Show how would you prepare a solution of 500 mL of a 0.15 M acetate buffer, pH 4.6 based on one of the three methods illustrated in class and in the supplementary readings. You have available the following: 6 M HCl, 4 M acetic acid, solid sodium acetate, solid sodium hydroxide.Given
Sodium acetate MW = 82
HCl MW = 36.5
Sodium hydroxide MW = 40
pK for acetic acid dissociation = 4.76
Well, that's tough. I didn't attend any of your classes and I don't have the supplemental readings. But here is what I would do. a is acid and b is base.
pH = pKa + log (b)/(a)
4.6 = 4.76 + (a)/(b)
Solve for a/b. That's equation 1.
Then (a) + (b) = 0.15, That's eqn 2.
Solve for (a) and (b) by solving the two equations simultaneously. You know (b) and that is the sodium acetate. Weigh out the proper amount of NaAc. You now what you need for the acid. Use HAc. If it is 4M you know it has 4 mols/L. measure ou the volume you need to obtain that many mols in 500 mL. That's one way. Post your work if you get stuck.
(a) = ? M
(b) = ? M.
Then
To prepare a solution of 500 mL of a 0.15 M acetate buffer with a pH of 4.6, you can use the method of combining acetic acid and sodium acetate in specific quantities. Here's a step-by-step guide on how to prepare the buffer solution:
Step 1: Calculate the moles of acetic acid needed.
The moles of acetic acid required can be determined using the formula:
moles = Molarity × Volume (in liters)
Given that the desired molarity is 0.15 M and the volume is 0.5 L (500 mL), you can calculate the moles of acetic acid:
moles of acetic acid = 0.15 M × 0.5 L = 0.075 moles
Step 2: Calculate the moles of sodium acetate needed.
Since we're aiming for a buffer solution, the moles of sodium acetate should be equal to the moles of acetic acid. Therefore, we need 0.075 moles of sodium acetate.
Step 3: Convert moles to grams.
To convert moles to grams, use the formula:
grams = moles × molecular weight (MW)
The molecular weight of sodium acetate is 82, so the mass of sodium acetate needed is:
mass of sodium acetate = 0.075 moles × 82 g/mol = 6.15 grams
Step 4: Prepare the sodium acetate solution.
Take 6.15 grams of solid sodium acetate and dissolve it in enough water to make a final volume of 500 mL. Ensure that the dissolution is complete by stirring the solution thoroughly.
Step 5: Calculate the volume of acetic acid.
To calculate the volume of acetic acid required, we need to know its concentration. Since the concentration of acetic acid is not provided, we will need to calculate it using the Henderson-Hasselbalch equation.
The Henderson-Hasselbalch equation is given by:
pH = pKa + log([A-]/[HA])
Given pH = 4.6 and pKa = 4.76, rearrange the equation to solve for the ratio [A-]/[HA]:
log([A-]/[HA]) = pH - pKa
[A-]/[HA] = 10^(pH - pKa)
Now, plug in the values to calculate [A-]/[HA]:
[A-]/[HA] = 10^(4.6 - 4.76) = 10^(-0.16)
Since the acetate buffer has an equimolar ratio of acetic acid (HA) and its conjugate base acetate (A-), [A-]/[HA] = 1.
Therefore, the required amount of acetic acid is equal to the amount of sodium acetate used, which is 0.075 moles.
Step 6: Convert moles to volume of acetic acid.
To convert moles to volume, use the formula:
Volume (in liters) = moles / Molarity
Given that we need 0.075 moles of acetic acid and the desired molarity is 4 M, you can calculate the volume of acetic acid as follows:
Volume of acetic acid = 0.075 moles / 4 M = 0.01875 L (18.75 mL)
Step 7: Adjust the pH using HCl or sodium hydroxide (NaOH).
To reach the desired pH of 4.6, you may need to adjust the pH using either HCl or NaOH.
If the pH is higher than 4.6, add a small amount of 6 M HCl dropwise until the desired pH is reached.
If the pH is lower than 4.6, add a small amount of 4 M NaOH dropwise until the desired pH is achieved. Note that HCl will react with sodium acetate, forming acetic acid, so it's important to use NaOH to increase the pH.
Make sure to monitor the pH using a pH meter or pH paper during the adjustment process.
Now, you have prepared a solution of 500 mL of a 0.15 M acetate buffer with a pH of 4.6, using the provided HCl, acetic acid, sodium acetate, and sodium hydroxide.