Question

Calculate the pH of each of the following buffered solutions. a. \(0.10 M\) acetic acid \(/ 0.25 M\) sodium acetate b. \(0.25 M\) acetic acid \(/ 0.10 M\) sodium acetate c. \(0.080 M\) acetic acid \(/ 0.20 M\) sodium acetate d. \(0.20 M\) acetic acid \(0.080 M\) sodium acetate

Short answer

The pH values for the given buffered solutions are: a. \(pH \approx 5.15\) b. \(pH \approx 4.35\) c. \(pH \approx 5.15\) d. \(pH \approx 4.35\)

Step-by-step solution

The equation is given as follows: \[pH = pKa + \log \frac{[A^-]}{[HA]}\] where \(pH\) is the pH value, \(pKa\) is the acidic dissociation constant, \([A^-]\) is the concentration of the conjugate base, and \([HA]\) is the concentration of the weak acid. #Step 2: Determine the pKa value of acetic acid#

The pKa value of acetic acid is \(4.75\). Now, let us calculate the pH of each buffered solution. #a. 0.10 M acetic acid / 0.25 M sodium acetate# #Step 3a: Plug in the concentration values in the equation#

We have \([HA] = 0.10 M\) and \([A^-] = 0.25 M\). By using the Henderson-Hasselbalch equation, we have \[pH = 4.75 + \log \frac{0.25}{0.10}\] #Step 4a: Solve for pH#

Calculate the value in the \(\log\) term: \[pH = 4.75 + \log(2.5)\] \[pH \approx 4.75 + 0.40 = 5.15\] The pH of solution a is approximately 5.15. #b. 0.25 M acetic acid / 0.10 M sodium acetate# #Step 3b: Plug in the concentration values in the equation#

We have \([HA] = 0.25 M\) and \([A^-] = 0.10 M\). By using the Henderson-Hasselbalch equation, we have \[pH = 4.75 + \log \frac{0.10}{0.25}\] #Step 4b: Solve for pH#

Calculate the value in the \(\log\) term: \[pH = 4.75 + \log(0.4)\] \[pH \approx 4.75 - 0.40 = 4.35\] The pH of solution b is approximately 4.35. #c. 0.080 M acetic acid / 0.20 M sodium acetate# #Step 3c: Plug in the concentration values in the equation#

We have \([HA] = 0.080 M\) and \([A^-] = 0.20 M\). By using the Henderson-Hasselbalch equation, we have \[pH = 4.75 + \log \frac{0.20}{0.080}\] #Step 4c: Solve for pH#

Calculate the value in the \(\log\) term: \[pH = 4.75 + \log(2.5)\] \[pH \approx 4.75 + 0.40 = 5.15\] The pH of solution c is approximately 5.15. #d. 0.20 M acetic acid 0.080 M sodium acetate# #Step 3d: Plug in the concentration values in the equation#

We have \([HA] = 0.20 M\) and \([A^-] = 0.080 M\). By using the Henderson-Hasselbalch equation, we have \[pH = 4.75 + \log \frac{0.080}{0.20}\] #Step 4d: Solve for pH#

Calculate the value in the \(\log\) term: \[pH = 4.75 + \log(0.4)\] \[pH \approx 4.75 - 0.40 = 4.35\] The pH of solution d is approximately 4.35.

Key concepts

Buffered Solutions

Buffered solutions are mixtures that resist changes in pH when small amounts of acid or base are added. They typically consist of a weak acid and its conjugate base or vice versa. The main function of a buffer is to maintain a stable pH environment, which is crucial in various chemical and biological systems.

Buffering action occurs because the equilibrium between the weak acid and its conjugate base counteracts the pH-changing effects of added substances. For example, if you add an acid to the buffer, the conjugate base will react with the added hydrogen ions to form the weak acid. This action minimizes the change in pH. A similar process happens when a base is added, this time the weak acid reacts with the added hydroxide ions to form water and the conjugate base.

• This ability to resist pH changes is essential for processes such as enzyme activity in biological systems.
• Buffers are used in fermentation, chemical manufacturing, medicine, and more.
• They are designed to operate over a specific pH range, depending on the pKa of the weak acid involved.

Understanding buffered solutions help us grasp how solutions maintain equilibrium, crucial for several chemical and biological functions.

pH Calculation

The pH of a solution is a measure of its acidity or alkalinity, determined by the concentration of hydrogen ions. In buffered systems, the pH can be calculated using the Henderson-Hasselbalch equation. It connects the pH with the concentrations of the weak acid and its conjugate base.

The equation is expressed as:\[ pH = pKa + \log \frac{[A^-]}{[HA]} \] where:- \( pH \) is the measure of acidity.- \( pKa \) is the acid dissociation constant, intrinsic to the weak acid.- \([A^-]\) is the concentration of the conjugate base.- \([HA]\) is the concentration of the weak acid.
By plugging in these values, we can predict how changes in component concentrations affect the pH. This equation reveals that when the concentrations of the acid and base are equal, the \(pH\) equals the \(pKa\).

• For a strong buffer, the ratio of \([A^-]\) to \([HA]\) should be close to 1.
• The pH changes smoothly, due to the logarithmic nature of the equation.
• Accurate measurements of concentrations are crucial for reliable pH predictions using this method.

The Henderson-Hasselbalch equation is pivotal for chemists when designing buffers to maintain stable pH environments in reactions.

Acetic Acid and Sodium Acetate Buffer

The acetic acid and sodium acetate buffer is a classic system used to maintain a stable pH. Acetic acid acts as the weak acid, while sodium acetate serves as the source of the acetate ion, the conjugate base.

In these buffers, acetic acid ( \(CH_3COOH\)) can donate a proton (H+) to neutralize added bases, while acetate ions ( \(CH_3COO^-\)) can absorb protons from added acids, both actions keeping the pH level relatively stable.Important points to consider:

• The buffer is highly effective near the \(pKa\) of acetic acid, which is 4.75. This makes it suitable for reactions that operate around this pH.
• It is commonly used in biochemical experiments, such as those involving enzymes, where maintaining a specific pH is critical to avoiding denaturation or other activity loss.
• The ratio between acetic acid and sodium acetate determines the exact pH within the buffer's effective range.

Using the acetic acid and sodium acetate buffer illustrates the efficiency of weak acid-conjugate base pair systems in maintaining pH stability, imperative in both laboratory experiments and industrial processes.