Question

For an amino acid such as alanine, the major species in solution at \(\mathrm{pH} 7\) is the zwitterionic form. Assume a \(\mathrm{p} K_{\mathrm{a}}\) value of 8 for the amino group and a \(\mathrm{p} K_{\mathrm{a}}\) 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 \(\mathrm{pH}\) 7.

Short answer

The ratio of the neutral species to the zwitterionic species is 0.00001.

Step-by-step solution

Understand the Problem

We need to find the ratio of the concentration of neutral alanine (COOH and NH2 form) to its zwitterionic form (COO^{-} and NH3^{+}) at pH 7.

Identify Key Equations

We'll use the Henderson-Hasselbalch equation: \[pH = pK_a + \log \left( \frac{[A^-]}{[HA]} \right)\]where \([A^-]\) is the deprotonated form and \([HA]\) is the protonated form.

Calculate Carboxylic Acid Proportion

For the carboxylic acid group, which can exist as COOH or COO^-, use its pK_a of 3:\[pH = pK_a + \log \left( \frac{[COO^-]}{[COOH]} \right)\]Substituting values and solving:\[7 = 3 + \log \left( \frac{[COO^-]}{[COOH]} \right)\]\[\log \left( \frac{[COO^-]}{[COOH]} \right) = 4\]\[\frac{[COO^-]}{[COOH]} = 10^4 = 10000\]Indicating almost all carboxyl groups are in the COO^- form.

Calculate Amino Group Proportion

For the amino group, which can exist as NH3^+ or NH2, use its pK_a of 8:\[pH = pK_a + \log \left( \frac{[NH_2]}{[NH_3^+]} \right)\]Substituting values and solving:\[7 = 8 + \log \left( \frac{[NH_2]}{[NH_3^+]} \right)\]\[\log \left( \frac{[NH_2]}{[NH_3^+]} \right) = -1\]\[\frac{[NH_2]}{[NH_3^+]} = 10^{-1} = 0.1\]Indicating that most amino groups are in the NH3^+ form.

Combine Ratios to Determine Concentration Ratio

The overall concentration ratio of neutral to zwitterionic species is determined by combining the proportion of carboxylic groups as COOH and amino groups as NH2.\[\frac{\text{Neutral}}{\text{Zwitterion}} = \frac{[COOH]}{[COO^-]} \times \frac{[NH_2]}{[NH_3^+]}\]\[= \frac{1}{10000} \times 0.1 = 0.00001\]

Key concepts

Zwitterion

In the world of chemistry, a zwitterion stands out as a unique type of molecule. It possesses both positive and negative charges, yet it remains overall neutral. For amino acids like alanine, the term zwitterion refers to a structure where the amino group is positively charged \( NH_3^+ \) and the carboxylic group is negatively charged \( COO^- \). This balance of charges usually occurs at a specific pH, often near neutral pH levels.

Understanding zwitterions is crucial because this is the form most amino acids adopt in physiological conditions, like in our bodies at pH 7. This form promotes stability and solubility in water, which are essential properties for biological functions. Recognizing when an amino acid is in the zwitterionic form helps in predicting how it will interact in different environments and in biochemical processes.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a valuable tool for understanding the relationship between pH, pKa, and the concentration of acid and base forms. It is expressed as: \[ pH = pK_a + \log \left( \frac{[A^-]}{[HA]} \right) \]

Here, \( [A^-] \) is the concentration of the base form, and \( [HA] \) is the concentration of the acid form. This equation helps calculate the pH of solutions containing weak acids or bases when the pKa value, a measure of acidity, is known.

In the context of amino acids, like alanine, this equation allows us to estimate the ratio between different protonation states of amino acids under specific pH conditions. For example, we can determine how much of alanine is in its zwitterionic form versus its fully protonated or deprotonated forms. This understanding is critical in fields like biochemistry and pharmacology, where the behavior of molecules in solutions is crucial.

pH and pKa Relationship

Understanding the relationship between pH and pKa is fundamental in predicting how molecules behave in solutions. pKa is the pH at which half of a species is deprotonated; it's a constant specific to each acidic group. ***pH*** is the measure of how acidic or basic a solution is.

When the pH of the environment is lower than the pKa of a group, that group tends to be protonated. Conversely, when the pH is higher than the pKa, it tends to be deprotonated. For alanine, with a carboxylic pKa around 3, the carboxylic acid will mostly lose its proton \( COO^- \) at physiological pH (around 7).

This relationship helps predict the ionization state of molecules in different environments. Knowing whether an amino group or a carboxyl group is protonated at a given pH helps in understanding the molecule's stability and reactivity, which is essential for scientific studies related to enzyme activity, drug design, and protein function.

Protonation States

Protonation states indicate how many protons a molecule has accepted or donated. Specifically for amino acids, protonation states determine which functional groups are charged. This is highly dependent on the surrounding pH compared to the molecule's pKa values.

For alanine, at a pH lower than its carboxyl group's pKa of 3, this group would be fully protonated \( COOH \). However, at physiological pH, it is in the deprotonated \( COO^- \) form. Meanwhile, the amino group with a pKa of 8 remains largely protonated \( NH_3^+ \) at pH 7.

Understanding protonation states is crucial for studying amino acids’ solubility, charge distribution, and interaction with other molecules. It plays a major role in biochemical processes and the formulation of solutions in laboratory and industrial settings. Knowing these states helps in tailoring the environment to support specific reactions or behaviors of biological molecules.