The question asks,

Consider the following weak acids and their Ka values

Acetic acid Ka = 1.8x10^-5
Phosphoric acid Ka = 7.5x10^-3
Hypochlorous acid Ka = 3.5x10^-8

What weak acid-conjugate base buffer system from the acids listed is the best chouce to prepare the following bufers?: Explain your reasoning.

(a) pH 2.8
(b) pH 4.5
(c) pH 7.5

I need to find out what kind of relationship Ka has to pH, does it have to do with pKa?

The way you do these is to convert those Ka values to pKa = -log Ka.

Then the best acid/conjugate base is the acid with a pKa = +/- 1 of the pH you want for the buffer. For example,
pKa for acetic acid is 4.74 and that would be the best acid (conjugate base is acetate ion) to use to prepare a buffer system with pH = 4.5.

Yes, the Ka value of a weak acid is related to its pKa value, which in turn is related to the pH of a solution containing the acid.

The pKa represents the negative logarithm (base 10) of the Ka value. In other words, pKa = -log10(Ka). It is a measure of the acidity strength of the weak acid. A lower pKa value corresponds to a stronger acid and a higher Ka value.

Now let's evaluate each pH value and select the best weak acid-conjugate base buffer system for each case.

(a) pH 2.8:
To prepare a buffer at pH 2.8, we would need a weak acid-conjugate base pair that can stabilize this acidic pH. Since the pH is quite low, the ideal choice would be an acid with a lower pKa value. Among the given acids, acetic acid (CH3COOH) has the lowest pKa value of 4.75. Therefore, acetic acid and its conjugate base (acetate ion) would be the best choice for this buffer system.

(b) pH 4.5:
In this case, we need a weak acid-conjugate base pair that can stabilize a pH of 4.5. The acid should have a pKa value close to this pH. From the given acids, acetic acid has the closest pKa value to 4.5. Therefore, acetic acid and acetate ion would still be a suitable choice for this buffer system.

(c) pH 7.5:
For a pH of 7.5, we would need a weak acid-conjugate base pair with a pKa value close to this pH. Among the given acids, the best choice would be phosphoric acid (H3PO4) since it has the closest pKa value of 2.12. Therefore, phosphoric acid and its conjugate base (hydrogen phosphate ion) would be the best choice for this buffer system.

To summarize:
- For pH 2.8, acetic acid (CH3COOH) and acetate ion (CH3COO-) would be the best buffer system.
- For pH 4.5, acetic acid (CH3COOH) and acetate ion (CH3COO-) would be the best buffer system.
- For pH 7.5, phosphoric acid (H3PO4) and hydrogen phosphate ion (HPO42-) would be the best buffer system.

The choice of the buffer system depends on the desired pH range and the pKa values of the weak acids.

Yes, the relationship between Ka and pH is related to pKa. The pKa is the negative logarithm (base 10) of the acid dissociation constant, Ka. In general, the lower the pKa, the stronger the acid, and the higher the pKa, the weaker the acid. pH, on the other hand, measures the acidity (or basicity) of a solution.

To determine the best weak acid-conjugate base buffer system for each target pH value, we need to consider the pKa values of the weak acids and choose the system that has its pKa closest to the target pH. This will allow the buffer to effectively resist changes in pH when small amounts of acids or bases are added.

Now, let's analyze each target pH value one by one:

(a) pH 2.8:
For a pH of 2.8, we need a fairly strong acid. Among the given weak acids, acetic acid has the lowest pKa value (pKa = -log(1.8x10^-5) ≈ 4.74). Since its pKa is higher than the desired pH, acetic acid will not be effective at buffering pH 2.8.

(b) pH 4.5:
For a pH of 4.5, we need a slightly stronger acid than acetic acid but weaker than pH 2.8. Looking at the given weak acids, acetic acid still has the lowest pKa value (pKa ≈ 4.74). It is close to the target pH, so acetic acid will be a suitable choice for buffering pH 4.5.

(c) pH 7.5:
For a pH of 7.5, we need a weak acid that is significantly stronger than acetic acid. Among the options, phosphoric acid has the lowest pKa value (pKa = -log(7.5x10^-3) ≈ 2.12), which is lower than the target pH. Therefore, phosphoric acid will be the best choice for preparing a buffer at pH 7.5.

In conclusion, acetic acid is the best choice for preparing a buffer at pH 4.5, while phosphoric acid is the best choice for preparing a buffer at pH 7.5.