a protein you have to know the amino acid sequence and understand the charges on each amino acid residue in the amino acid sequence. To do this, you have to know the charge on each weak acid on the protein before and after dissociation.

To find the average charge at pH 9.5, find the average charge (= fraction charged * charge) for each charged group, then sum the charges:

N-term NH3 + :

ratio: [NH_2] / [NH₃⁺] = 10^pH-pKa = 10^9.5-9= 10^0.5= 3.16 = 3.16/1 = ratio: [NH_2] / [NH₃⁺]

fraction charged: [NH₃⁺] / [NH₃⁺]+ [NH₂] = 1 / 3.16 +1 = 0.24