Question

You have three solutions labeled \(\mathrm{A}, \mathrm{B},\) and \(\mathrm{C}\). You know only that each contains a different cation \(-\mathrm{Na}^{+}\) \(\mathrm{NH}_{4}^{+},\) or \(\mathrm{H}_{3} \mathrm{O}^{+} .\) Each has an anion that does not contribute to the solution \(\mathrm{pH}\) (e.g., \(\mathrm{Cl}^{-}\) ). You also have two other solutions, Y and Z, each containing a different anion, \(\mathrm{Cl}^{-}\) or \(\mathrm{OH}^{-},\) with a cation that does not influence solution \(\mathrm{pH}\) (e.g., \(\mathrm{K}^{+}\) ). If equal amounts of B and Y are mixed, the result is an acidic solution. Mixing A and Z gives a neutral solution, whereas B and Z give a basic solution. Identify the five unknown solutions. (Adapted from D. H. Barouch: Voyages in Conceptual Chemistry, Boston, Jones and Bartlett, 1997.)

Short answer

A: Na⁺, B: H₃O⁺, C: NH₄⁺. Y: Cl⁻, Z: OH⁻.

Step-by-step solution

Analyze the results of mixing B and Y

When solution B is mixed with solution Y, the resulting mixture is acidic. This implies that solution B must contain a cation that increases acidity when paired with a neutral anion, like \( \mathrm{Cl}^{-} \) from Y. Thus, solution B is \( \mathrm{H}_{3} \mathrm{O}^{+} \).

Analyze the results of mixing A and Z

Mixing solution A with solution Z results in a neutral solution. Solution Z contains \( \mathrm{OH}^{-} \), a strong base, which when it neutralizes a strong acid, results in a neutral solution. Thus, solution A must contain \( \mathrm{H}_{3} \mathrm{O}^{+} \), however based on previous analysis, it cannot. Therefore, solution A contains \( \mathrm{Na}^{+} \) as it cannot alter the pH on its own when mixed with \( \mathrm{OH}^{-} \).

Analyze the results of mixing B and Z

Mixing solution B with solution Z yields a basic solution. Given that B contains \( \mathrm{H}_{3} \mathrm{O}^{+} \) and Z contains \( \mathrm{OH}^{-} \), the amount of \( \mathrm{OH}^{-} \) must overcome the presence of \( \mathrm{H}_{3} \mathrm{O}^{+} \) in solution B, making the solution basic. This further confirms the composition of B being \( \mathrm{H}_{3} \mathrm{O}^{+} \).

Determine the content of solution C

With B containing \( \mathrm{H}_{3} \mathrm{O}^{+} \) and A being \( \mathrm{Na}^{+} \), solution C must contain the remaining cation \( \mathrm{NH}_{4}^{+} \). This ion would act with any anion present in a manner distinct from either of the cases involving A or B.

Identify solutions Y and Z

Since mixing B (containing \( \mathrm{H}_{3} \mathrm{O}^{+} \)) with Y results in an acidic solution, solution Y must contain \( \mathrm{Cl}^{-} \), a neutral anion. Consequently, solution Z contains \( \mathrm{OH}^{-} \), which when paired with \( \mathrm{Na}^{+} \) (in A), results in a neutral solution and with \( \mathrm{H}_{3} \mathrm{O}^{+} \) (in B), results in a basic solution.

Key concepts

Solution pH

The pH of a solution is a crucial measure of its acidity or basicity. It ranges from 0 to 14, with lower values indicating acidic solutions, higher values suggesting basic ones, and a neutral solution having a pH of 7.
Understanding the pH helps identify reactions and interactions within mixtures as certain ions contribute to different pH levels.
To assess the pH of our given solutions, we need to understand which ions affect it:

• Hydronium ions ( \( \mathrm{H}_{3} \mathrm{O}^{+} \)): Contributes to acidity, lowering the pH of the solution.
• Hydroxide ions ( \( \mathrm{OH}^{-} \)): Contributes to basicity, raising the pH of the solution.
• Neutral ions (e.g., \( \mathrm{Na}^{+} \) and \( \mathrm{Cl}^{-} \)): Generally do not affect the pH directly.

In the given exercise, analyzing the combination of different solutions and their resultant pH gives us clues about the ions present in each solution.

Acid-Base Reactions

An acid-base reaction involves the transfer of protons (\( \mathrm{H}^{+} \)) from an acid to a base. This type of reaction is fundamental in understanding how substances will interact in a solution.
For our exercise:

• When solution B, containing \( \mathrm{H}_{3} \mathrm{O}^{+} \), is mixed with solution Y that doesn't alter pH, acidity in the mixture means an acid is reacting.
• The presence of acids or bases in a mixture can result in different pH outcomes depending on which ions predominate.
• These reactions are essential in determining the characteristics of the unknown solutions based on their interactions.

The analysis during mixing allows identification of acidic or basic solutions due to the acid-base reactions occurring with each mix.

Neutralization Reactions

Neutralization occurs when an acid reacts with a base to produce water and, usually, a salt. This reaction is particularly telling in determining unknown solutions due to its predictable outcome of reaching a neutral pH of 7.
In the exercise:

• Neutralization is evident when solution A with \( \mathrm{Na}^{+} \) is combined with solution Z containing \( \mathrm{OH}^{-} \)
• The resulting mixture highlighted as neutral suggests that neither solution \( \mathrm{H}_{3} \mathrm{O}^{+} \) nor strong bases are present in overpowering amounts.
• This relationship between the acid and base confirms the identity of cations in solution A as being neutral and not contributing to the overall pH change.

By observing these reactions, we draw conclusions on which solutions react to produce neutral solutions and uncover more about the involved ions.

Chemical Mixtures

Chemical mixtures involve the combination of two or more substances that may react or not, altering the properties and behaviors of each component in the process.
For identifying unknowns:

• The results from mixing solutions inform the determination of specific ions, e.g., acidic, basic, or neutral outcomes from mixtures provide key insights.
• In the progression of mixing A and Z resulting in neutral and B and Y resulting in acidic solutions, alignment of expected outcomes with results confirms the identity of the solutions.
• Understanding these mixtures aids in predicting the presence and behavior of ions based on known ionic interactions.

Thus, observing how different chemical mixtures influence each other guides the problem-solving process regarding these solutions.

Ions in Solution

Ions play an essential role in the properties of a solution, dictating whether it's acidic, basic, or neutral.
Key ions in this context include:

• \( \mathrm{H}_{3} \mathrm{O}^{+} \)
• \( \mathrm{NH}_{4}^{+} \)
• \( \mathrm{Na}^{+} \)
• Neutral anions like \( \mathrm{Cl}^{-} \)
• Basic anions like \( \mathrm{OH}^{-} \)

Knowing which ions are present provides crucial information to decipher the nature of the solutions.
The proper identification of ions allows for the understanding of solution behavior, like whether solution B is acidic due to containing \( \mathrm{H}_{3} \mathrm{O}^{+} \).
These insights are crucial for resolving the problem of determining the specifics of the solutions in an educational context.