Question

To \(1.0\) liter of a \(1.0 \mathrm{M}\) solution of glycine at the isoelectric \(\mathrm{pH}\) is added \(0.3\) mole of \(\mathrm{HCl}\), What will be the \(\mathrm{pH}\) of the resultant solution? What would be the \(\mathrm{pH}\) if \(0.3\) mole of \(\mathrm{NaOH}\) were added instead?

Short answer

After adding 0.3 moles of HCl to the 1.0 liter of a 1.0 M solution of glycine at the isoelectric pH, the pH of the resultant solution is approximately 2.88. If 0.3 moles of NaOH were added instead, the pH of the resultant solution would be approximately 9.06.

Step-by-step solution

Understanding the isoelectric point of glycine and its structure

The isoelectric point (pI) is the pH at which a molecule carries no net electrical charge. For amino acids like glycine, this occurs when the amino group (NH₃⁺) and the carboxyl group (COO⁻) are both present in their respective charged forms. In the case of glycine, the isoelectric point is given as pH = 6.0. The structure of glycine at the isoelectric pH is as follows: \[ \mathrm{H_{3}N^{+}-CH_{2}-COO^{-}} \]

Calculate the moles of glycine and HCl

First, determine the moles of glycine in the 1.0 L solution: Moles of glycine = 1.0 M × 1.0 L = 1.0 mol The problem also states that 0.3 moles of HCl are added to the solution. So, the moles of H⁺ ions in HCl = 0.3 mol.

Calculate the moles of glycine species after adding HCl

Adding HCl (an acid) to the glycine solution will result in the donation of H⁺ ions to the COO⁻ group of glycine, converting it to COOH. Moles of glycine after adding the HCl: Moles of zwitterionic (neutral) glycine = 1.0 mol - 0.3 mol = 0.7 mol Moles of protonated (positively charged) glycine = 0.3 mol Now, the glycine in the solution consists of 0.7 moles zwitterionic glycine and 0.3 moles of protonated glycine.

Calculate the new pH after adding HCl

To calculate the new pH after adding the HCl, we use Henderson-Hasselbalch equation for acidic form of glycine, which is: \[ \mathrm{pH} = \mathrm{pK_a} + \log \Big(\frac{\mathrm{[COO^{-}]}}{\mathrm{[COOH]}}\Big) \] For glycine, pKa = 2.34 (given). Now, plug the moles of the species into the equation and solve for the new pH after adding HCl: \[ \mathrm{pH} = 2.34 + \log \Big(\frac{0.7}{0.3}\Big) = 2.34 + 0.54 \approx{2.88} \] Thus, the pH of the resultant solution after adding HCl is approximately 2.88.

Calculate the moles of glycine species after adding NaOH

Instead of HCl, let's now add 0.3 moles of NaOH. Adding NaOH (a base) to the glycine solution will result in the removal of H⁺ ions from the NH₃⁺ group, converting it into NH₂. Moles of glycine after interaction with the NaOH: Moles of zwitterionic (neutral) glycine = 1.0 mol - 0.3 mol = 0.7 moles Moles of deprotonated (negatively charged) glycine = 0.3 moles Now, the glycine in the solution consists of 0.7 moles zwitterionic glycine and 0.3 moles deprotonated glycine.

Calculate the new pH after adding NaOH

To calculate the new pH after adding the NaOH, we use the Henderson-Hasselbalch equation for the basic form of glycine: \[ \mathrm{pH} = \mathrm{pK_a'} + \log \Big(\frac{\mathrm{[NH_{2}]}}{\mathrm{[NH_{3}^{+}]}}\Big) \] For glycine, pKa' = 9.60 (given). Now, plug in the moles of the species into the equation and solve for the new pH after adding NaOH: \[ \mathrm{pH} = 9.60 + \log \Big(\frac{0.3}{0.7}\Big) = 9.60 - 0.54 \approx{9.06} \] Thus, the pH of the resultant solution after adding NaOH is approximately 9.06.

Key concepts

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is an indispensable tool in the realm of biochemistry, frequently used to relate the pH of a solution to the pKa (acid dissociation constant) of a buffer component and the ratio of its protonated to deprotonated forms. The equation is articulated as:

\[ pH = pKa + \text{log} \left( \frac{[A^-]}{[HA]} \right) \]

In this context, \( [A^-] \) signifies the concentration of the base form of the buffer component, and \( [HA] \) represents the concentration of the acid form. The Henderson-Hasselbalch equation assumes that the concentrations of acid and its conjugate base at equilibrium represent the relative strengths of the buffer system, enabling one to predict how the pH will shift upon the addition of acids or bases. For amino acids with both acidic and basic groups, the equation may be applied to specific functional groups, considering the relevant pKa values.

Amino Acid Properties

Amino acids are the foundational units of proteins and possess unique attributes due to their structure. Each amino acid comprises a central carbon atom that binds to an amino group (NH₃⁺), a carboxylic acid group (COO⁻), a hydrogen atom, and an R-group or side chain that defines its characteristics.

Glycine, the simplest amino acid due to its hydrogen R-group, is capable of carrying a net positive, net negative, or no charge, depending on the pH of the environment. This dynamic leads to the existence of different ionic forms: a positively charged form when the pH is below the isoelectric point (pI), a neutral form (zwitterion) when the pH equals the pI, and a negatively charged form when the pH is above the pI. This multifaceted behavior is crucial for the acid-base properties of amino acids and their reactions during titrations.

pH Determination

Determining the pH of a solution is essential for understanding the acidity or basicity of the medium, which in turn can influence biological and chemical processes. The pH scale ranges from 0 to 14, with lower values denoting higher acidity and values above 7 indicating alkalinity.

The pH can be computed from the concentration of hydrogen ions \([H^+]\) using the formula \(pH = -\text{log} [H^+]\). However, direct measurement of hydrogen ion concentration can be challenging; thus, the Henderson-Hasselbalch equation offers a more practical approach when dealing with buffer systems or solutions containing weak acids and bases. By relating the pH to the ratio of related chemical forms and known constants, one can accurately estimate the pH after adding specific amounts of acid or base, as demonstrated in the glycine example.

Acid-Base Titration

Acid-base titration is a quantitative analytical technique utilized to determine the concentration of an acid or a base in a solution. The method involves the gradual addition of a titrant (a solution of known concentration) to the solution being analyzed, with the reaction monitored via a pH indicator or a pH meter.

When titrating amino acids like glycine, one can observe a shift in pH reflecting the neutralization of the acid by the base or vice versa. The titration curve typically exhibits buffering regions around the pKa values, where the pH changes minimally despite the addition of titrant, as well as equivalence points where equal moles of acid and base have reacted. Understanding the titration process and interpreting the corresponding data allows researchers and students to determine crucial information about the acid-base properties and the isoelectric points of amino acids.