How many grams of acetic acid (MW = 60 g/mol, pKa=4.75) are needed to change 1000 L of water with a pH of 11 to a pH of 5.5?

To answer this question, we need to understand the acid-base properties of acetic acid and how it can be used to change the pH of a solution.

Step 1: Write the balanced chemical equation for the dissociation of acetic acid:
CH3COOH ⇌ CH3COO- + H+

Acetic acid (CH3COOH) acts as a weak acid, meaning it partially dissociates in water to form acetate ions (CH3COO-) and hydrogen ions (H+).

Step 2: Calculate the initial concentration of hydrogen ions (H+) in the 1000 L of water at pH 11.
pH is a measure of the concentration of hydrogen ions in a solution. The formula to calculate the hydrogen ion concentration from pH is:

[H+] = 10^-pH

[H+] = 10^-11

[H+] = 1 x 10^-11 M

Step 3: Calculate the desired concentration of hydrogen ions (H+) at pH 5.5.
Similar to step 2, we can use the formula to calculate the desired hydrogen ion concentration:

[H+] = 10^-pH

[H+] = 10^-5.5

[H+] = 3.162 x 10^-6 M

Step 4: Calculate the concentration of acetic acid needed to achieve the desired change in pH.
Since the concentration of acetic acid is equivalent to the concentration of hydrogen ions at equilibrium, we can approximate it as the desired concentration of hydrogen ions:

[CH3COOH] ≈ [H+] ≈ 3.162 x 10^-6 M

Step 5: Convert the concentration of acetic acid to grams.
To convert from molar concentration to grams, we need to use the molecular weight (MW) of acetic acid:

[CH3COOH] = grams of acetic acid / MW

Rearrange the equation:

grams of acetic acid = [CH3COOH] * MW

grams of acetic acid = (3.162 x 10^-6 M) * (60 g/mol)

grams of acetic acid ≈ 1.8972 x 10^-4 g

Therefore, approximately 0.00018972 grams of acetic acid are needed to change 1000 L of water with a pH of 11 to a pH of 5.5.