Problem 113 - Chemistry and Chemical Reactivity

Question

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

Step-by-Step Solution

Answer

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

Step 1: Analyze Information for Solution Y (pH Impact)

Since mixing solutions B and Y results in an acidic solution, Y must contain an anion that influences pH towards acidity. As such, \(Y\) cannot contain \(\mathrm{OH}^{-}\), which would make the solution basic. Thus, Y must contain \(\mathrm{Cl}^{-}\).

Step 2: Analyze Information for Solution Z (pH Impact)

Solution Z reacts to form neutral and basic solutions. When A and Z are mixed, they result in a neutral solution, and when B and Z are mixed, they produce a basic solution. The increment in pH when mixed with B indicates Z contains \(\mathrm{OH}^{-}\).

Step 3: Determine Cation for Solution A

Since mixing \(A\) and \(Z\) results in a neutral solution and A may contain \(\mathrm{Na}^{+}\), \(\mathrm{NH}_{4}^{+}\), or \(\mathrm{H}_{3} \mathrm{O}^{+}\), the cation that contributes to maintaining neutrality by introducing neither acidity nor basicity is \(\mathrm{Na}^{+}\). Therefore, \(A\) has \(\mathrm{Na}^{+}\).

Step 4: Determine Cation for Solution B

Mixing \(B\) and \(Z\) results in a basic solution. Thus, B must contain either \(\mathrm{NH}_{4}^{+}\) or \(\mathrm{H}_{3} \mathrm{O}^{+}\). Since mixing \(B\) and \(Y\) results in an acidic solution, \(B\) must contain \(\mathrm{H}_{3} \mathrm{O}^{+}\), making it acidic.

Step 5: Determine Cation for Solution C

Since \(A\) is \(\mathrm{Na}^{+}\) and \(B\) is \(\mathrm{H}_{3} \mathrm{O}^{+}\), solution C must, therefore, be \(\mathrm{NH}_{4}^{+}\) by process of elimination.

Step 6: Verify Consistency of Findings

Confirm that our findings are consistent, knowing Z's anion makes things basic (\(\mathrm{OH}^{-}\)), Y contributes \(\mathrm{Cl}^{-}\), A contains \(\mathrm{Na}^{+}\), B has \(\mathrm{H}_{3} \mathrm{O}^{+}\), and C must be \(\mathrm{NH}_{4}^{+}\). Each condition bears true within provided information.

Key Concepts

Cation Identification

In chemistry, ions play a crucial role in determining a solution's properties. Here, we focus on identifying cations (positively charged ions) in solutions A, B, and C. These solutions each contain one unique cation from the following: \(\mathrm{Na}^{+}\), \(\mathrm{NH}_{4}^{+}\), and \(\mathrm{H}_{3} \mathrm{O}^{+}\).
Understanding what each cation does helps us systematically identify where each fits:

• \(\mathrm{Na}^{+}\): A neutral ion that does not alter pH levels significantly.
• \(\mathrm{NH}_{4}^{+}\): Often acts as a weak acid in water, potentially lowering pH.
• \(\mathrm{H}_{3} \mathrm{O}^{+}\): This is hydronium, intrinsically raising the solution's acidity.

By analyzing which solution becomes neutral, acidic, or remains unchanged when combined with others, we can deduce:

• Solution A contains \(\mathrm{Na}^{+}\) due to its neutrality when mixed with a basic solution, \(\mathrm{Z}\).
• Solution B provides an acidic outcome when mixed with solution \(\mathrm{Y}\), suggesting the presence of \(\mathrm{H}_{3} \mathrm{O}^{+}\).
• Solution C is left with \(\mathrm{NH}_{4}^{+}\) ultimately, as it is the remaining option.

Anion Influence on pH

Anions, those negatively charged ions in solutions, can significantly influence the pH of a solution. In our scenario, we needed to understand how the presence of \(\mathrm{Cl}^{-}\) and \(\mathrm{OH}^{-}\) affects solution acidity or basicity. Certain anions can either stabilize a solution or drastically change its pH.
Here, the focus shifts to solutions Y and Z where these differences are highlighted:

• \(\mathrm{Cl}^{-}\): Generally doesn't affect pH heavily and will maintain a neutral solution unless paired with other influencing ions like \(\mathrm{H}_{3} \mathrm{O}^{+}\).
• \(\mathrm{OH}^{-}\): When present, it introduces basic characteristics to an otherwise neutral or acidic environment.

Thus in Solution Y, which results in acidity when mixed with B, must contain \(\mathrm{Cl}^{-}\), whereas Solution Z, which increases basicity when mixed with B, holds \(\mathrm{OH}^{-}\). This distinction is pivotal in identifying the unique properties of mixed solutions.

Acid-Base Reactions

When we mix different solutions, acid-base reactions can occur. These reactions are fundamental to chemistry as they alter the solution's properties considerably. Acid-base balance is essentially pH-focused:

• Mixing an acid with a base can neutralize the solution if in correct proportions.
• An acid like \(\mathrm{H}_{3} \mathrm{O}^{+}\) will increase acidity upon introduction to water or neutral environments.
• A base like \(\mathrm{OH}^{-}\) raises pH, creating a basic solution.

For example, when solution B containing \(\mathrm{H}_{3} \mathrm{O}^{+}\) is combined with \(\mathrm{OH}^{-}\) in solution Z, it's neutralization we're observing. Meanwhile, B mixed with Y made acidic by \(\mathrm{H}_{3} \mathrm{O}^{+}\) illustrates the direct acid introduction. Understanding these interactions helps predict outcomes in practical chemistry application.

Solution Mixing Outcomes

The mixing of solutions can yield various outcomes based on the ions present, which may result in neutral, acidic, or basic solutions. To predict these outcomes, one must observe the nature of the ions in each solution.
Consider the observations:

• Mixing A and Z results in neutrality as both \(\mathrm{Na}^{+}\) and \(\mathrm{OH}^{-}\) result in a balanced pH.
• B and Y create an acidic solution due to \(\mathrm{H}_{3} \mathrm{O}^{+}\) overpowering the neutral \(\mathrm{Cl}^{-}\).
• Lastly, when B is combined with Z, the presence of \(\mathrm{OH}^{-}\) eventually neutralizes our acid, turning towards basicity.

These outcomes depend on the initial pH shifts when solutions meet and interact. Such exercises make us better equipped in understanding real-world chemistry scenarios.