A student is asked to make an acetic acid/ acetate buffer with a pH of 4.10. The only materials on hand are 300 mL of white vinegar (5.00% by mass acetic acid, density = 1.006g/mL) and potassium acetate. How should the student proceed?
5% by mass means 5 g HAc/100 g soln.
5g = 5/60 mols = 0.0833.
volume = mass/density = 100/1.006 = 99.4 mL.
M = about 0.8M but you need to confirm that and do it more accurately than I.
pH = pKa + log (base)/(acid)
mols HAc = 0.300L x 0.8M = about 0.25
pKa = about 4.74 but use the value from your text.
4.10 = 4.74 + log (base)/(0.25)
Solve for mols base (this isn't the concn but is mols since you substituted mols for HAc.
Then convert mols KAc to grams. g = mols x molar mass.
To make an acetic acid/acetate buffer with a pH of 4.10, the student will need to calculate the amount of acetic acid and potassium acetate needed to achieve the desired pH. Here's how the student should proceed:
Step 1: Calculate the amount of acetic acid needed
Since the student has 300 mL of white vinegar, which is 5.00% by mass acetic acid, they need to determine the mass of acetic acid present in the vinegar. The density of the vinegar is given as 1.006 g/mL.
Mass of vinegar = volume × density = 300 mL × 1.006 g/mL = 301.8 g
Now, calculate the mass of acetic acid in 300 mL of vinegar:
Mass of acetic acid = mass of vinegar × percentage of acetic acid = 301.8 g × 0.0500 = 15.09 g
Step 2: Calculate the amount of potassium acetate needed
Since the student has not been given the concentration of potassium acetate, they will need to assume a specific concentration or use a standard concentration value. Let's assume they have a 0.1 M (Molar) potassium acetate solution.
To calculate the volume of the potassium acetate solution needed, we can use the equation:
Molarity = Moles of solute / Volume of solution (in liters)
We want to achieve a specific pH, so we need to calculate the concentration of acetic acid (CH3COOH) and acetate ion (CH3COO-) at that pH.
The pKa value for acetic acid is approximately 4.76. The Henderson-Hasselbalch equation relates the pH, pKa, and the concentrations of weak acid and its conjugate base. The equation is:
pH = pKa + log [A-]/[HA]
Where:
pH = 4.10 (given)
pKa = 4.76
[A-] = concentration of acetate ion
[HA] = concentration of acetic acid
We need to rearrange the equation to solve for the ratio [A-]/[HA]:
[A-]/[HA] = 10^(pH - pKa)
[A-]/[HA] = 10^(4.10 - 4.76) = 0.444
We want the concentrations of acetic acid and acetate in the buffer to be equal. Consequently:
[HA] = [A-] = 0.444 (approximately)
Now we can calculate the number of moles of acetate ion needed:
Moles of acetate ion = Molarity × Volume of solution (in liters) = 0.1 M × Volume (in liters)
Moles of acetate ion = 0.1 × Volume
Since we want the concentration of acetate ion and acetic acid to be roughly the same, the moles of acetic acid needed will also be approximately 0.1 × Volume.
Step 3: Determine the total volume of the buffer solution
To create the buffer solution, the student needs to decide on the total volume they want for the buffer. Assume they want to make a final volume of 500 mL.
Step 4: Calculate the volume of white vinegar to use
To do this calculation, we need to convert the mass of acetic acid in grams to volume in milliliters.
Volume of acetic acid (in mL) = Mass of acetic acid (in grams) / Density
Volume of acetic acid = 15.09 g / 1.006 g/mL = 14.99 mL (approximately)
Step 5: Calculate the volume of potassium acetate solution to use
Now, we need to calculate the volume of the potassium acetate solution we determined earlier.
Volume of potassium acetate solution = Moles of acetate ion / Molarity
Volume of potassium acetate solution = (0.1 × Volume) / 0.1 M = Volume
Step 6: Combine the solutions
Finally, the student should combine the calculated volumes of white vinegar and potassium acetate solution in a container to achieve a buffer solution with a pH of 4.10.
In summary, to make the acetic acid/acetate buffer with a pH of 4.10 using 300 mL of white vinegar (5.00% by mass acetic acid) and assuming a 0.1 M potassium acetate solution, the student should mix approximately 14.99 mL of white vinegar with approximately the same volume of potassium acetate solution in a final volume of 500 mL.
To make an acetic acid/acetate buffer with a pH of 4.10 using white vinegar (5.00% acetic acid by mass) and potassium acetate, the student should follow these steps:
1. Calculate the volume of acetic acid needed:
- First, determine the mass of acetic acid present in the 300 mL of white vinegar:
mass of acetic acid = volume of vinegar x density x percentage by mass of acetic acid
mass of acetic acid = 300 mL x 1.006 g/mL x 0.0500 (5.00% expressed as decimal)
- Convert the mass of acetic acid to moles using the molar mass of acetic acid (60.05 g/mol).
2. Calculate the volume of potassium acetate needed:
- The ratio of acetic acid to acetate ions needed for a pH of 4.10 is 1:1. Therefore, the moles of acetic acid calculated in step 1 will be equal to the moles of acetate ions.
- Convert the moles of acetate ions to mass using the molar mass of potassium acetate (CH3COOK).
3. Prepare the buffer solution:
- Add the calculated mass of potassium acetate to the vinegar, ensuring complete dissolution of the salt.
- If necessary, adjust the volume of the solution to 300 mL by adding distilled water or more vinegar.
4. Measure the pH of the buffer solution using a pH meter. If the pH is not precisely 4.10, adjust it by adding small amounts of either acetic acid or potassium acetate, depending on whether the pH needs to be lowered or raised.
This procedure will allow the student to make an acetic acid/acetate buffer solution with a pH of 4.10 using the available materials.