Question

Equal volumes of two monoprotic acid solutions \((\mathrm{A}\) and \(\mathrm{B})\) are titrated with identical \(\mathrm{NaOH}\) solutions. The volume need to reach the equivalence point for solution \(\mathrm{A}\) is twice the volume required to reach the equivalence point for solution \(\mathrm{B}\) , and the \(\mathrm{pH}\) at the equivalence point of solution \(\mathrm{A}\) is higher than the \(\mathrm{pH}\) at the equivalence point for solution \(\mathrm{B}\) . Which statement is true? a. The acid in solution \(A\) is more concentrated than in solution \(B\) and is also a stronger acid than that in solution B. b. The acid in solution \(A\) is less concentrated than in solution \(B\) and is also a weaker acid than that in solution B. c. The acid in solution \(A\) is more concentrated than in solution \(B\) and is also a weaker acid than that in solution B. d. The acid in solution \(A\) is less concentrated than in solution \(B\) and is also a stronger acid than that in solution B.

Short answer

The correct answer is d. The acid in solution A is less concentrated than in solution B and is also a stronger acid than that in solution B.

Step-by-step solution

- Understand Titration and Equivalence Point

When a solution of a monoprotic acid is titrated with a strong base like NaOH, the equivalence point is reached when the number of moles of H+ ions from the acid equals the number of moles of OH- ions from the base. A higher volume of NaOH is needed for a solution with fewer moles of acid per unit volume (a less concentrated solution). The pH at the equivalence point depends on the strength of the acid; strong acids have a lower pH at the equivalence point than weak acids.

- Compare Volume of NaOH Used for Titration

Since solution A required twice the volume of NaOH to reach the equivalence point compared to solution B, solution A must be less concentrated than solution B. This is because more base was required to neutralize the same volume of acid solution, indicating there were fewer moles of acid per unit volume in solution A.

- Compare the pH at the Equivalence Point

The pH at the equivalence point for solution A is higher than for solution B. This indicates that the acid in solution A is a weaker acid, as the salt formed upon neutralization has a basic character, which is only possible if the acid is weak.

- Identify the Correct Statement

Given the information that solution A is less concentrated and has a higher pH at the equivalence point, the correct statement is that the acid in solution A is less concentrated and weaker than that in solution B.

Key concepts

Monoprotic Acid

A monoprotic acid is a type of acid that is capable of donating one proton or hydrogen ion per molecule to an aqueous solution. Common examples include hydrochloric acid ($HCl$) and acetic acid ($CH\_3COOH$). Understanding the behavior of monoprotic acids is essential in acid-base chemistry. When acids dissolve in water, they release hydrogen ions ($H^+$), which can react with base to form water or salt. The term 'monoprotic' refers to the acid only having one proton to offer, which is significant when considering the stoichiometry of acid-base reactions such as titrations.

In the case of our textbook exercise, the fact that the acids in solutions $A$ and $B$ are monoprotic is crucial. It informs us that each molecule of acid from both solutions can neutralize one molecule of the base Sodium Hydroxide ($NaOH$), leading to a stoichiometry ratio of 1:1. This understanding helps us calculate concentrations and make comparisons between the two solutions during titration.

pH at Equivalence Point

The pH at the equivalence point in a titration of an acid with a base is a significant indicator of the nature of the acid involved. The equivalence point is the stage in the titration where the amount of the titrant is stoichiometrically equivalent to the amount of substance being titrated. Regarding pH, it reflects the concentration of hydrogen ions ($H^+$) remaining in the solution. In an acid-base titration, a monoprotic weak acid will show a higher pH at the equivalence point due to the formation of a basic salt and water, resulting in a somewhat basic solution.

Such is the scenario in our exercise, where solution $A$ has a higher pH at the equivalence point compared to solution $B$. This observation is aligned with the behavior of a weaker acid, which upon being neutralized forms a conjugate base that slightly increases the solution's pH. It's important to recognize that while strong acids completely dissociate in water, resulting in a lower pH at the equivalence point, weak acids do not fully dissociate, leading to a less acidic (higher pH) environment when neutralized.

Acid-Base Titration

Acid-base titration is an analytical procedure used to determine the concentration of an acid or base in a solution. This is achieved by reacting a known volume of a solution with known concentration (titrant) with a solution of unknown concentration (analyte) until the reaction reaches the equivalence point, indicating that stoichiometric amounts of the acid and base have reacted.

During a titration, indicators or pH meters are often used to detect the equivalence point—the moment the number of hydrogen ions equals the number of hydroxide ions in the solution. In our exercise example, equal volumes of acid solutions are titrated with a strong base (NaOH). The volume of NaOH needed to reach equivalence provides information about the concentration of the acids in solutions $A$ and $B$. This data is essential to the comparison, as it illustrates that solution $A$ is less concentrated since it requires more titrant to reach equivalence. Remember, the procedure's accuracy largely depends on precise measurements and an understanding of the reaction's stoichiometry.

Acid Strength

Acid strength refers to an acid's ability to donate protons to bases. It's indicated by the acid's dissociation constant ($K\_a$), where a larger value signifies a stronger acid. Strong acids completely dissociate into their ions in water, while weak acids only partially dissociate. The strength of an acid affects the pH of the solution after neutralization, with stronger acids resulting in lower pH.

In the context of our exercise, the difference in volume of NaOH needed to reach the equivalence point implies a difference in acid strength between solutions $A$ and $B$. A higher pH at equivalence suggests that solution $A$ contains a weaker acid compared to the acid in solution $B$, since at the point of neutralization, a weaker acid forms a salt that slightly increases the solution's pH. Knowing how to interpret these clues allows students to discern the relative strengths of acids based on empirical data from titration experiments.