Question

A student is asked to prepare a buffer solution at \(\mathrm{pH}\) 8.60 , using one of the following weak acids: HA \(\left(K_{\mathrm{a}}=2.7 \times 10^{-3}\right), \mathrm{HB}\left(K_{\mathrm{a}}=4.4 \times 10^{-6}\right), \mathrm{HC}\left(K_{\mathrm{a}}=2.6 \times\right.\) \(10^{-9}\) ). Which acid should the student choose? Why?

Short answer

Choose acid HC. It has a pKa closest to the desired pH of 8.60.

Step-by-step solution

Understanding the Henderson-Hasselbalch Equation

To choose the suitable weak acid for preparing a buffer solution at a specific pH, we use the Henderson-Hasselbalch equation: \[ \text{pH} = \text{pKa} + \log \left(\frac{[A^-]}{[HA]}\right) \] where \( \text{pKa} = -\log(K_a) \). A buffer is most effective at a pH close to its pKa.

Calculate pKa Values

Determine the pKa for each weak acid using their Ka values: - For HA: \[ \text{pKa}_\text{HA} = -\log(2.7 \times 10^{-3}) \approx 2.57 \] - For HB: \[ \text{pKa}_\text{HB} = -\log(4.4 \times 10^{-6}) \approx 5.36 \] - For HC: \[ \text{pKa}_\text{HC} = -\log(2.6 \times 10^{-9}) \approx 8.59 \]

Compare pKa to Desired pH

Compare the pKa of each weak acid to the desired pH of 8.60. - HA's pKa (2.57) is much lower than 8.60. - HB's pKa (5.36) is still lower than 8.60. - HC's pKa (8.59) is very close to 8.60, making it the most suitable choice.

Choose the Appropriate Acid

Since a buffer is most effective when its pKa is close to the desired pH, HC with a pKa of 8.59 is the best choice for preparing a buffer solution at pH 8.60.

Key concepts

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is a valuable formula used to estimate the pH of a buffer solution. A buffer solution is a liquid system that resists changes in pH upon the addition of small amounts of acid or base. The equation is given by:\[\text{pH} = \text{pKa} + \log \left(\frac{[A^-]}{[HA]}\right)\]In this equation:

• pH stands for the power of hydrogen or the concentration of hydrogen ions in the solution.
• pKa is the negative logarithm of the acid dissociation constant \(K_a\).
• [A^-] represents the concentration of the conjugate base.
• [HA] is the concentration of the weak acid remaining in the solution.

This equation is particularly helpful in biochemistry and medicine to create solutions that mimic natural conditions, such as in blood or cellular fluids. Using this equation allows one to calculate the expected pH of a solution when the acid/base ratio is known, or inversely to determine the required acid/base ratio to reach a desired pH.

pKa calculation

Calculating the pKa of an acid is essential in using the Henderson-Hasselbalch equation for buffer solutions. The pKa is derived from the acid dissociation constant \(K_a\), which measures the strength of an acid in solution. It is calculated using the formula:\[\text{pKa} = -\log(K_a)\]The procedure of calculating pKa from given \(K_a\) values is straightforward:

• First, identify the \(K_a\) value for the acid, which shows how easily the acid donates its proton in water.
• Apply the formula \(\text{pKa} = -\log(K_a)\) to convert the \(K_a\) value into the more convenient pKa form.

A smaller pKa value indicates a stronger acid, which means it dissociates more completely in water. In the context of preparing buffers, choosing an acid with a pKa close to the desired pH ensures effective buffering capacity. Understanding how to calculate and interpret pKa is vital for anyone studying chemistry or working in fields requiring precise pH control.

weak acids

Weak acids are acids that partially dissociate in solution. Unlike strong acids, which fully ionize, weak acids establish an equilibrium between their ionized and unionized forms. This property is crucial in forming buffer solutions.For example, in a solution containing acetic acid, only a small fraction of the acetic acid molecules donate protons to form acetate ions and hydrogen ions. Here's a simplified equation:\[\text{CH}_3\text{COOH} \leftrightarrow \text{CH}_3\text{COO}^- + \text{H}^+\]This equilibrium allows weak acids to minimize changes in the pH when acids or bases are added to the solution. They act as a pH modulator because the reaction can shift to either form to absorb excess H+ or OH- ions.Weak acids are chosen based on their pKa value relative to the desired pH of the buffer. By ensuring the pKa is close to the target pH, we ensure the buffer effectively keeps the pH stable despite minor changes in composition, making weak acids an indispensable tool in both laboratory and natural systems.

buffer effectiveness

Buffer effectiveness refers to the ability of a buffer to maintain a stable pH when acids or bases are added. The effectiveness of a buffer is largely determined by two main factors: the pKa of the acid and the concentrations of the acid and its conjugate base.For a buffer to be effective:

• The pH should be within ±1 of the pKa of the weak acid used in the buffer.
• There should be significant quantities of both the weak acid and its conjugate base in solution, typically close to equal concentrations.

A buffer works best when it is at its optimum range, around the pKa, because the system can absorb either additional hydrogen ions \(\text{H}^+\) or hydroxide ions \(\text{OH}^-\) without a significant change in pH. Additionally, the buffering capacity is maximized when the concentrations of the acid and base are high. However, practicality often limits the amount of buffer that can be added to a solution, so finding a balance is necessary. Overall, understanding and utilizing buffer effectiveness is crucial for anyone involved in chemical processes, where maintaining a stable pH is essential.