Calculate Ph of 0.10m Aquous Solution of Glutamic Acid

Introduction

Glutamic acid (C₅H₉NO₄) is an α-amino acid that plays a crucial role in many biological processes. In aqueous solution, it can donate two protons, making it a diprotic acid with two dissociation constants: pK₁ for the first dissociation and pK₂ for the second dissociation.

The pH of a glutamic acid solution depends on its concentration and the dissociation constants. For a 0.10 molar solution, we can calculate the pH using the Henderson-Hasselbalch equation, which relates pH to the ratio of conjugate base to acid concentrations.

pH Calculation Formula

The pH of a glutamic acid solution can be calculated using the Henderson-Hasselbalch equation for diprotic acids:

For a 0.10 molar solution, we assume complete dissociation of the first proton (since pK₁ is 2.15 and the solution is dilute). Therefore, [A⁻] = 0.10 M and [HA] = 0.

Worked Example

Let's calculate the pH of a 0.10 molar solution of glutamic acid:

1. Identify the dissociation constants: pK₁ = 2.15, pK₂ = 4.25
2. Since the solution is dilute (0.10 M), assume complete dissociation of the first proton
3. Apply the Henderson-Hasselbalch equation:

   pH = pK₁ + log₁₀([A⁻]/[HA]) = 2.15 + log₁₀(0.10/0)

4. The term log₁₀(0.10/0) approaches negative infinity, indicating the solution is strongly acidic
5. The actual pH will be slightly less than pK₁ due to the second dissociation, but for practical purposes at this concentration, we consider it ≈ 2.15

Interpreting Results

The calculated pH of approximately 2.15 indicates a strongly acidic solution. This is expected because glutamic acid is a weak acid with a pK₁ of 2.15. The solution will be dominated by the undissociated glutamic acid molecules.

For more accurate results, especially at higher concentrations or when considering both dissociations, numerical methods or specialized software may be required.