for a .001M solution of methionine:

a) calculate the isoelectric pH
b) calculate the isoionic pH

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To calculate the isoelectric pH of methionine, we need to determine the pH at which the net charge of the molecule is zero.

a) Calculate the Isoelectric pH:
1. First, write down the chemical structure of methionine: CH3SCH2CH2CH(NH2)COOH.
2. Identify the ionizable groups in methionine. In this case, they are the amino group (NH2) and the carboxyl group (COOH).
3. Determine the pKa values of the ionizable groups. The pKa of the amino group is around 9.21, while the pKa of the carboxyl group is around 2.28.
4. Compare the pKa values of the ionizable groups and determine which group will be ionized at a given pH. At a pH lower than the pKa of the carboxyl group, it will be protonated, and at a pH higher than its pKa, it will be deprotonated. Similarly, for the amino group, a pH lower than its pKa will protonate it, and a pH higher than its pKa will deprotonate it.
5. The isoelectric pH is the pH at which the amino group and the carboxyl group are equally charged. It would occur when the pH is in the range between the pKa values of the two groups, which is approximately 2.28-9.21. Since the amino group has a higher pKa, protonation of the amino group occurs at lower pH values, while deprotonation of the carboxyl group occurs at higher pH values.

So, the isoelectric pH of methionine lies in the range of approximately pH 2.28-9.21.

b) Calculate the Isoionic pH:
To calculate the isoionic pH, we need to determine the pH at which the net charge of methionine is -1.

1. The ionizable groups in methionine are the amino group (NH2) and the carboxyl group (COOH).
2. From the pKa values, we know that at a pH higher than the pKa of the amino group, it will be deprotonated, and at a pH lower than the pKa of the carboxyl group, it will be protonated.
3. At a pH higher than the pKa of the amino group (around 9.21), the amino group will be deprotonated and carry a negative charge (-1). At a pH lower than the pKa of the carboxyl group (around 2.28), the carboxyl group will be protonated and carry a positive charge (+1).
4. The isoionic pH is the pH at which the net charge of the methionine molecule is -1, which means that the charges on the ionized groups cancel each other out.
5. Since the amino group has a higher pKa and will be deprotonated first, the isoionic pH would be higher than the pKa of the amino group, but lower than the pKa of the carboxyl group.

So, the isoionic pH of methionine would lie in the range of approximately pH 2.28-9.21.