How many mL of 4.50M sodium hydroxide must be acetic acid solutions to make a buffer with pHb. How many mL of 4.50 M sodium hydroxide must be added to 250.0 mL of a 0.200 Mc. Calculate the pH of a formic acid solution that contains 1.45% formic acid by mass.Question 4a. The pH of the acid and its conjugate base pairbuffer solution can be calculated by using(Assume a density of 1.01 g/mL for the solution.)acetic acid solution to make a buffer with pH = 5.000?the Anderson Hassel Balch equation:=5.000
The correct answer and explanation is :
To address the queries regarding buffer preparation and pH calculations, let’s break down each question systematically.
1. Preparing a Buffer Solution with a Desired pH:
To prepare a buffer solution with a specific pH, we can use the Henderson-Hasselbalch equation:
[ \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) ]
Where:
- pH is the desired pH of the buffer.
- pKₐ is the acid dissociation constant of the weak acid.
- [( \text{A}^- )] is the concentration of the conjugate base (acetate ion, CH₃COO⁻, in the case of acetic acid).
- [( \text{HA} )] is the concentration of the weak acid (acetic acid, CH₃COOH).
For acetic acid (CH₃COOH), the pKₐ is approximately 4.76. To achieve a buffer with a pH of 5.00, we can rearrange the Henderson-Hasselbalch equation to solve for the ratio of the base to acid concentrations:
[ \frac{[\text{A}^-]}{[\text{HA}]} = 10^{\text{pH} – \text{pK}_a} = 10^{5.00 – 4.76} \approx 1.737 ]
This means the ratio of acetate ion concentration to acetic acid concentration should be approximately 1.737. By adjusting the amounts of acetic acid and sodium acetate (the sodium salt of the acetate ion), you can achieve this ratio, thereby preparing a buffer with the desired pH.
2. Adding Sodium Hydroxide to Acetic Acid to Achieve a Specific pH:
When sodium hydroxide (NaOH) is added to acetic acid (CH₃COOH), it reacts to form sodium acetate (CH₃COONa) and water:
[ \text{CH}_3\text{COOH} + \text{OH}^- \rightarrow \text{CH}_3\text{COO}^- + \text{H}_2\text{O} ]
To determine the volume of 4.50 M NaOH required to achieve a specific pH, we can use the Henderson-Hasselbalch equation as described above. By knowing the initial concentrations of acetic acid and sodium acetate, and the desired pH, we can calculate the necessary ratio of base to acid concentrations. From this ratio, we can calculate the amount of NaOH to add, ensuring that the final solution reaches the desired pH.
3. Calculating the pH of a Formic Acid Solution:
Formic acid (HCOOH) is a weak acid with a pKₐ of approximately 3.75. The pH of a solution of formic acid can be calculated using the formula:
[ \text{pH} = \frac{1}{2} \left( \text{pK}_a – \log [\text{HA}] \right) ]
Where:
- pKₐ is the acid dissociation constant of formic acid.
- [( \text{HA} )] is the concentration of formic acid.
For a 1.45% by mass solution of formic acid, assuming a density of 1.01 g/mL, the molarity can be calculated as follows:
- Calculate the mass of formic acid in 1 liter of solution:
- Mass of solution = 1000 g (since density is 1.01 g/mL, and volume is 1000 mL)
- Mass of formic acid = 1.45% of 1000 g = 14.5 g
- Convert mass to moles:
- Moles of formic acid = 14.5 g / 46.025 g/mol ≈ 0.314 mol
- Calculate molarity:
- Molarity = 0.314 mol / 1 L = 0.314 M
Using this molarity in the pH formula:
[ \text{pH} = \frac{1}{2} \left( 3.75 – \log 0.314 \right) \approx \frac{1}{2} \left( 3.75 – (-0.503) \right) \approx \frac{1}{2} \times 4.253 \approx 2.126 ]
Therefore, the pH of the formic acid solution is approximately 2.13.
4. Buffer Solution pH Calculation Using the Henderson-Hasselbalch Equation:
As demonstrated in the first point, the Henderson-Hasselbalch equation is a fundamental tool for calculating the pH of buffer solutions. By knowing the pKₐ of the acid and the concentrations of the acid and its conjugate base, you can determine the pH of the buffer. This equation is particularly useful in biochemical and industrial applications where maintaining a specific pH is crucial for the stability and activity of various compounds.
In summary, understanding the principles of acid-base equilibria and the use of the Henderson-Hasselbalch equation allows for precise control over the pH of solutions, which is essential in many chemical and biological processes.