Question

Relationship Between \(\mathrm{p} K_{\text {a }}\) and pH Which aqueous solution has the lowest pH: \(0.1 \mathrm{~m}\) hydrofluoric acid \(\left(\mathrm{p} K_{\mathrm{a}}=3.20\right) ; 0.1 \mathrm{M}\) acetic acid \(\left(\mathrm{p} K_{\mathrm{s}}=4.86\right) ; 0.1 \mathrm{~m}\) formic acid \(\left(\mathrm{p} K_{\mathrm{a}}=3.75\right) ;\) or \(0.1 \mathrm{~m}\) lactic acid \(\left(\mathrm{p} K_{\mathrm{a}}=7.86\right) ?\)

Short answer

0.1 M hydrofluoric acid has the lowest pH.

Step-by-step solution

Understand the Relationship

The pH of a weak acid solution is influenced by its concentration and its strength, which is represented by its pK_a value. A lower pK_a value indicates a stronger acid, which typically results in a lower pH for a given concentration.

List Given Information

We are given the pK_a values for hydrofluoric acid (pK_a = 3.20), acetic acid (pK_a = 4.86), formic acid (pK_a = 3.75), and lactic acid (pK_a = 7.86). All acids have the same concentration of 0.1 M.

Identify the Strongest Acid

Compare the pK_a values. Hydrofluoric acid has the lowest pK_a value of 3.20, followed by formic acid at 3.75, acetic acid at 4.86, and lactic acid at 7.86. The lowest pK_a value indicates the strongest acid.

Determine the Solution with the Lowest pH

Since hydrofluoric acid has the lowest pK_a value, it is the strongest among the given acids. Hence, the 0.1 M hydrofluoric acid solution will have the lowest pH of all the solutions.

Key concepts

Weak Acids

Weak acids are a fascinating group of acids that partially dissociate in water. This means they do not release all their hydrogen ions into the solution. Because of this partial dissociation, the solution of a weak acid does not reach the same level of acidity as a strong acid at the same concentration.
Consider these points about weak acids:

• They have a higher pK_a value compared to strong acids, indicating their lower tendency to donate protons.
• The pH of a weak acid solution depends on both the pK_a value and the concentration of the acid.
• Weak acids are commonly found and include substances like acetic acid and formic acid, which are found in vinegar and ant stings, respectively.

For example, in the exercise, hydrofluoric acid, acetic acid, and formic acid are all weak acids, but with varying strengths and pK_a values.

Acid Strength

Acid strength refers to the ability of an acid to donate its protons (H+ ions) in a solution. This concept is vital when comparing different acids to determine which one will exhibit a lower pH when dissolved in the same concentration of solution.
Strength is measured via the pK_a value, which inversely indicates the strength of an acid:

• The lower the pK_a value, the stronger the acid, meaning it dissociates more in solution.
• A strong acid will produce more H+ ions, leading to a lower pH in the solution.
• In our example, hydrofluoric acid with a pK_a of 3.20 is stronger than formic acid with a pK_a of 3.75, indicating that hydrofluoric acid will create a more acidic solution.

This is why the hydrofluoric acid solution has the lowest pH among the acids listed.

Concentration

The concentration of an acid solution represents the number of moles of acid per liter of solution. It is a key player in determining the resulting pH of a solution, as it works together with the acid's strength.
When considering concentration:

• All things equal, a higher concentration of a given acid will result in a lower pH.
• In the exercise, all acids are presented with the same concentration of 0.1 M, which allows pK_a to be the main factor affecting the pH.
• By equalizing concentration, the comparison of acid strengths (indicated by pK_a) becomes straightforward and clearly highlights which acids have a stronger impact on the solution's acidity.

Thus, understanding both concentration and pK_a is crucial in predicting and comparing the pH values of acid solutions.