Question

You have the following reagents on hand: \begin{tabular}{|ll|} \hline Solids \(\left(\mathrm{p} \boldsymbol{K}_{\mathrm{a}}\right.\) of Acid Form Is Given) & Solutions \\ \hline Benzoic acid (4.19) & \(5.0 \mathrm{M} \mathrm{HCl}\) \\ Sodium acetate (4.74) & \(1.0 \mathrm{M}\) acetic acid (4.74) \\ Potassium fluoride (3.14) & \(2.6 \mathrm{M} \mathrm{NaOH}\) \\ Ammonium chloride (9.26) & \(1.0 \mathrm{M} \mathrm{HOCl}(7.46)\) \\ \hline \end{tabular} What combinations of reagents would you use to prepare buffers at the following \(\mathrm{pH}\) values? a. \(3.0\) b. \(4.0\) c. \(5.0\) d. \(7.0\) e. \(9.0\)

Short answer

a. Potassium fluoride + 1.0 M acetic acid b. Benzoic acid + 5.0 M HCl, or Sodium acetate + 2.6 M NaOH c. Sodium acetate + 1.0 M acetic acid d. 1.0 M HOCl + ammonium chloride e. Ammonium chloride + 1.0 M HOCl, or Ammonium chloride + 2.6 M NaOH

Step-by-step solution

Review the Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is given by: \[pH = pKa + \log_{10}\left(\frac{[\mathrm{A}^-]}{[\mathrm{HA}]}\right)\] where: - \(pH\) is the desired pH value of the buffer solution - \(pKa\) is the acid dissociation constant of the weak acid - \([\mathrm{A}^-]\) is the concentration of the conjugate base of the weak acid - \([\mathrm{HA}]\) is the concentration of the weak acid We will use this equation to identify proper combinations of reagents for each given pH value.

Identify appropriate reagent combinations for each given pH value

For each pH value, we will look for a reagent pair whose pKa value is closest to the desired pH value. Once we have a pair, we can use the reagents to adjust the concentrations of \([\mathrm{A}^-]\) and \([\mathrm{HA}]\) to achieve the desired pH value. a. Desired pH: 3.0 The closest pKa value is 3.14 for potassium fluoride. We can combine potassium fluoride with a weak acid, such as 1.0 M acetic acid (4.74). b. Desired pH: 4.0 The closest pKa values are 4.19 for benzoic acid and 4.74 for sodium acetate. We can combine either benzoic acid or sodium acetate with a strong acid, such as 5.0 M HCl or a weak base, such as 2.6 M NaOH. c. Desired pH: 5.0 The closest pKa value is 4.74 for sodium acetate. We can combine sodium acetate with a weak acid, such as 1.0 M acetic acid (4.74). d. Desired pH: 7.0 The closest pKa value is 7.46 for 1.0 M HOCl. We can combine 1.0 M HOCl with a weak base, such as ammonium chloride (9.26). e. Desired pH: 9.0 The closest pKa value is 9.26 for ammonium chloride. We can combine ammonium chloride with a weak acid, such as 1.0 M HOCl (7.46), or a strong base, such as 2.6 M NaOH. By selecting appropriate reagents and adjusting their concentrations, we can prepare the desired buffer solutions at various pH values.

Key concepts

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is a fundamental formula used in acid-base chemistry to estimate the pH of a buffer solution. This equation is expressed as: \[pH = pKa + \log_{10}\left(\frac{[A^-]}{[HA]}\right)\] Here, \(pH\) is the measure of how acidic or basic a solution is. The \(pKa\) value represents the acid dissociation constant, which is the point where the acid is half dissociated. It tells you the strength of the weak acid.

• \([A^-]\) represents the concentration of the conjugate base.
• \([HA]\) stands for the concentration of the weak acid itself.

This equation helps to calculate the \(pH\) of a solution when the concentrations of the acid and its conjugate base are known.
It's an essential tool in buffer solution preparation because it allows the calculation of the necessary proportions of acid and conjugate base needed to maintain a certain \(pH\). By matching conditions to desired pH values, the equation assists in keeping solutions stable against drastic pH changes.

Acid-Base Chemistry

In acid-base chemistry, the study revolves around the reactions between acids and bases, and the transfer of hydrogen ions (or protons) that occurs during these reactions.
An *acid* is a substance that donates hydrogen ions, \(H^+\), while a *base* is a substance that accepts hydrogen ions.

• When an acid donates a proton, it forms its *conjugate base*.
• The base, upon accepting a proton, forms its *conjugate acid*.

Understanding this relationship is crucial in preparing buffer solutions, as it involves choosing reagents that exist in equilibrium between these states.
Weak acids and their conjugate bases are typically used in buffers due to their ability to resist changes in pH. Strong acids and bases tend to dissociate completely in water, making them unsuitable for maintaining a buffer equilibrium.
The strength of an acid or base, therefore, is directly related to its ability to dissociate and donate or accept protons, defined by its \(pKa\) or \(pKb\).

pH Calculation

Calculating the pH of a solution involves determining how acidic or basic the solution is. The pH scale typically ranges from 0 to 14, where:

• A lower pH (0-6) indicates an acidic solution.
• A pH of 7 is neutral (such as pure water).
• A higher pH (8-14) signifies a basic or alkaline solution.

The pH calculations become especially significant when preparing buffer solutions. This is because you must accurately measure the balance needed between a weak acid and its conjugate base.
The Henderson-Hasselbalch equation is often employed in these calculations to find the correct ratio to achieve the required pH level.
In practice, one might start with known concentrations of either the acid or base and adjust it by adding more acid or conjugate base until the desired pH is reached. Accurate pH meters are used to measure these changes precisely. The key is to start with reagents whose pKa values are close to the desired pH. This allows for easy adjustment and stabilization of the pH in the desired range.

Weak Acid and Strong Base Pairs

When preparing buffer solutions, understanding the use of weak acid and strong base pairs is critical.
A buffer solution, ideally, is composed of a mixture of a weak acid and its conjugate base or a weak base and its conjugate acid.
Strong bases such as NaOH are not typically part of a buffer mix but can be used to adjust the pH by neutralizing part of the weak acid to form its conjugate base.
This combination helps maintain a stable pH because it can absorb additional \(H^+\) or \(OH^-\) ions without significantly changing the \(pH\):

• **Weak acids** only partially dissociate, supplying a less complete donation of \(H^+\) ions.
• **Conjugate bases**, formed from the neutralization of the weak acid by the strong base, can accept \(H^+\) ions, converting back into the weak acid.

For example, in the preparation of a buffer around a pH of 4.0, a combination of weak acid like benzoic acid and its conjugate base can effectively stabilize the solution.
The buffer capacity is affected by the absolute concentrations of the buffer components, i.e., a 1.0 M buffer solution has a higher capacity than a 0.1 M solution. Effective buffer action typically requires the pH to be within one unit of the pKa value of the weak acid utilized.