Describe the 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.
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To prepare a 5 liter acetate buffer solution with a pH of 4.47, you'll need to follow a two-step process:
Step 1: Calculate the volumes of acetic acid (2 M) and potassium acetate (2.5 M) required to make a 5 liter 0.3 M acetate buffer solution.
To determine the specific volumes needed, we'll use the Henderson-Hasselbalch equation:
pH = pKa + log ([A-]/[HA])
In this case, acetic acid (HA) is acting as the weak acid, and acetate ion (A-) is acting as the conjugate base. The pKa of acetic acid is 4.76.
Since we are aiming for a pH of 4.47 (slightly lower than pKa), the acetate-to-acetic acid ratio should be slightly greater than 1, i.e., [A-]/[HA] > 1.
Let's assume we take x liters of acetic acid (2 M) and (5 - x) liters of potassium acetate (2.5 M) to make the 5 liter buffer solution.
Using the given information, we can write the equation:
4.47 = 4.76 + log ([A-]/[HA])
Simplifying:
-0.29 = log ([A-]/[HA])
Taking Antilog:
10^(-0.29) = ([A-]/[HA])
Approximately, [A-]/[HA] = 0.516
Substituting the concentrations and volumes:
(2.5 M) (5 - x) / (2 M) x = 0.516
Now, we can solve this equation for the value of x (volume of acetic acid).
Multiply through by 2x:
2.5(5 - x) = 0.516(2x)
Simplifying:
12.5 - 2.5x = 1.032x
Rearranging terms:
3.532x = 12.5
x = 12.5 / 3.532
x ≈ 3.536 liters
Therefore, you will need approximately 3.536 liters of 2 M acetic acid (CH3COOH) and (5 - 3.536) ≈ 1.464 liters of 2.5 M potassium hydroxide (KOH) to prepare a 5 liter, 0.3 M acetate buffer solution with a pH of 4.47.
Step 2: Add the calculated volumes of acetic acid and potassium acetate to make the buffer solution.
- Measure out 3.536 liters of 2 M acetic acid (CH3COOH) using a volumetric flask or a graduated cylinder.
- Measure out 1.464 liters of 2.5 M potassium hydroxide (KOH) using a separate volumetric flask or graduated cylinder.
- Pour the acetic acid into a suitable container, such as a beaker or a large glass bottle.
- Slowly add the potassium hydroxide to the acetic acid while stirring gently.
- Keep stirring until both solutions are well-mixed and homogeneous.
- Check the pH of the resulting buffer solution using a pH meter or pH indicator strips. Adjust it if necessary by adding small amounts of either acetic acid or potassium acetate until the desired pH (4.47) is reached.