Final answer:
To prepare the buffer, you would need 0.25 moles of acetic acid (12 M) to add to the 500 mL of 0.5 M sodium acetate.
Step-by-step explanation:
To calculate the amount of 12 M acetic acid needed to prepare a buffer of pH 4.76, we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA]),
where [A-] is the concentration of the conjugate base (sodium acetate) and [HA] is the concentration of the weak acid (acetic acid).
In this case, we want a pH of 4.76, which matches the pKa of acetic acid. So, [A-] = [HA].
We are given that the initial concentration of sodium acetate is 0.5 M and the volume is 500 mL. We can determine the number of moles of sodium acetate using the equation moles = concentration x volume.
moles = 0.5 M x 0.5 L = 0.25 mol.