Problem 14 - Chemistry: An Atoms-Focused Approach

Question

Identify a suitable buffer system to maintain a pH of 3.0 in an aqueous solution.

Step-by-Step Solution

Answer

Answer: The suitable buffer system to maintain a pH of 9.0 in an aqueous solution would be the ammonium hydroxide (NH4OH) and its conjugate acid, ammonium cation (NH4+).

Step 1: Understand the Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation establishes the relationship between the pH of a solution, the pKa of the weak acid involved, and the ratio of the concentrations of the conjugate base to the weak acid: pH = pKa + log ([A-]/[HA]) where pH is the desired pH, pKa is the acid dissociation constant, [A-] is the molar concentration of the conjugate base, and [HA] is the molar concentration of the weak acid.

Step 2: Choose suitable buffer candidates

Consider weak acids with pKa values close to the desired pH of 9.0. Some common weak acids with their pKa values close to 9.0 are: 1. Ammonium carbonate (NH4HCO3), pKa = 9.2 (formed from carbonic acid H2CO3 and ammonia) 2. Ammonium hydroxide (NH4OH), pKa = 9.25 (formed from water H2O and ammonia) These buffer systems could function well in maintaining a pH close to 9.0 in an aqueous solution.

Step 3: Determine the optimal buffer system

Comparing the pKa values of the two candidate buffer systems: 1. Ammonium carbonate (NH4HCO3), pKa = 9.2 2. Ammonium hydroxide (NH4OH), pKa = 9.25 The pKa value of ammonium hydroxide (NH4OH) with pKa = 9.25 is closer to the desired pH of 9.0 than ammonium carbonate (NH4HCO3) with pKa = 9.2. Therefore, the suitable buffer system to maintain a pH of 9.0 in an aqueous solution would be the ammonium hydroxide (NH4OH) and its conjugate acid, ammonium cation (NH4+). The ammonium hydroxide/ammonium cation buffer system can be prepared by mixing NH4OH solution with NH4Cl solution.

Key Concepts

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a fundamental tool in chemistry, particularly when it comes to understanding buffer systems. This equation helps us relate the pH of a solution to the pKa of a weak acid and the concentrations of the acid and its conjugate base. Mathematically, it is expressed as follows: \[ \text{pH} = \text{pKa} + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \]

• pH: The measure of acidity or basicity of a solution.
• pKa: The acid dissociation constant, a measure of the strength of an acid.
• [A-]: The concentration of the conjugate base.
• [HA]: The concentration of the weak acid.

The equation is particularly useful for calculating the pH of a buffer solution. It allows scientists to determine how changes in concentration or addition of acids/bases influence the pH. Understanding these relationships is crucial for creating effective buffer systems that maintain desired pH levels in various biochemical and industrial processes.

pH

pH is a scale used to specify the acidity or basicity of an aqueous solution. The term "pH" stands for "potential of hydrogen" or "power of hydrogen." It is an essential concept in chemistry and biology because many biological and chemical processes depend on the pH level. The pH scale ranges from 0 to 14:

• A pH less than 7 is acidic.
• A pH of 7 is neutral, which is typically the pH of pure water.
• A pH greater than 7 is basic (alkaline).

The pH of a solution can have significant effects on chemical reactions, biological processes, and the solubility of compounds. In many cases, maintaining a stable pH is essential. For example, in our bodies, blood pH is tightly regulated around a pH of 7.4. Understanding and manipulating pH is crucial in industries like pharmaceuticals, agriculture, and environmental science.

pKa

pKa is a vital concept in chemistry that represents the acid dissociation constant. It provides insight into the strength of an acid. pKa is essentially the negative logarithm of the equilibrium constant (\[ \text{K}_a \] ) for the dissociation of a weak acid:\[ \text{pKa} = -\log(\text{K}_a) \]

• Lower pKa: Indicates a stronger acid, which more readily donates its protons.
• Higher pKa: Indicates a weaker acid, with lower proton donation tendency.

The concept of pKa is used extensively when choosing buffer systems. A good buffer should have a pKa close to the desired pH level. For example, if you need a buffer at pH 9.0, choosing an acid with a pKa around 9 will be most effective. This is because the buffer will resist changes in pH most effectively when the concentrations of acid and conjugate base are approximately equal. Knowing the pKa helps in predicting reaction directions, understanding molecular stability, and designing better chemical processes.