Which statements are correct about the mixture of lysine (pI$ = 9.6$) and glycine (pI$ = 5.97$), separated by electrophoresis method or by solubility method?
(A) At pH$ = 5.97$, glycine does not migrate while lysine moves to the cathode.
(B) At pH$ = 5.97$, glycine does not migrate while lysine moves to the anode
(C) At pH$ = 9.6$, lysine does not migrate while glycine moves to the anode
(D) At pH$ = 5.97$ of the mixture of the solution, glycine precipitates out while lysine remains in the solution.

Hint: Electrophoresis is the motion of dispersed particles relative to a fluid under the influence of a spatially uniform electric field. It is a chromatography technique by which a mixture of charged molecules is separated according to the size, when placed in an electric field whereas in solubility method Le chatelier’s principle can be used.

Complete step by step solution:
In a mixed aqueous solution of glycine and lysine, the ionization of both amino acids increases due to proton transfer from glycine zwitterion to lysine zwitterion.
A zwitterion is a molecule that contains an equal number of positively and negatively charged functional groups.
Now, we will justify each and every statement.
Firstly,
Consider option A and B, at pH$ = 5.97$ glycine does not migrate while lysine moves to the cathode.
At this pH, glycine is present in the form of zwitterion, as the pH is equal to the isoelectric point of glycine. Isoelectric point is the pH at which a molecule carries no net electric charge or is electrically neutral in the statistical mean.
Further, Lysine is present in the protonated form i.e. it contains an $\alpha $ amino group , an $\alpha $ carboxylic acid group and a side chain lysine, classifying it as a basic, charged aliphatic amino acid.
Now consider option C, at pH $= 9.6$, lysine does not migrate while glycine moves to anode.
At this pH, lysine is present in the form of zwitterion as the pH is equal to the isoelectric point of lysine.
Therefore, glycine is present in the protonated form.
Now consider the next option, at pH $ = 5.97$ of the mixture of the solution, glycine precipitates out as it is present as zwitterion while lysine remains in the solution.

Hence, option A, C and D are correct.

Note: The stereochemistry of molecules won’t have any effect on electrophoretic mobility since it is dependent on velocity and intensity. Further, gel electrophoresis is a technique used to separate DNA fragments according to their size. The DNA samples are loaded into wells (indentations) at one end of the gel and an electric current is applied to pull them through the gel. DNA fragments are negatively charged so they move toward the positive electrode.