Question

A student wishes to prepare a buffer solution at \(\mathrm{pH}=\) \(8.60 .\) Which of these weak acids should she choose and why: HA \(\left(K_{\mathrm{a}}=2.7 \times 10^{-3}\right),\) HB \(\left(K_{\mathrm{a}}=4.4 \times\right.\) \(10^{-6}\) ), or HC \(\left(K_{\mathrm{a}}=2.6 \times 10^{-9}\right) ?\)

Short answer

The student should choose weak acid HC to prepare the buffer solution, as its pKa value is closest to the desired pH of 8.60.

Step-by-step solution

Convert Ka values to pKa values

To convert Ka to pKa, use the formula \( \text{pKa} = -\log(K_a) \). Thus, the pKa for HA is \( -\log(2.7 \times 10^{-3}) = 2.57 \), for HB is \( -\log(4.4 \times 10^{-6}) = 5.36 \), and for HC is \( -\log(2.6 \times 10^{-9}) = 8.59.

Compare pKa values with the desired pH

The pKa for the acid should be close to the desired pH for the buffer solution. In this case, the desired pH is 8.60. So, by comparing the calculated pKa values with the desired pH, it can be seen that the pKa of HC (\(8.59\)) is closest to the desired pH.

Select the appropriate weak acid

The student should select the weak acid with a pKa value closest to the desired pH. In this case, HC is the appropriate weak acid to be chosen to prepare the buffer solution.

Key concepts

Understanding pKa

The term pKa might seem like a complex chemical concept, but it's easy to break down. pKa is an important factor when working with acid-base reactions, especially in the creation of buffer solutions. It represents the negative logarithm of an acid's ionization constant (K_a). The formula to find it is \[ \text{pKa} = -\log(K_a) \]. This measure helps indicate the strength of an acid or how easily it donates protons.

Lower pKa values mean stronger acids because these acids ionize more fully in solution. Higher pKa values suggest weaker acids. When creating a buffer, you need an acid with a pKa close to the target pH because the buffer's capacity to neutralize added acids and bases is best when the pH is close to the pKa. Finding the right balance will keep your solution stable.

What are Weak Acids?

Weak acids are distinct from strong acids because they only partially ionize in water. This means they do not release all their hydrogen ions in solution, making them less reactive.

When you dissolve a weak acid in water, the reaction doesn't go to completion. Instead, an equilibrium is established between the acid molecules and the ions. This equilibrium means you have a mix of undissociated acid and ions.

• This partial ionization is what gives weak acids their buffer properties.
• The more an acid tends to release protons in solution, the stronger it is.
• For weak acids like those in the exercise, it's this limited ionization that makes them useful as buffering agents.

Understanding weak acids is essential for creating effective buffer solutions. They provide the perfect balance of reactivity and stability, which is invaluable in maintaining the desired pH.

The Role of Acid Dissociation Constant in Buffer Solutions

The acid dissociation constant, denoted as K_a , is a critical chemical concept used to describe the extent to which an acid can donate protons to water, thus ionizing in a solution.

It indicates the strength of an acid in a solution. The K_a value helps us understand how much of an acid forms ions in solution. Consequently, for weak acids, K_a is usually smaller because they don't fully dissociate.

Naturally, K_a values help us in designing buffer solutions. When we attempt to establish a buffer, we look for an acid whose pKa (derived from K_a ) is near the desired pH of the solution. This proximity means the acid and its conjugate base form a system that can effectively counteract any added acid or base, thereby maintaining a stable pH.

In the exercise above, by converting K_a into pKa, it becomes easier to select the weak acid that will provide the most effective buffering action at the desired pH.