Chapter 8: Problem 83
Do a \(1.0 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\) solution and a \(1.0 \mathrm{M} \mathrm{HCl}\) solution require the same amount of \(1.0 \mathrm{M} \mathrm{NaOH}\) to hit a titration end point? Explain.
Short Answer
Expert verified
No, because acetic acid is a weak acid, requiring more NaOH for complete neutralization.
Step by step solution
01
Understand the Acids Involved
We have two acids: acetic acid \( \text{CH}_3\text{COOH} \) and hydrochloric acid \( \text{HCl} \). Acetic acid is a weak acid, meaning it doesn't fully dissociate in solution, while \( \text{HCl} \) is a strong acid, meaning it fully dissociates.
02
Write the Reaction Equations
For acetic acid: \( \text{CH}_3\text{COOH} \) dissociates as \( \text{CH}_3\text{COO}^- + \text{H}^+ \). For hydrochloric acid: \( \text{HCl} \to \text{H}^+ + \text{Cl}^- \). Both release \( \text{H}^+ \) ions which react with \( \text{NaOH} \), neutralizing the solution.
03
Consider the Equivalence Point
The equivalence point occurs when the moles of \( \text{H}^+ \) from the acid equal the moles of \( \text{OH}^- \) from the base. For \( \text{HCl} \), the equivalence point is reached quickly because it fully dissociates, providing all \( \text{H}^+ \) ions.
04
Determine NaOH Requirement for Each Solution
Both solutions start at \( 1.0 \text{ M} \), so you would initially presume equal \( \text{NaOH} \) is needed. However, due to incomplete dissociation, more \( \text{NaOH} \) is needed to neutralize 50% of the acetic acid's \( 1.0 \text{ M} \) solution than its \( 1.0 \text{ M} \) indicates, versus the \( \text{HCl} \).
05
Use the Formula for Neutralization
The formula used is \( C_1V_1 = C_2V_2 \) (where \( C \) is concentration and \( V \) is volume). For \( \text{HCl} \), \( C_1 = C_2 \), so volumes assume equality. However, \( \text{CH}_3\text{COOH} \) requires accounting weak acid dissociation, which changes volume required.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Weak Acid Dissociation
A weak acid, like acetic acid (\(\text{CH}_3\text{COOH}\)), only partially dissociates in water. This means only some of the acid molecules release their hydrogen ions (\(\text{H}^+\)) into the solution. In contrast, strong acids like hydrochloric acid (\(\text{HCl}\)) completely dissociate and release all their hydrogen ions. Understanding this behavior is crucial when considering titrations. Since weak acids do not fully dissociate, the effective concentration of \(\text{H}^+\) ions in a solution is less than the original concentration of the acid. As a result, calculating the exact amount of base needed for complete neutralization involves considering the dissociation constant, \(K_a\), of the weak acid. For acetic acid, around half of the molecules remain in the non-ionized form at any given time in solution, influencing how they react with a base like sodium hydroxide (\(\text{NaOH}\)).
- Partial dissociation: Only a fraction of the \(\text{CH}_3\text{COOH}\) molecules dissociate into \(\text{CH}_3\text{COO}^-\) and \(\text{H}^+\).
- Comparison: Unlike \(\text{HCl}\), which provides a straightforward calculation, the weak acid requires modification of the neutralization equation to account for this limited dissociation.
Equivalence Point
The equivalence point of a titration is a key milestone. It is reached when the number of moles of hydrogen ions (\(\text{H}^+\)) present in the acid equals the number of moles of hydroxide ions (\(\text{OH}^-\)) added from the base. For strong acids like \(\text{HCl}\), determining this point is straightforward due to complete dissociation, which supplies a full concentration of \(\text{H}^+\) ions.However, for weak acids such as acetic acid, the equivalence point must be carefully calculated. Since \(\text{CH}_3\text{COOH}\) does not fully dissociate, fewer \(\text{H}^+\) ions are initially available to react.The process of approaching the equivalence point is unpredictable with weak acids, requiring:
- Careful calculations: Understanding the initial and final concentrations for precise titrant addition.
- Use of indicators: Often phenolphthalein or similar pH indicators are used to visually signal when the equivalence point is close.
Neutralization Reaction
A neutralization reaction involves the reaction between an acid and a base, leading to the formation of water and a salt. For our context of titration using \(\text{NaOH}\) (a base) and acids like \(\text{HCl}\) and \(\text{CH}_3\text{COOH}\), this process is central.In a neutralization scenario, the \(\text{NaOH}\) provides \(\text{OH}^-\) ions which react with \(\text{H}^+\) ions from the acid, forming water (\(\text{H}_2\text{O}\)):\[\text{H}^+ + \text{OH}^- \rightarrow \text{H}_2\text{O}\]This equation highlights why measuring the exact amounts of acid and base is crucial in titration scenarios, bringing the solution to a neutral state where \(\text{H}^+\) and \(\text{OH}^-\) ions are balanced.
- Acetic acid: Because it’s a weak acid, more \(\text{NaOH}\) might be needed to reach neutrality because not all \(\text{H}^+\) ions are available initially.
- Hydrochloric acid: Strong and fully dissociated, meaning less calculation complexity, providing direct balance with stoichiometric amounts of \(\text{NaOH}\).