Question

Sketch the titration curve for the titration of a generic weak base B with a strong acid. The titration reaction is $$ \mathrm{B}+\mathrm{H}^{+} \rightleftharpoons \mathrm{BH}^{+} $$ On this curve, indicate the points that correspond to the following: a. the stoichiometric (equivalence) point b. the region with maximum buffering c. \(\mathrm{pH}=\mathrm{p} K_{\mathrm{a}}\)

Short answer

The titration curve for the titration of a weak base B with a strong acid starts at a pH greater than 7 and gradually decreases in pH. The stoichiometric point is the inflection point where the pH decreases rapidly, indicating the equivalence of added strong acid and weak base. Maximum buffering occurs halfway to the stoichiometric point, where the slope of the curve is minimal, and pH changes slowly with added strong acid. The point where pH = pKa is at the midpoint of the buffering region, corresponding to the pH value between the initial pH and the pH at the stoichiometric point.

Step-by-step solution

Sketch the titration curve

First, we need to draw the titration curve for the titration of a weak base with a strong acid. At the beginning of the titration, the solution consists of a weak base, so the pH is greater than 7. As we add strong acid, the pH decreases, eventually reaching the stoichiometric point. After that point, the pH is dominated by the strong acid and decreases rapidly.

Identify the stoichiometric point

The stoichiometric or equivalence point is where the amount of strong acid added is equivalent to the amount of weak base originally present in the solution. At this point, the titration reaction is complete, and the pH will depend on the relative strength of the conjugate acid formed. On the titration curve, the stoichiometric point corresponds to the inflection point, where the curve changes from gradually decreasing pH to sharply decreasing pH.

Identify the region with maximum buffering

A buffer is a solution that resists changes in pH when small amounts of strong acid or strong base are added. The maximum buffering occurs when the concentration of weak base and its conjugate acid are equal, which is halfway to the equivalence point. In this region, the slope of the titration curve is minimal, indicating that the pH changes slowly as more strong acid is added.

Identify the point where pH = pKa

The pKa value is a measure of the relative strength of a weak acid. For a generic weak base B, we have the following relation: \[pH = pK_a + log(\frac{[\mathrm{B}]}{[\mathrm{BH^{+}}]})\] When the pH is equal to the pKa, the concentration of the weak base (B) and its conjugate acid (BH⁺) are equal. This is also the midpoint of the buffering region. On the titration curve, this point can be found at the pH value corresponding to the midpoint between the initial pH and the pH at the stoichiometric point.

Key concepts

Weak Base Titration

Understanding the titration of a weak base with a strong acid is crucial for grasping important concepts in chemistry. During titration, a strong acid is gradually added to a weak base solution, causing a neutralization reaction. Initially, the solution has a high pH due to the weak base, which only partially ionizes in water, leaving many of the base molecules intact.

As the titration progresses, the added strong acid reacts with the base to form its conjugate acid. This process is visually represented by a titration curve, which plots the pH of the solution against the volume of acid added. One characteristic feature of a weak base titration curve is that it starts at a higher pH and gradually decreases as more acid is added, before dropping sharply near the equivalence point.

An essential thing to note is the shape of the curve. Unlike strong base titrations, where the curve has symmetric appearance, the curve of weak base titrations is asymmetric due to the differing properties of the weak base and the strong acid.

Buffering Capacity

The buffering capacity of a solution is an expression of its ability to resist changes in pH upon the addition of small quantities of acid or base. In a titration setting, when equal amounts of a weak base and its conjugate acid are present, the solution exhibits maximum buffering capacity. This is because the weak base will neutralize added acid and the conjugate acid will neutralize added base.

It's important to understand that the buffering capacity is at its peak when the pH of the solution is approaching the pKa value of the conjugate acid of the base being titrated. At this point in the titration curve, there is typically a region where the curve levels off slightly, indicating a resistance to pH change. This flat region is the optimal buffering range and is an essential concept for biological systems and industrial processes where maintaining a stable pH is critical.

Equivalence Point

The equivalence point of a titration is a fundamental concept that signifies the moment when the amount of titrant (in this case, a strong acid) added is exactly equivalent to the amount of substance present in the solution initially (the weak base).

On the titration curve, the equivalence point is identified by a significant change in the pH over a small addition of titrant, often producing a steep incline or decline on the graph, known as an inflection point. For weak base strong acid titrations, the pH at the equivalence point is typically less than 7, because the conjugate acid formed is stronger than the water molecule, leading to an excess of H⁺ ions.

Finding the equivalence point is crucial for determining the concentration of the weak base in the solution and is a primary aim of performing a titration. Understanding where this point lies on the curve and how it affects the overall titration is vital for accurate measurements and analysis in laboratory settings.

pKa and pH Relationship

The relationship between pKa and pH is integral to understanding acid-base chemistry. pKa is a numerical value that represents the strength of an acid; when referring to a weak base titration, it concerns the conjugate acid of the base. A lower pKa value indicates a stronger acid, which means it more readily donates protons in solution.

The Henderson-Hasselbalch equation, written as \(pH = pKa + \text{log}\frac{[\text{Base}]}{[\text{Conjugate Acid}]}\text{,}\) relates pKa to the pH of a solution. During the midpoint of a titration, where there are equal amounts of the weak base and its conjugate acid, the logarithmic term becomes zero because the concentrations are the same. At this juncture, the pH of the solution is equal to the pKa. This is a pivotal point because it's where the buffering capacity is maximized and is also used for the analytical determination of pKa.

This relationship helps predict how the pH will change with the addition of acid or base in a buffer system and is a key concept for anyone working with solutions that require a specific pH range.