Calculate the volume, in liters, of 1.551 M KOH that must be added to a 0.128 L

Question

Calculate the volume, in liters, of 1.551 M KOH that must be added to a 0.128 L solution containing 9.43 g of glutamic acid hydrochloride (H3Glu Cl–, MW = 183.59 g/mol) to achieve a pH of 10.20. Glutamic acid (Glu) is an amino acid with pKa values of pKa1 = 2.23, pKa2 = 4.42, pKa3 = 9.95.

Calculate the volume, in liters, of 1.551 M KoH that must be added to a 0.128 L solution containing 9.43 g of glutamic acid hydrochloride (H3Glu CIT, MW 183.59 g/mol) to achieve a pH of 10.20. Glutamic acid (Glu) is an amino acid with pKa values of pKa 2.23, pKa2 4.42, pKa3 9.95. NH3 Number H-CH2- CH2-C-OH Glutamic Acid Hydrochloride

Explanation / Answer

As pH of 10.20 is required, you have to consider the pKa3.

moles of glutamic acid used = 9.43gm/183.59g/mol = 0.051 moles

Suppose volume of KOH required = X L

moles of KOH added = X L * 1.551 M = 1.551 L moles

moles of glutamic acid present after the addition = 0.051 - 1.551 L

pH = pKa + log [glutamate/glutamic acid]

or, 10.20     = 9.95 + log [1.551 X/0.051-1.551 X]

or, 1.551 X/0.051-1.551 X = 1.78

or, 1.551X = 1.78 (0.051-1.551X)

or, 1.551 X = 0.091 - 2.76 X

or, X = 0.0211 L

Volume of KOH added = 0.0211 L

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