Final answer:
To make an acetate buffer at pH 4.76 using a 0.4 M sodium acetate solution, the addition of 0.1 M HCl (Option b) is correct. This will convert some of the sodium acetate to acetic acid, creating a balanced buffer system.
Step-by-step explanation:
To create an acetate buffer with a pH of 4.76 (the same as the pK), starting with 500 mL of a 0.4 M solution of sodium acetate, you need to add an acid or base to adjust the ratio of acetate ion to acetic acid to be 1:1, i.e., a 50:50 mixture. However, since no initial concentration of acetic acid is provided, we need to assume that this solution is purely a salt (sodium acetate) solution, and therefore ample acetic acid must be added to achieve the desired pH. Since acetic acid reacts with NaOH to form sodium acetate and water, you could add the proper amount of a strong acid, such as HCl, to achieve the necessary ratio.
Option b) 0.1 M HCl is the correct choice to add to the sodium acetate solution to create the desired acetate buffer at pH 4.76. Adding a strong acid will convert some of the sodium acetate to acetic acid, helping to establish the correct ratio for the buffer system.
In terms of buffer capacity, an acetate buffer maintains its pH more effectively when the concentrations of the acetic acid and acetate are higher. If the buffer is 0.4 M or higher, adding even a moderate volume of 0.1 M NaOH or 0.1 M HCl results in only a minimal change in pH. This is due to the buffer's ability to soak up added hydrogen or hydroxide ions without significantly affecting the pH. For example, with a 0.50 M concentration for both acetic acid and sodium acetate, the addition of 10.0 mL of 1.0 M HCl to 1.0 L of buffer will only change the pH fractionally.