Answer:
See explanation below
Step-by-step explanation:
To solve this problem, we need to use the Henderson - Hasselbach equation which is the following:
pH = pKa + log ([A⁻] / [HA]) (1)
Where:
[A⁻] = concentration of the acetate
[HA] = concentration of the acetic acid.
With the above expression, we can calculate the ratio of [A⁻] / [HA]. This concentration ratio will be used to calculate the individual concentrations. We know that a buffer is made as a mix of the acid and it's ion, in other words:
[HA] + [A⁻] = [Buffer] (2)
So, with the concentration ratio, we can replace it here in (2) and then, we can calculate each concentration required.
First, let's use (1) to get the concentration ratio:
5 = 4.76 + log ([A⁻] / [HA])
5 - 4.76 = log ([A⁻] / [HA])
0.24 = log ([A⁻] / [HA])
[A⁻] / [HA] = 10⁰°²⁴
[A⁻] / [HA] = 1.7378
From this ratio, we can express either HA or A in function of the result. In this case, we will solve for A:
[A⁻] = 1.7378[HA]
With this expression, we can replace it in (2) to solve for [HA]:
[HA] + 1.7378[HA] = 0.2
2.7378[HA] = 0.2
[HA] = 0.0731 M
Now all we have to do is replace this value in [A] to get the concentration:
[A⁻] = 1.7378 * 0.0731
[A⁻] = 0.1270 M