Question

For an amino acid such as alanine, the major species in solution at pH 7 is the zwitterionic form. Assume a p K a value of 8 for the amino group and a p K a value of 3 for the carboxylic acid. Estimate the ratio of the concentration of the neutral amino acid species (with the carboxylic acid protonated and the amino group neutral) to that of the zwitterionic species at pH 7

Answer 1

The correct answer is 1 x 10⁻⁵

Step-by-step explanation:

In order to solve the problem, we can use the Henderson-Hasselbach equation to find the ratio alanine-COOH/alanine-COO⁻ (amino acid species with carboxylic acid protonated) and the ratio alanine-NH₂/alanine-NH₃⁺ (amino acid species with amino group neutral):

Henderson-Hasselbach equation:
`pH= pKa + log ([A^(-) ])/([HA])`

For carboxylic acid group (pKa= 3) at pH 7:

`7 = 3 + log ([Ala-COO^(-) ])/([Ala-COOH])`

`4= log ([ Ala-COO^(-) ])/([Ala-COOH])`

`10^(4) = ([Ala-COO^(-) ])/([Ala-COOH ])`

We need the ratio of species with protonated carboxylic acid group, so we need the inverse:

`10^(-4)= ([Ala-COOH ])/([Ala-COO^(-) ] )`

For amino group (pKa= 8) at pH 7:

`7= 8 + log ([Ala-NH_(2) ])/([Ala-NH_(3) ^(+) ])`

`-1= log ([ Ala-NH_(2) ])/([Ala-NH_(3) ^(+) ])`

`10^(-1) = ([Ala-NH_(2) ])/([Ala-NH_(3) ^(+) ])`

Finally, to find the ratio of neutral species we multiply the ratios:

`([Ala-COOH ])/([Ala-COO^(-) ])` X
`([Ala-NH_(2) ] )/([ Ala-NH_(3) ^(+) ])`= 10⁻⁴ x 10⁻¹= 10⁻⁵