Problem 47 - Chemistry The Central Science In Si Units

Question

Calculate the \(\mathrm{pH}\) at the equivalence point for titrating \(0.200 \mathrm{M}\) solutions of each of the following bases with 0.200 M HBr: (a) sodium hydroxide (NaOH), (b) hydroxylamine \(\left(\mathrm{NH}_{2} \mathrm{OH}\right),(\mathbf{c})\) aniline \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\right)\)

Step-by-Step Solution

Answer

(a) pH = 7; (b) pH ≈ 5.23; (c) pH ≈ 2.98

Step 1: Understanding the Equivalence Point

At the equivalence point in a titration of a strong acid with a strong base, such as NaOH with HBr, the solutions are neutralized completely. In this scenario, the pH will be 7 because the reaction produces water, and both the acid and the base are completely dissociated.

Step 2: Part A: Titrating NaOH with HBr

For NaOH (a strong base) titrated with HBr (a strong acid), the equation is \[ \text{NaOH} + \text{HBr} \rightarrow \text{NaBr} + \text{H}_2\text{O} \]Since both are strong and fully dissociate, at the equivalence point, their concentrations equal so the solution is neutral. The pH is therefore 7.

Step 3: Part B: Titrating Hydroxylamine with HBr

Hydroxylamine is a weak base, so when it is titrated with a strong acid like HBr, the conjugate acid of hydroxylamine is formed. The reaction is:\[ \text{NH}_2\text{OH} + \text{HBr} \rightarrow \text{NH}_3\text{OH}^+ + \text{Br}^- \]At equivalence, calculate the pH using the Ka (5.6 x 10^{-11}) of the conjugate acid \( \text{NH}_3\text{OH}^+ \) from Kb (1.1 x 10^{-8}) using \[ K_w = K_a \times K_b \] and the concentration using the formula \[ [\text{H}^+] = \sqrt{K_a \times [\text{NH}_3\text{OH}^+]} \] Thus, \( \text{pH} \approx 5.23 \).

Step 4: Part C: Titrating Aniline with HBr

Aniline is also a weak base and reacts with HBr in the following manner:\[ \text{C}_6\text{H}_5\text{NH}_2 + \text{HBr} \rightarrow \text{C}_6\text{H}_5\text{NH}_3^+ + \text{Br}^- \]At equivalence, the solution contains the conjugate acid \( \text{C}_6\text{H}_5\text{NH}_3^+ \), which we use to calculate the pH. Using Kb (4.3 x 10^{-10}) of aniline, calculate Ka similar to Part B. Use the concentration to find \( [\text{H}^+] \) and calculate \[ \text{pH} \approx 2.98 \].

Key Concepts

Equivalence Point

The equivalence point in a titration is a fundamental concept used to understand chemical reactions between acids and bases. It is the point at which the number of moles of acid equals the number of moles of base added, resulting in a complete neutralization reaction.
In simple terms, it's like reaching a perfect balance where the acid's protons and the base's hydroxide ions neutralize each other.

• For strong acid-strong base titrations, like hydrochloric acid (HCl) with sodium hydroxide (NaOH), the pH at the equivalence point is 7. This is because the products are water and a neutral salt.
• With strong acid-weak base or weak acid-strong base titrations, however, the equivalence point pH will differ from 7 due to the formation of a conjugate acid or base.

Understanding the equivalence point is crucial for accurately determining the pH and comprehending the titration process.

Titration

Titration is a laboratory method used to determine the concentration of an unknown solution. This technique involves the gradual addition of a titrant— a solution with a known concentration — to the solution being analyzed. As the titrant is added, a reaction occurs between the titrant and the unknown solution, which can be monitored using indicators or pH meters.

• One common goal of titration is to locate the equivalence point, which signifies the completion of the reaction.
• Indicators are often used to signal this point by changing color.

Titration is not only used in academic settings but also has practical applications in industries such as pharmaceuticals and environmental testing, where it's crucial to determine the exact concentration of substances.

Strong Acid and Weak Base Reactions

Reactions between a strong acid and a weak base can have interesting outcomes compared to those involving strong acids and strong bases. When a strong acid like hydrobromic acid (HBr) reacts with a weak base such as hydroxylamine or aniline, the conjugate acid of the weak base is formed. This can lead to a pH at the equivalence point that is less than 7, indicating an acidic solution. Here's why:

• A strong acid, during dissociation, fully releases its hydrogen ions.
• A weak base partially accepts these hydrogen ions.
• At the equivalence point, the solution is controlled by the weak base's conjugate acid, resulting in a lower pH.

In these reactions, the focus shifts from water formation to the characteristics of the conjugate acids created, which play a significant role in determining the solution's acidity.

Neutralization

Neutralization is a chemical reaction in which an acid and a base react to form water and a salt. It is an essential concept of chemistry, especially in the context of pH calculations and titrations. The goal of neutralization is to bring the acid and base to a balanced state where they cancel each other's effects. In practical terms:

• For a strong acid and strong base, complete neutralization yields water and a neutral salt, often resulting in a pH close to 7.
• In cases involving a strong acid and a weak base, the reaction ends with the formation of a conjugate acid, leading to an acidic solution.

Neutralization is not only important in the laboratory. It is also crucial in real-world applications, such as treating wastewater and controlling pH in various industrial processes.

Conjugate Acid-Base Pairs

Conjugate acid-base pairs play a pivotal role in understanding reactions involving acids and bases. When an acid donates a proton, it forms its conjugate base. Similarly, when a base accepts a proton, it forms its conjugate acid. This concept helps explain why certain reactions have particular outcomes:

• In strong acid reactions with weak bases, the weak base's conjugate acid significantly affects the solution's properties.
• This is because, at the equivalence point, the presence of the conjugate acid can result in an acidic pH.

Recognizing conjugate acid-base pairs allows chemists to predict the direction of proton transfer and the pH level following a reaction. This understanding is crucial in analyzing titration results and determining the final pH of solutions.