Question

A buffer solution is prepared by mixing 75.0 \(\mathrm{mL}\) of 0.275 \(\mathrm{M}\) fluorobenzoic acid \(\left(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{O}_{2} \mathrm{F}\right)\) with 55.0 \(\mathrm{mL}\) of 0.472 \(\mathrm{M}\) sodium fluorobenzoate. The \(\mathrm{pK}_{\mathrm{a}}\) of this weak acid is \(2.90 .\) What is the pH of the buffer solution?

Short answer

The pH of the buffer solution is approximately 3.12. This is calculated using the Henderson-Hasselbalch equation, by first finding the moles and concentrations of the weak acid and conjugate base in the solution, and then plugging these values into the equation: pH ≈ 2.90 + 0.2172 = 3.1172.

Step-by-step solution

Find the moles of weak acid (HA) and conjugate base (A-)

We will use the given volumes and molarities to find the moles of HA and A- present in the solution. Moles of HA = volume (HA) × molarity (HA) = 75.0 mL × 0.275 M = 20.625 mmol Moles of A- = volume (A-) × molarity (A-) = 55.0 mL × 0.472 M = 25.96 mmol

Calculate the final volume of the buffer solution

Next, we need to find the total volume of the buffer solution by adding the volumes of both components: Total volume = volume (HA) + volume (A-) = 75.0 mL + 55.0 mL = 130.0 mL

Find the concentrations of HA and A- in the buffer solution

Divide the moles of HA and A- by the total volume of the buffer solution to find their respective concentrations: \[Concentration \ of \ HA = \frac{20.625 \ mmol}{130.0 \ mL} = 0.1587 \ M\] \[Concentration \ of \ A^{-} = \frac{25.96 \ mmol}{130.0 \ mL} = 0.1997 \ M\]

Calculate the pH using the Henderson-Hasselbalch equation

We'll now use the Henderson-Hasselbalch equation with the pKa, and the concentrations of HA and A- that we found in the previous steps. pH = pKa + log10([A-]/[HA]) = 2.90 + log10(0.1997/0.1587) pH ≈ 2.90 + 0.2172 = 3.1172 So, the pH of the buffer solution is approximately 3.12.

Key concepts

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is crucial in understanding how buffers work. It's used to calculate the pH of a buffer solution, allowing us to understand the delicate balance between an acid and its conjugate base. This equation is expressed as:

\[pH = pK_{a} + \log_{10}\left(\frac{[A^-]}{[HA]}\right)\]

Here, \( pH \) is the acidity of the solution, \( pK_{a} \) is the acid dissociation constant of the weak acid, \([A^-]\) is the concentration of the conjugate base, and \([HA]\) is the concentration of the weak acid.

• It shows how the pH of a buffer depends on the ratio of the concentrations of the base and acid.
• pH changes in a buffer solution can be minimized by choosing the right ratio of base to acid.

This equation is particularly useful in scenarios where maintaining a stable pH is critical, such as in biological systems.

Acid-Base Chemistry

Acid-base chemistry explores the properties and reactions of acids and bases. In short, acids release hydrogen ions in a solution, while bases remove them.

When dealing with buffers, we focus on weak acids and their conjugate bases. A buffer solution consists typically of:

• A weak acid (like fluorobenzoic acid in our exercise).
• Its conjugate base (sodium fluorobenzoate serving this role).

These components maintain a stable pH by neutralizing added acids or bases. Here's how they work:

• The weak acid can donate protons to neutralize added bases.
• The conjugate base can accept protons to neutralize added acids.
• This dual ability ensures that pH changes are minimized, making buffer solutions indispensable in processes needing consistent pH levels.

pH Calculation

Calculating pH, especially in buffer solutions, is a vital skill in chemistry. In our example, the buffer was made from fluorobenzoic acid and sodium fluorobenzoate, with specific steps to find its pH.

The pH calculation process involves:

• Determining the moles of the acid and its conjugate base using their volume and molarity.
• Assessing the total volume of the buffer to find the concentration of each component.
• Applying the Henderson-Hasselbalch equation using these concentrations.

In this case, the equation yielded a pH of approximately 3.12. This reflects the stability of the buffer system, showing how effective it is in maintaining the desired pH range.

Through careful adjustments and understanding of each component, accurate pH control is achievable, crucial for experiments and applications needing specific pH levels.