Question

Each of the solutions in the table has the same volume and the same concentration, \(0.1 \mathrm{M}\). $$ \begin{array}{llll} \hline \text { Acid } & \mathrm{pH} & \text { Acid } & \mathrm{pH} \\ \hline \text { HCl } & 1.0 & \text { Acetic } & 2.9 \\ \text { Formic } & 2.3 & \text { HCN } & 5.2 \end{array} $$ Which solution requires the greatest volume of \(0.1-\mathrm{M}\) \(\mathrm{NaOH}\) to titrate to the equivalence point? Explain your answer.

Short answer

Each solution needs the same volume of NaOH, due to equal initial moles of acid.

Step-by-step solution

Understanding the problem

We need to determine which acidic solution requires the most volume of a 0.1 M NaOH solution to titrate it to an equivalence point. The equivalence point in an acid-base titration is reached when the amount of acid equals the amount of base in moles. Each solution in the table has the same concentration and volume, but the acids differ in their strength as indicated by their pH values.

Analyze the given pH information

Examine the pH values provided for each acid. HCl is a strong acid with a pH of 1.0, meaning it fully dissociates in water. Acetic acid, formic acid, and HCN are weak acids, with respective pH values of 2.9, 2.3, and 5.2. These pH values show that, under the same conditions, HCl has the greatest concentration of hydrogen ions \(H^+\), while HCN has the lowest.

Determine the strongest acid

Since HCl is a strong acid, it fully dissociates, providing the maximum number of moles of \(H^+\). However, since all solutions are of 0.1 M concentration and equal volume, each has the same number of moles of their respective acids initially. Therefore, the volume needed to titrate is determined by the ability of the acid to supply \(H^+\).

Calculate moles of H^+ available

For each acid, the initial concentration \(C_a\) is 0.1 M, and let's denote the volume of acid as V. The moles of \(H^+\) are determined by the degree of dissociation. HCl, being a strong acid, contributes 0.1 V moles of \(H^+\) directly. The weak acids dissociate partially, contributing fewer moles of \(H^+\). However, the initial concentration is the same; hence initial moles of acid need to be fully countered by \(OH^-\).

Choose the acid needing maximum NaOH

Complete dissociation of HCl makes no difference since every acid in the table (given equal conditions) will need exactly 0.1 moles of Na^+(numerically equal to 0.1 L of 0.1 M NaOH) to reach the equivalence point regardless of starting \(H^+\) concentration present due to dissociation dynamics.

Key concepts

Equivalence Point

In an acid-base titration, the equivalence point is a key moment. It occurs when the number of moles of acid equals the number of moles of base. At this point, the acid is completely neutralized by the base.
When titrating, it's crucial to match the acid and base precisely. The equivalence point is often indicated by a color change if an indicator is used.
For example:

• In the titration of hydrochloric acid (HCl) with sodium hydroxide (NaOH), the equivalence point is reached when all the HCl is neutralized.
• The same holds true for any acid, regardless of its dissociation strength.

pH

The pH of a solution indicates its acidity or basicity. On a scale of 0 to 14, lower values mean more acid, and higher values mean more basic.
The pH is essential for understanding the strength of an acid:

• Strong acids have low pH values (e.g., HCl with a pH of 1.0).
• Weak acids have higher pH values (e.g., acetic acid with a pH of 2.9).

The pH affects how a solution reacts during titration, as it indicates the concentration of hydrogen ions ( H^+ ). More acidic solutions have more H^+ , making them react faster with a base.

Weak Acids

Weak acids, like acetic acid and formic acid, do not fully dissociate in water. This means they release fewer hydrogen ions ( H^+ ), resulting in a higher pH.
This partial dissociation affects titration:

• In a titration, weak acids only partially react until more base is added.
• Full neutralization requires as much base as there are initial acid moles.
• This process makes pH changes more gradual until the equivalence point is reached.

Understanding weak acids helps predict how they behave in different chemical reactions, including titration.

Strong Acids

Strong acids, like hydrochloric acid (HCl), fully dissociate in water. They release a large number of hydrogen ions ( H^+ ), which explains their low pH values.
During titration, strong acids behave predictably:

• They immediately react with bases almost in a one-to-one ratio.
• The pH change is sharp and quick as the equivalence point is approached.
• This makes the titration endpoint easier to detect, especially with an indicator.

Understanding strong acids is crucial for accurately predicting reactions and calculating the amounts needed for neutralization.