# Video: Calculating the pH of Weak Acids from the Acid Dissociation Constant K_a

Which acid in the table is most appropriate for the preparation of a buffer solution with a pH of 3.1? [A] HNO₂ [B] HSO₄⁻ [C] HCNO [D] CH₃CO₂H [E] HF

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### Video Transcript

Which acid in the table is most appropriate for the preparation of a buffer solution with a pH of 3.1? A) HNO₂, B) HSO₄⁻, C) HCNO, D) CH₃CO₂H, or E) HF.

Before we get cracking with the question, let’s make sure we know the names of all the acids, so we can keep track. HNO₂ is nitrous acid. HSO₄⁻ is the hydrogen sulfate ion. HCNO is fulminic acid. CH₃CO₂H is ethanoic acid or acetic acid. And, HF is hydrofluoric acid. For all our acids, we’ve been given the corresponding monoprotic dissociations, the reactions with water releasing a single proton.

We’ve also been given the acid dissociation constants for each acid at 25 degrees Celsius. The acid dissociation constant is the equilibrium constant for the monoprotic dissociation. It’s equal to the concentration of hydronium ions multiplied by the concentration of the conjugate base all divided by the concentration of the acid. The higher the K a, the stronger the acid. So, we can rank these acids by their strength from the hydrogen sulphate ion at the top to ethanoic acid at the bottom.

The question mentions we’re looking for a candidate to make a buffer solution. A buffer solution is a mixture of weak acid and conjugate base, or the reverse that is resistant to changes in pH. Our best, most flexible buffer, is achieved when the concentration of acid is equal to the concentration of the conjugate base. This gives the solution the greatest flexibility to respond to both acid and base. It’s under these conditions that the pH of the buffer will equal the pK a. This can be seen from the Henderson–Hasselbalch equation, which will tell you that the pH of a buffer based on its pK a and the concentration of acid and conjugate base.

If we plug equivalent concentrations of the two into the Henderson–Hasselbalch equation, we’ll produce a value of zero for the logarithm, producing pH equals pK a. We want to produce the best candidate for producing a buffer solution with a pH of 3.1. So, in order to do that, we need to calculate the pK as for all our acids. The pK a is just a way of simplifying the acid dissociation constant values. So, we take the negative logarithm to the base 10 of K a to get the pK a.

For nitrous acid, we get about 3.3. For the hydrogen sulphate ion, we get about 1.9. Fulminic acid has a pK a of about 3.7. Ethanoic acid’s pK a is about 4.7. And, the pK a of hydrofluoric acid is about 3.2. Our next job is to find the closest value to our pH. The closer the pK a of our acid is to the pH, the less strange the buffer will be if we compose it to have that pH. You could do it by eye. But, the best way is to calculate the difference for each and find the smallest value.

This is what we get when we work out how far away are pK a values after a pH of 3.1. Whether it’s a positive difference or a negative difference doesn’t matter here. So, I’ve just left off the sign. The acid with the pK a closest to our target pH of 3.1 is hydrofluoric acid with a pK a of 3.17. So, our most appropriate acid for the preparation of the buffer solution with a pH of 3.1 out of these five candidates is E, hydrofluoric acid.

You might be interested to know that if we did want to use hydrofluoric acid to make our buffer, we could mix it with sodium fluoride. And make our pH 3.1 buffer using 0.100 molar hydrofluoric acid and 0.086 molar sodium fluoride. These aren’t the only concentrations that would work but it is a good example. It’s normally recommended that the pK a of a weak acid in the buffer is within a plus or minus one range with the desired pH. We’re well within that boundary.

However, just a word of warning. In practice, hydrofluoric acid would probably be a bad choice to produce a buffer solution with this pH. Hydrofluoric acid is very dangerous, and it’s expensive to handle safely. This is because it can very easily pass through your skin, cause deep chemical burns, and remove calcium from your bones. However, this question just relies on you understanding the principles of pK a and pH. On that basis alone, HF is our candidate.