The p K a of lysine's carboxyl group, amino group, and side chain are 2.2, 9.0, and 10.5, respectively. If lysine is in a pH 13 solution, what is the net charge on each lysine molecule?

The net charge on each lysine molecule would be - 1.

Explanation:

When the pH is above 2.2 the deprotonated form of the carboxylic acid is more present, while the amino group and side chain (which is also amino) remain protonated (with a positive charge):

R-COOH ↔ R-COO⁻

R-NH₃⁺

R'-NH₃⁺

Net charge = + 1

When pH is above 9.0, the carboxyl group remains deprotonated, while the amino group is deprotonated and the side chain is protonated:

R-COOH ↔ R-COO⁻

R-NH₂

R'-NH₃⁺

Net charge = 0

When pH is above 10.5, the carboxyl group remains deprotonated, while both the amino group and the side chain are deprotonated:

R-COOH ↔ R-COO⁻

R-NH₂

R'-NH₂

Net charge = - 1

So at pH=13 (which is above 10.5) the net charge is - 1.