Describe preparation of 5 liters of a 0.3 M acetate buffer, pH 4.47, starting from a 2 M solution of acetic acid and a 2.5 M solution of KOH.
I will use millimoles to work this problem although technically the Henderson-Hasselbalch equation uses concentrations in mols/L (M). However, it's easier for me to use moles or millimoles and not mols/L. The answer is the same so here goes.
You want 5 L of a 0.3 M acetate buffer solution of pH 4.47 made with 2 M HAc and 2.5 M KOH. Using the HH equation acid = a = HAc and base = b = Ac^-. pH = pKa + log (base)/(acid)
4.47 = 4.77 + log b/a
log b/a = -0.3 and
b/a = 0.501 which I will call 0.5. You may want to redo it with 0.501 and you will a lightly different answer but not by much. So b = 0.5a
You want 5 L of a 0.3 M buffer so you want 1500 millimoles. The next equation you need is
a + b = 1500. Substituting frm above for b = 0.5a
a + 0.5a = 1500 and
a = 1000 mmoles and b = 500 mmoles.How we get that with 2 M HAc and 2.5 M KOH.
....................HAc + KOH ==> KAc + H2O
I...................x mmol................0............0
add............................ymmol...........................
C.................-y...........-y...........+y................
E...............x-y..........0..............y................
Yiy want x-y to be 1000 mmols. You want y to be 500. So x initially must be 1500 mmols acid and you want to add 500 KOH to make 500 mmols acetate. How do you do that.
mL x M = millimoles.
mL x 2 = 1000 mmols HAc
mL HAc = 1000/2 = 500 mL
mL x M = millimoles KOH
mL x 2.5 = 500
mL KOH = 200
So you place 500 mL of the acid and 200 mL of the KOH into a 5 L volumetric flask (be careful--it will get VERY hot)--let it cool, make to the mark with DI water. stopper, mix thoroughly, label. Done.
You may want to put those numbers into the HH equation to see if the pH is 4.47. pH = 4.77 + log (500/1000) = ?
I've done this with such detail you shouldn't have any doubt but post our work if you get stuck somewhere.
Sir,
In the HH equation, you assumed that PKA is 4.77 although it is not given, how did you acquire that number because I have tried to calculate it but there is insufficient data.
Thanks in advance.
To prepare 5 liters of a 0.3 M acetate buffer with a pH of 4.47, you will need to follow these step-by-step instructions:
Step 1: Calculate the amount of acetic acid and potassium acetate required:
Given:
- Desired volume of buffer solution (V) = 5 liters
- Desired molarity of acetate buffer (M) = 0.3 M
- Concentration of acetic acid (C1) = 2 M
- Concentration of KOH (C2) = 2.5 M
The Henderson-Hasselbalch equation can be used to calculate the amount of acetic acid and potassium acetate required.
pH = pKa + log ([A-]/[HA])
Given that the pH is 4.47, we need to find the pKa value for acetic acid to solve this equation.
Step 2: Determine the pKa value for acetic acid:
The pKa value for acetic acid is approximately 4.76.
Step 3: Calculate the amount of acetic acid needed (HA):
Using the Henderson-Hasselbalch equation, set the pH, pKa, and the ratio of [A-]/[HA] to solve for [HA].
4.47 = 4.76 + log ([A-]/[HA])
Let [A-]/[HA] = 10^x
4.47 = 4.76 + x
x = -0.29
[A-]/[HA] = 10^(-0.29) = 0.501
Therefore, the ratio of [A-] to [HA] in the buffer is 0.501.
To calculate the amount of HA (acetic acid) needed, we can assume that [A-] and [HA] will be equal in concentration in a 0.3 M buffer. So, let [A-] = [HA] = 0.3 M.
Therefore, the amount of acetic acid (HA) needed is:
Volume of acetic acid (V1) = (0.3 M) x (5 liters) = 1.5 moles
Step 4: Calculate the amount of potassium acetate needed (A-):
The concentration of potassium acetate (A-) needed is 0.3 M. Therefore, the amount of A- needed is:
Volume of potassium acetate (V2) = (0.3 M) x (5 liters) = 1.5 moles
Step 5: Determine the amounts of acetic acid and potassium acetate in terms of volumes required:
To find the volume of each solution needed, divide the amount required (in moles) by the concentration of the respective solutions.
Volume of acetic acid solution needed (V1') = (1.5 moles) / (2 M) = 0.75 liters or 750 mL
Volume of potassium acetate solution needed (V2') = (1.5 moles) / (2.5 M) = 0.6 liters or 600 mL
Step 6: Prepare the buffer solution:
- Take 0.75 liters (750 mL) of the 2 M acetic acid solution and pour it into a container.
- Add 0.6 liters (600 mL) of the 2.5 M KOH solution into the same container.
- Stir the solution until it is homogeneous.
Step 7: Adjust the pH:
To adjust the pH of the buffer solution, use a pH meter or pH indicator paper. If the pH is not precisely 4.47, you can add small amounts of either KOH or acetic acid to adjust the pH accordingly.
You have now successfully prepared 5 liters of a 0.3 M acetate buffer solution with a pH of 4.47.
To prepare a 5-liter solution of a 0.3 M acetate buffer with a pH of 4.47, starting from a 2 M solution of acetic acid and a 2.5 M solution of KOH, you will need to follow these steps:
1. Calculate the amount of acetic acid (CH3COOH) needed:
- We know that the final volume of the solution is 5 liters and the desired concentration is 0.3 M.
- Using the formula C1V1 = C2V2, where C represents concentration and V represents volume, we can calculate the amount of acetic acid needed. Rearranging the formula, we have: V1 = (C2V2) / C1.
- Plugging in the values, we get: V1 = (0.3 M * 5 L) / 2 M = 0.75 L (or 750 mL) of acetic acid is needed.
2. Calculate the amount of potassium acetate (CH3COOK) needed:
- The buffer requires an equal number of moles of the conjugate base (acetate) and the weak acid (acetic acid).
- Since the concentration of acetic acid is 0.3 M and the final volume is 5 L, we need to calculate the number of moles: moles = concentration * volume.
- Moles of acetic acid = 0.3 M * 5 L = 1.5 mol.
- Since acetate acts as the conjugate base, we require an equal number of moles.
- Therefore, we need 1.5 mol of potassium acetate.
3. Calculate the amount of KOH needed:
- Since the concentration of the KOH solution is 2.5 M and the moles of potassium acetate required is 1.5 mol, we can calculate the volume of KOH for this:
- V = moles / concentration.
- V = 1.5 mol / 2.5 M = 0.6 L (or 600 mL) of KOH solution is needed.
4. Start preparing the buffer:
- Take a clean container and add 0.75 L (or 750 mL) of acetic acid (CH3COOH).
- Add 1.5 mol (or the required weight in grams) of potassium acetate (CH3COOK) to the container.
- Then, add 0.6 L (or 600 mL) of the 2.5 M KOH solution.
- After carefully adding each component, bring the total volume up to 5 liters with distilled water.
5. Adjust the pH:
- Use a pH meter or pH indicator paper to measure the actual pH of the buffer solution.
- In this case, the desired pH is 4.47, but it may need adjustment.
- If the pH is higher than 4.47, you can add a small amount of dilute acetic acid to lower it.
- If the pH is lower than 4.47, you can add a small amount of dilute KOH to raise it.
- Repeat the measurements and adjustments until the desired pH of 4.47 is achieved.
By following these steps, you will be able to prepare 5 liters of a 0.3 M acetate buffer with a pH of 4.47, using a 2 M solution of acetic acid and a 2.5 M solution of KOH.