Calculate the concentration of acetic acid (pka 54.76) and sodium acetate necessary to prepare a 0.2 m buffer solution at pH 5.0

See explanation below

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