Problem 102 - Chemistry: The Central Science in SI Units, Global Edition

Question

The amino acid glycine can act as a weak acid: If the \(1^{\text {st }} \mathrm{p} K_{a}\) for the protonated amino group of glycine is \(9.8,\) what is the ratio of the neutral to anionic form of glycine in blood at \(\mathrm{pH} 7.4 ?\)

Step-by-Step Solution

Answer

The ratio of the neutral form of glycine to the anionic form of glycine in blood at pH 7.4 is approximately 0.00398, using the Henderson-Hasselbalch equation.

Step 1: Understand the Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is given by: \[ \mathrm{pH} = \mathrm{p}K_a + \log{\frac{[\text{Conjugate Base}]}{[\text{Acid}]}} \] In our case: - Acid: Protonated amino group of glycine (neutral form) - Conjugate Base: Anionic form of glycine We are given the pH and pKa value, and we are to find the ratio, which is: \[ \text{Ratio} = \frac{[\text{Anionic form of glycine}]}{[\text{Neutral form of glycine}]} \]

Step 2: Use the Henderson-Hasselbalch equation to find the ratio

Plug in the given values into the Henderson-Hasselbalch equation: \[ 7.4 = 9.8 + \log{\frac{[\text{Anionic form of glycine}]}{[\text{Neutral form of glycine}]}} \]

Step 3: Solve for the ratio

We'll perform the following steps to solve for the ratio: 1. Subtract 9.8 from both sides of the equation: \[ -2.4 = \log{\frac{[\text{Anionic form of glycine}]}{[\text{Neutral form of glycine}]}} \] 2. Use the properties of logarithms to remove the log: \[ 10^{-2.4} = \frac{[\text{Anionic form of glycine}]}{[\text{Neutral form of glycine}]} \] 3. Calculate the value of \(10^{-2.4}\): \[ 0.00398 \approx \frac{[\text{Anionic form of glycine}]}{[\text{Neutral form of glycine}]} \] The ratio of the neutral form of glycine to the anionic form of glycine in blood at pH 7.4 is approximately 0.00398.

Key Concepts

Understanding Weak Acids

Weak acids only partially dissociate in water, meaning they do not release all their hydrogen ions into the solution. This property sets them apart from strong acids, which completely dissociate. The dissociation of weak acids can be understood by looking at their equilibrium in solution. At equilibrium, there is a balance between the undissociated acid and the ions it forms.

• In the context of the Henderson-Hasselbalch equation, the weak acid is represented by the acid form of a molecule, and its conjugate base is the dissociated form, also known as the anionic form.
• For glycine, a common amino acid, the neutral form acts as the weak acid, and the anionic form is created when it loses a proton.

Since we calculate ratios using the Henderson-Hasselbalch equation, it is important to use a weak acid because it provides a measurable pKa value that informs us about the acid's strength.

Amino Acids and Their Dual Nature

Amino acids are organic compounds that serve as building blocks for proteins. They feature both amino ( H_2N ) and carboxyl ( COOH ) functional groups, making them amphoteric, meaning they can act both as acids and bases.

• In the exercise, glycine's amino group acts as a weak acid, demonstrating its ability to donate a proton.
• Glycine, like other amino acids, can exist in different forms depending on the pH of the environment, including a neutral form and an ionic form.

Understanding the dual nature of amino acids is crucial for comprehending their behavior in biological systems and how they maintain pH balance in blood. Thus, they are not only essential for protein structure but also for metabolic pathways.

The Role of pH and pKa in Biochemical Systems

pH is a crucial measure of the acidity or basicity of an aqueous solution, indicating the concentration of hydrogen ions. In our exercise, the focus is on blood, which typically maintains a pH of around 7.4, slightly basic.

• pKa, on the other hand, provides a numerical value that illustrates the strength of an acid, depicting how easily an acid releases a proton.
• The Henderson-Hasselbalch equation is used to relate pH, pKa, and the concentrations of an acid and its conjugate base, offering meaningful insights into biochemical equilibria.

The main takeaway is that the closer the pH is to the pKa, the more equally distributed are the acid and conjugate base forms. However, when the pH is much lower than the pKa, like in the given exercise, the acid form predominates. This concept helps us understand physiological processes where pH and pKa determine the active forms of various biomolecules.