Problem 50 - Chemistry

Question

Which of the following solutions has the highest \(\mathrm{pH}\) : (a) \(0.40 \mathrm{M} \mathrm{HCOOH}\) (b) \(0.40 \mathrm{M} \mathrm{HClO}_{4}\) (c) \(0.40 \mathrm{M}\) \(\mathrm{CH}_{3} \mathrm{COOH} ?\)

Step-by-Step Solution

Answer

The 0.40 M \( \mathrm{CH}_{3} \mathrm{COOH} \) solution has the highest \( \mathrm{pH} \).

Step 1: Determine the type of acid

Identify the type of acid present in each solution. \( \mathrm{HClO}_{4} \) is a strong acid, \( \mathrm{HCOOH} \) (formic acid) and \( \mathrm{CH}_{3} \mathrm{COOH} \) (acetic acid) are weak acids.

Step 2: Define acid strength

A strong acid like \( \mathrm{HClO}_{4} \) completely dissociates in water, contributing more \( \mathrm{H}^+ \) ions and thus a lower \( \mathrm{pH} \). A weak acid partially dissociates, resulting in fewer \( \mathrm{H}^+ \) ions, leading to a relatively higher \( \mathrm{pH} \).

Step 3: Compare weak acids

Compare the strength of the weak acids \( \mathrm{HCOOH} \) and \( \mathrm{CH}_{3} \mathrm{COOH} \). Acetic acid (\( \mathrm{CH}_{3} \mathrm{COOH} \)) is weaker than formic acid (\( \mathrm{HCOOH} \)), meaning it releases less \( \mathrm{H}^+ \) and has a higher \( \mathrm{pH} \) than formic acid when at the same concentration.

Step 4: Identify solution with highest pH

Since \( \mathrm{CH}_{3} \mathrm{COOH} \) is the weakest acid among the given options, the \( 0.40 \ \mathrm{M} \ \mathrm{CH}_{3} \mathrm{COOH} \) solution will have the highest \( \mathrm{pH} \) as it releases the fewest \( \mathrm{H}^+ \) ions.

Key Concepts

Strong Acid

A strong acid is one that completely dissociates in water. This means it breaks apart to release all its hydrogen ions ( H^+ ) into the solution. An example of a strong acid from the exercise is perchloric acid ( HClO_4 ).

• Strong acids contribute many H^+ ions to the solution.
• Because of the high concentration of H^+ ions, strong acids result in a lower pH.
• Common strong acids not only include HClO_4 but also HCl , HNO_3 , and H_2SO_4 .

When working with strong acids, always remember that they can significantly lower the pH of a solution due to their complete dissociation.

Weak Acid

Weak acids only partially dissociate in water. This means only a small fraction of their hydrogen ions ( H^+ ) disassociate into the solution.

Examples from the exercise include formic acid ( HCOOH ) and acetic acid ( CH_3COOH ).

• Because they don't fully dissociate, weak acids contribute fewer H^+ ions.
• This partial dissociation results in a higher pH compared to strong acids.
• Weak acids are common in everyday life; for example, vinegar contains acetic acid, which is a weak acid.

Understanding weak acids helps in predicting the acidity of a solution when it contains acids that don't fully break apart.

Dissociation

Dissociation refers to the process where molecules split into smaller particles, usually ions, when they dissolve in water. It is a key concept when dealing with acids, as it determines how much H^+ is available in the solution.

• In strong acids, dissociation is complete, meaning nearly all the acid molecules break apart.
• For weak acids, dissociation is partial, and a significant amount of the acid remains undissociated.
• The amount of dissociation directly impacts the concentration of hydrogen ions and, therefore, the pH of the solution.

Understanding dissociation helps in evaluating the strength of acids and the resulting characteristics of the solutions they form.

pH

pH is a measure of the acidity or basicity of a solution, essentially reflecting the concentration of hydrogen ions. The scale ranges from 0 to 14, with 7 being neutral, numbers less than 7 indicating acidity, and numbers greater than 7 indicating basicity.

• In general, lower pH values indicate stronger acidity due to higher H^+ concentration.
• In the exercise, the pH of a solution with CH_3COOH is higher compared to solutions with HCOOH or HClO_4 .
• Thus, measuring pH helps determine how acidic or basic a solution is based on its H^+ ion concentration.

Knowing how to interpret pH can assist you in comparing how acidic or basic different solutions are, aiding in many scientific and practical applications.