Question

You have to prepare a pH \(=3.50\) buffer, and you have the following 0.10\(M\) solutions available: \(\mathrm{HCOOH}, \mathrm{CH}_{3} \mathrm{COOH}\) , \(\mathrm{H}_{3} \mathrm{PO}_{4}, \mathrm{HCOONa}, \mathrm{CH}_{3} \mathrm{COONa}\) , and \(\mathrm{NaH}_{2} \mathrm{PO}_{4} .\) Which solutions would you use? How many milliliters of each solution would you use to make approximately 1 L of the buffer?

Short answer

To prepare a pH 3.50 buffer using the available solutions, formic acid \(\mathrm{(HCOOH)}\) and sodium formate \(\mathrm{(HCOONa)}\) should be used, as their pKa and concentrations are most suitable. To make approximately 1 L of the buffer, you would need about 923 mL of 0.10 M formic acid solution and 77 mL of 0.10 M sodium formate solution.

Step-by-step solution

1. Identify the suitable weak acids and conjugate bases

Given solutions are: \(\mathrm{HCOOH}\) (Formic acid), \(\mathrm{CH}_{3}\mathrm{COOH}\) (Acetic acid), \(\mathrm{H}_{3}\mathrm{PO}_{4}\) (Phosphoric acid), \(\mathrm{HCOONa}\) (Sodium formate), \(\mathrm{CH}_{3}\mathrm{COONa}\) (Sodium acetate), \(\mathrm{NaH}_{2}\mathrm{PO}_{4}\) (Sodium dihydrogen phosphate) From these solutions, we can identify the pairs of weak acids and their conjugate bases: \(\mathrm{HCOOH}\) and \(\mathrm{HCOONa}\) (formic acid and sodium formate) \(\mathrm{CH}_{3}\mathrm{COOH}\) and \(\mathrm{CH}_{3}\mathrm{COONa}\) (acetic acid and sodium acetate) \(\mathrm{H}_{3}\mathrm{PO}_{4}\) and \(\mathrm{NaH}_{2}\mathrm{PO}_{4}\) (phosphoric acid and sodium dihydrogen phosphate)

2. Compare pKa values and select the appropriate buffer system

We need to find the pKa of these acids and compare it with the desired pH of the buffer which is 3.50. pKa of formic acid (HCOOH): 3.75 pKa of acetic acid (CH3COOH): 4.76 For phosphoric acid (H3PO4), there are three acidic protons, and the pKa values are 2.15, 7.20, and 12.35. Looking at these values, we can see that the pKa of formic acid is closest to the desired pH. Therefore, we will use formic acid and sodium formate to prepare the buffer.

3. Use the buffer equation to determine the ratio of acid and conjugate base

Using the Henderson-Hasselbalch equation for a buffer system: pH = pKa + log10([Base]/[Acid]) For this problem, pH = 3.50 pKa of formic acid = 3.75 Both the formic acid and sodium formate solutions are 0.10 M. Now, we need to find the ratio of the concentrations: 3.50 = 3.75 + log10([Sodium formate]/[Formic acid])

4. Calculate the ratio of concentrations

Subtract pKa from pH: -0.25 = log10([Sodium formate]/[Formic acid]) Now solve for the ratio: 10^(-0.25) = [Sodium formate]/[Formic acid]

5. Determine the volumes of each solution needed

We want to prepare approximately 1 L of a buffer solution. Let V1 be the volume of formic acid, and V2 be the volume of sodium formate. Their sum should be close to 1 L: V1 + V2 ≈ 1 L Since we know the ratio of concentrations, let x = [Sodium formate]: [Formic acid] = x / 10^(-0.25) The relationship between concentration and volume is as follows: x * V2 = 0.10 * V1 (for Sodium formate) [x / 10^(-0.25)] * V1 = 0.10 * V2 (for Formic acid) Now we can solve for volumes V1 and V2: V2 = (0.10 * V1) / x V1 + [(0.10 * V1) / x] ≈ 1 V1 ≈ 0.923 * x Similarly, we can find V2: V2 ≈ 0.077 * x For preparing buffer solution of approximately 1 L, you can use any value of x for which V1+V2≈1L, as the concentration and ratio will remain the same. For example, you can keep x=0.1M: V1 ≈ 0.923 L V2 ≈ 0.077 L So, you would need approximately 923 mL of 0.10 M formic acid solution and 77 mL of 0.10 M sodium formate solution to prepare approximately 1 L of pH = 3.50 buffer.

Key concepts

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is a fundamental formula used in preparing buffers, a key concept in chemistry that helps maintain pH levels. This equation helps calculate the pH of a solution when you know the concentration of a weak acid and its conjugate base. It is expressed as:
\[\text{pH} = \text{pK}_a + \log_{10}\left(\frac{[\text{Base}]}{[\text{Acid}]}\right)\]
The pH represents how acidic or basic a solution is, while pK_a is the acid dissociation constant, showing the strength of the acid.
In the equation, the base and acid are the concentrations of the conjugate base and the weak acid, respectively. Adjusting this ratio allows chemists to design buffers with specific desired pH values.
A buffer solution resists drastic changes in pH, which is vital in biological systems. By using the Henderson-Hasselbalch equation, one can find the optimal ratio between the weak acid and its base to achieve the needed pH.

• Start by finding the pK_a value close to your desired pH.
• Use the equation to find the necessary ratio of base to acid.
• Adjust the concentrations of your solutions accordingly.

weak acid and conjugate base pairs

Weak acid and conjugate base pairs play a crucial role in buffer solutions. A weak acid is only partially ionized in solution, making it ideal for establishing equilibrium with its conjugate base.
When a weak acid, like formic acid \(\text{(HCOOH)}\), donates a proton, it forms a conjugate base, in this case, formate ion \(\text{(HCOO}^-\text{)}\). The conjugate base can then accept a proton back, participating in reversible reactions essential in buffer systems.
Buffer solutions are made up of such weak acid-conjugate base pairs. For effective buffering, the pH of the environment should be close to the pK_a of the weak acid.

• A lower pH environment uses more acids; a higher one leans on basic forms.
• This balance maintains the pH by neutralizing added acids or bases.
• Choosing the right pair is critical to buffer design.

A good buffer system dampens changes when a strong acid or base is added, stabilizing pH levels crucial for biochemical and industrial processes.

buffer pH calculations

Buffer pH calculations are essential in determining how much of the weak acid and its conjugate base is needed to prepare a buffer with the desired pH. This process involves:

• Identifying suitable acid-base pairs based on pK_a values close to desired pH levels.
• Using the Henderson-Hasselbalch equation as a guide for calculations.
• Solving for concentrations or volumes of components to make a specific buffer solution.

For example, when preparing a buffer solution with pH=3.50 using formic acid and sodium formate, the first step is finding the pK_a of formic acid, which is 3.75.
Plugging known values into the Henderson-Hasselbalch equation allows solving for the ratio of formate ions to formic acid. The calculated ratio guides the volumes of each 0.1 M solution to mix for creating the buffer.
Buffers made this way have broad applications, from helping maintain biological system stability to facilitating chemical reactions with precise pH requirements.

• Ensure volume adjustments maintain the correct concentration ratios.
• Validate mixing calculations by confirming pH with precision instruments.
• Fine-tune mixtures as necessary to match experimental requirements.

Through understanding and applying buffer pH calculations, creating reliable buffer solutions becomes a structured and measurable task.