Problem 35 - Chemistry The Central Science In Si Units

Question

The samples of nitric and acetic acids shown here are both titrated with a \(0.100 \mathrm{M}\) solution of \(\mathrm{NaOH}(a q)\). \(25.0 \mathrm{~mL}\) of \(1.0 \mathrm{MHNO}_{3}(a q) \quad 25.0 \mathrm{~mL}\) of \(1.0 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}(a q)\) Determine whether each of the following statements concerning these titrations is true or false. (a) A larger volume of \(\mathrm{NaOH}(a q)\) is needed to reach the equivalence point in the titration of \(\mathrm{HNO}_{3}\) (b) The \(\mathrm{pH}\) at the equivalence point in the \(\mathrm{HNO}_{3}\) titration will be lower than the \(\mathrm{pH}\) at the equivalence point in the \(\mathrm{CH}_{3} \mathrm{COOH}\) titration. (c) Phenolphthalein would be a suitable indicator for both titrations.

Step-by-Step Solution

Answer

(a) False; (b) True; (c) False.

Step 1: Determine Equivalent Volume Needed for Titrations

To reach the equivalence point in a titration, you must add an amount of titrant (NaOH) that exactly neutralizes the moles of acid present. Both \(HNO_3\) and \(CH_3COOH\) have the same concentration and volume, i.e., \(C = 1.0 \text{ M}\) and \(V = 25.0 \text{ mL} = 0.025 \text{ L}\). The moles of acid for both are \(n = C \times V = 1.0 \text{ M} \times 0.025 \text{ L} = 0.025 \text{ mol}\). Therefore, an equal amount of \(0.1 \text{ M}\) NaOH is needed for both solutions, that is \(V = 0.025 \text{ mol} / 0.1 \text{ mol/L} = 0.25 \text{ L} = 25.0 \text{ mL}\).

Step 2: Compare pH at Equivalence Points

The \(HNO_3\) is a strong acid, and its titration with \(NaOH\) will lead to a neutral solution at the equivalence point, where \( ext{pH} = 7\). However, \(CH_3COOH\) is a weak acid, and the equivalence point will be basic due to the presence of a weak conjugate base, acetate ion, leading to \( ext{pH} > 7\). Thus, the \( ext{pH}\) at the equivalence point of \(HNO_3\) will be lower than that of \(CH_3COOH\).

Step 3: Determine Suitability of Phenolphthalein as an Indicator

Phenolphthalein changes color in the \( ext{pH} \) range from approximately 8.2 to 10.0. In the titration of strong acid with a strong base (e.g., \(HNO_3 + ext{NaOH}\)), equivalence \( ext{pH} \) is around 7, so phenolphthalein is not ideal. However, for \(CH_3COOH\), which has an equivalence point with \( ext{pH} > 7\), phenolphthalein would be more suitable.

Key Concepts

Equivalence Point

In an acid-base titration, the equivalence point is a key concept that marks the moment when the amount of titrant added is exactly enough to completely react with the acid or base in the solution. At the equivalence point, the moles of acid equal the moles of base.

For the exercise involving nitric ( HNO_3 ) and acetic acid ( CH_3COOH ) titration with NaOH , both acids were given in equal concentrations and volumes, meaning the amount of base needed to reach the equivalence point is the same for both. Each requires 25 mL of 0.1 ext{ M} NaOH to neutralize the initial 0.025 moles of acid.

Understanding the equivalence point allows us to determine when a titration is complete and to begin analyzing the next important property— the pH.

pH

The pH scale is a measure of how acidic or basic a solution is and is critical for understanding reactions in a titration. At the equivalence point in a strong acid-strong base titration (e.g., HNO_3 + NaOH ), the solution typically reaches a neutral pH of 7. This is because the reaction products, water and a salt, do not affect the pH.

However, when titrating a weak acid like acetic acid ( CH_3COOH ), the pH at the equivalence point is greater than 7. This is due to the formation of the conjugate base, acetate ion, which slightly increases the basicity of the solution. Therefore, in comparison, the pH at the equivalence point for CH_3COOH will be higher than for HNO_3 .

This characteristic shift in pH values at the equivalence point is crucial for selecting an appropriate acid-base indicator.

Strong and Weak Acids

Understanding the nature of acids—whether they are strong or weak—helps explain the behavior of acids during titration. Strong acids like HNO_3 dissociate completely in water, releasing all their H^+ ions, which leads to a straightforward neutralization with bases.

Weak acids like CH_3COOH only partially dissociate in solution, which means not all acidic hydrogen ions are available for reaction initially. As a result, the titration curve for weak acids has a more gradual slope. Additionally, weak acids in titrations result in a buffer solution before reaching the equivalence point.

The unique behavior of weak versus strong acids is fundamental for accurately determining the outcome of titration reactions and their resultant pH values.

Acid-Base Indicators

In titrations, acid-base indicators are vital for visually detecting the equivalence point. These indicators change color within specific pH ranges. For example, phenolphthalein, which changes color between pH 8.2 and 10.0, is suitable for weak acid-strong base titrations such as CH_3COOH with NaOH .

Yet, phenolphthalein is not suitable for strong acid-strong base titrations (like HNO_3 with NaOH ), where the pH at the equivalence point is around 7. In such scenarios, bromothymol blue, which changes color near a neutral pH, would be more appropriate.

Selecting the right indicator ensures precise determination of the equivalence point and operates as a simple, effective tool for chemists conducting titrations.