1L of a buffer composed of acetic acid and sodium acetate has a pH of 4.3 (total molarity=0.0774) what is the capacity of 200mL of the buffer to survive an addition of HCl without changing by more than 0.4 pH units?

i am so lost please help!
i know you use the henderson hasselbach equation but i don't know what to do...

Don't worry, I'm here to help! Let's break down the problem step by step.

To determine the capacity of the buffer to resist pH changes, we need to calculate the amount of acid and its conjugate base in the buffer solution.

1. First, let's calculate the pKa of acetic acid using the Henderson-Hasselbalch equation:
pKa = pH + log([A-]/[HA])

Since the pH is given as 4.3, we can substitute the known values and solve for pKa.

2. Next, we need to calculate the concentrations of acetic acid and sodium acetate in the buffer solution.
Let's assume the concentration of acetic acid (HA) is x M. Therefore, the concentration of sodium acetate (A-) will also be x M.

Given that the total molarity of the buffer is 0.0774 M, we can write the equation:
0.0774 M = concentration of HA (acetic acid) + concentration of A- (sodium acetate)
Substitute x for both the concentration of acetic acid and sodium acetate since they are equal.

3. Now we need to calculate the moles of HCl (acid) that can be added to the buffer without changing the pH by more than 0.4 units.

For the buffer solution, the moles of acid and base will combine with the added moles of HCl.

Let's assume that n moles of HCl is added to the buffer, then the moles of acid (HA) in the solution will be x + n, and the moles of conjugate base (A-) will also be x + n.

The pH change can be calculated using the Henderson-Hasselbalch equation as follows:
ΔpH = log10 ([A-]/[HA])

4. Now we can solve for n.

According to the problem, the pH change should not exceed 0.4 units.
So we can set up the equation:
log10 ([A-]/[HA]) ≤ 0.4

Substitute the known values and solve for n.

So by following these steps, you should be able to calculate the capacity of the buffer to survive the addition of HCl without changing by more than 0.4 pH units.