Question

A buffer contains a weak acid, HX, and its conjugate base. The weak acid has a \(\mathrm{p} K_{a}\) of \(4.5,\) and the buffer has a \(\mathrm{pH}\) of \(4.3 .\) Without doing a calculation, predict whether \([\mathrm{HX}]=\left[\mathrm{X}^{-}\right]\) \([\mathrm{HX}]>\left[\mathrm{X}^{-}\right],\) or \([\mathrm{HX}]<\left[\mathrm{X}^{-}\right] .\) Explain. \([\) Section 17.2\(]\)

Short answer

In the buffer solution, the pH is 4.3, which is lower than the pKa of the weak acid HX (4.5), indicating a more acidic environment. According to the Henderson-Hasselbalch equation, when pH < pKa, it means that \(\frac{[\mathrm{X}^{-}]}{[\mathrm{HX}]}\) is less than 1, indicating that the concentration of the conjugate base, X-, is less than that of the weak acid, HX. Therefore, without doing any calculations, we can predict that \([\mathrm{HX}] > [\mathrm{X}^-]\) in this buffer solution.

Step-by-step solution

First, look at the pH and pKa given in the problem: pH = 4.3 and pKa = 4.5. We can notice that the pH is lower than the pKa, which means the environment is more acidic than the Ka equilibrium. This information will help us determine which species has higher concentration in the solution. #Step 2: Understand the relationship between pH, pKa, and concentrations in the Henderson-Hasselbalch equation#

According to the Henderson-Hasselbalch equation, if the pH is less than the pKa, then the fraction under the logarithm (i.e., \(\frac{[\mathrm{X}^{-}]}{[\mathrm{HX}]}\)) must be less than 1. This means that the concentration of the conjugate base, X-, in the solution should be less than the concentration of the weak acid, HX. #Step 3: Predict the relationship between the concentrations of HX and X^-#

Given the information from the Henderson-Hasselbalch equation and the comparison of pH and pKa values, we can predict that: \[ [\mathrm{HX}] > [\mathrm{X}^-] \] This means that the concentration of the weak acid, HX, is higher than the concentration of its conjugate base, X-, in the buffer solution. #Step 4: Explain the prediction#

Since the pH of the solution is lower than the pKa of the weak acid, this indicates that the solution is more acidic than the Ka equilibrium, favoring the acidic species (HX) over the basic species (X-). As a result, the concentration of HX is higher than the concentration of X- in the buffer solution.

Key concepts

Understanding the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is paramount in comprehensively understanding buffer solutions. It is an equation used to estimate the pH of a buffer solution containing a weak acid and its conjugate base. The beauty of this equation lies in its simplicity and usefulness in laboratory and industrial processes. The equation is written as:
\[\text{pH} = \text{pKa} + \log\left(\frac{[\text{Conjugate Base}]}{[\text{Weak Acid}]}\right)\]
Here’s a deeper dive into the equation's components. The \(\text{pKa}\) represents the acid dissociation constant, which gives us insight into the acidity of the weak acid in question. It’s the pH value where the acid is half dissociated, essentially acting as a tipping point. For any buffer solution, understanding that the pH is determined by the ratio of the concentrations of the conjugate base to the weak acid allows you to predict the solution's behavior under various conditions. If the pH is lower than the \(\text{pKa}\), the equation suggests that the concentration of the acid is higher than that of the conjugate base, resulting in a more acidic solution.

The Interplay between pKa and pH

Digging deeper into buffer chemistry, we encounter the delicate dance between \(\text{pKa}\) and \(\text{pH}\). The \(\text{pKa}\) value of an acid is a direct indication of its strength; the lower the value, the stronger the acid. What is essential for students to grasp is the inherent relationship between \(\text{pKa}\) and \(\text{pH}\): a buffer's \(\text{pH}\) lives in relation to its acid's \(\text{pKa}\). When the \(\text{pH}\) equals the \(\text{pKa}\), a unique equilibrium is achieved where the concentrations of the weak acid and its conjugate base are equal.

If we slide the pH scale below the \(\text{pKa}\), the acidic form predominates, signifying more undissociated acid is present. Likewise, a higher \(\text{pH}\) suggests a shift towards the basic form, with a predominant concentration of the conjugate base. This interrelationship is pivotal in predicting and controlling the acid-base balance within a buffer system.

Conjugate Acid-Base Pairs in Buffers

At the heart of buffer solutions lie conjugate acid-base pairs. These remarkable duos work synergistically to resist drastic pH changes in a solution. To understand this, a foundational knowledge of what constitutes a conjugate acid-base pair is vital. Simply put, they are two species that transform into one another by the loss or gain of a proton (H+).

For instance, when a weak acid (HX) loses a proton, it becomes its conjugate base (X-). Upon encountering an excess proton, the base reverts to the acid, creating a self-regulating system. This is the secret behind a buffer's resilience. It's not about a single species acting alone but about the interplay of the conjugate acid-base pair, working together to neutralize any added acids or bases. Hence, a buffer with a conjugate base stronger than its acid tends to have a higher \(\text{pH}\), and vice versa. When constructing a buffer or analyzing its composition, it is of utmost importance to consider both members of the pair and how they interact with each other to maintain the desired pH level.