Problem 149 - General Chemistry

Question

A solution of weak base is titrated to the equivalence point with a strong acid. Which one of the following statements is most likely to be correct? a. The \(\mathrm{pH}\) of the solution at the equivalence point is 7.0 . b. The \(\mathrm{pH}\) of the solution is greater than 13.0 . c. The \(\mathrm{pH}\) of the solution is less than 2.0 . d. The \(\mathrm{pH}\) of the solution is between 2.0 and 7.0 . e. The \(\mathrm{pH}\) of the solution is between 7.0 and 13.0 .

Step-by-Step Solution

Answer

The correct answer is d: pH between 2.0 and 7.0.

Step 1: Understanding the Problem

We are determining the pH at the equivalence point of a titration involving a weak base and a strong acid. At the equivalence point, the moles of the base initially present are equal to the moles of the acid added.

Step 2: Recognizing the Nature of the Reaction

The weak base reacts with the strong acid to form its conjugate acid, which tends to lower the pH of the solution. Therefore, the solution formed is slightly acidic because the conjugate acid of the weak base can donate protons to the solution.

Step 3: Analyzing the pH implications

For a weak base titrated with a strong acid, the resulting solution will lean towards the acidic side due to the formation of the conjugate acid. Thus, the pH will be below 7.0.

Step 4: Eliminating Incorrect Options

Options a, b, and e can be eliminated because they imply neutral or basic conditions. Option c, with a pH less than 2, is too acidic. The correct range for the pH of a weak base titrated with a strong acid is between 2.0 and 7.0.

Step 5: Choosing the Correct Answer

Based on the analysis, option d is correct. A weak base titrated with a strong acid will result in a pHvalue between 2.0 and 7.0 due to the presence of a conjugate acid.

Key Concepts

Weak Base

A weak base is a substance that partially dissociates in solution, meaning it does not release all its hydrogen ions into the solution. This limited dissociation implies that the weak base does not fully convert to hydroxide ions (\( OH^- \)) in water.
This is in contrast to a strong base, which completely dissociates. In a titration involving a weak base, you are likely to encounter the conjugate acid of the base, as the base reacts with the acid.

• Weak bases usually have higher K values than strong acids.
• This partial ionization results in a less basic solution as not all base molecules dissociate.
• The presence of a conjugate acid tends to make the resulting solution slightly acidic.

Strong Acid

Strong acids completely dissociate in a solution, releasing all their hydrogen ions. This full dissociation characteristic makes them highly reactive.
In the context of a titration with a weak base, the strong acid will donate protons readily, reacting with the base to form water and a conjugate acid.

• Strong acids have high dissociation constants, indicating complete ionization.
• Examples include hydrochloric acid (\( HCl \)), sulfuric acid (\( H_2SO_4 \)), and nitric acid (\( HNO_3 \)).
• The excess hydrogen ions from the strong acid contribute to lowering the pH of the solution.

Equivalence Point

The equivalence point in titration is the moment when the amount of titrant added is chemically equivalent to the substance in the solution.
For a titration of a weak base with a strong acid, the equivalence point is reached when the moles of acid added are equal to the moles of the base originally present.

• At this point, the solution will contain the conjugate acid of the original weak base.
• Although no base is left to react, the solution remains acidic due to the presence of the conjugate acid.
• It is important to note that for a weak base and strong acid titration, the equivalence point does not coincide with a pH of 7.

pH Calculation

Understanding the pH calculation involves knowing the relationship between hydrogen ions (\( H^+ \)) concentration and pH. pH is calculated using the formula: \[pH = -\log[H^+]\]
In this titration, we are interested in the pH at the equivalence point.

• The pH is determined by the concentration of hydrogen ions in the solution after the neutralization reaction takes place.
• For a weak base titrated with a strong acid, the resulting pH is acidic due to the formation of the conjugate acid.
• The expected pH range for the solution at the equivalence point is between 2.0 and 7.0, as the presence of the conjugate acid lowers the pH from neutrality.