Problem 27 - Chemistry: The Central Science in SI Units, Global Edition

Question

Separate samples of a solution of an unknown salt are treated with dilute solutions of \(\mathrm{HBr}, \mathrm{H}_{2} \mathrm{SO}_{4},\) and \(\mathrm{NaOH}\). A precipitate forms in all three cases. Which of the following cations could be present in the unknown salt solution: \(\mathrm{K}^{+}, \mathrm{Pb}^{2+}, \mathrm{Ba}^{2+} ?\)

Step-by-Step Solution

Answer

The cation present in the unknown salt solution is Pb\(^{2+}\) because it forms precipitates when reacting with all three given solutions (HBr, H\(_2\)SO\(_4\), and NaOH) according to their solubility rules.

Step 1: Analyze the solubility rules

To identify which cation is present in the unknown salt, we will examine the solubility rules for the possible combinations of cations and anions. This will help us to eliminate any cations that do not form precipitates with the given anions.

Step 2: Examine possible reactions with HBr

Analyze the possible reactions between the cations and the anion from HBr (Br-) and determine which would form a precipitate: - K+ and Br- : When combined, they form KBr, which is soluble and does not form a precipitate (according to solubility rules). - Pb2+ and Br- : When combined, they form PbBr2, which is insoluble and forms a precipitate. - Ba2+ and Br- : When combined, they form BaBr2, which is soluble and does not form a precipitate. Thus, only the combination of Pb2+ and Br- forms a precipitate in this case.

Step 3: Examine possible reactions with H2SO4

Now, analyze the possible reactions between the cations and the anion from H2SO4 (SO42-) and determine which would form a precipitate: - K+ and SO42- : When combined, they form K2SO4, which is soluble and does not form a precipitate. - Pb2+ and SO42- : When combined, they form PbSO4, which is insoluble and forms a precipitate. - Ba2+ and SO42- : When combined, they form BaSO4, which is insoluble and forms a precipitate. Both Pb2+ and Ba2+ form precipitates in this case.

Step 4: Examine possible reactions with NaOH

Lastly, analyze the possible reactions between the cations and the anion from NaOH (OH-) and determine which would form a precipitate: - K+ and OH- : When combined, they form KOH, which is soluble and does not form a precipitate. - Pb2+ and OH- : When combined, they form Pb(OH)2, which is insoluble and forms a precipitate. - Ba2+ and OH- : When combined, they form Ba(OH)2, which is soluble (at high concentrations) and does not form a precipitate. In this case, only the combination of Pb2+ and OH- forms a precipitate.

Step 5: Identify the cation present in the unknown salt

Since the problem states that a precipitate forms in all three cases (with HBr, H2SO4, and NaOH), we can now conclude that the cation present in the unknown salt solution is Pb2+ because it is the only cation that forms precipitates in all three reactions.

Key Concepts

Precipitation Reactions

Precipitation reactions are fascinating processes in chemistry where two soluble substances in a solution form an insoluble solid, or precipitate. These reactions occur when ions from different compounds combine to form a new compound that is not soluble in water. Such processes are governed by solubility rules, which help predict whether a precipitate will form.

• Solubility rules help determine if particular ion combinations will remain dissolved or become solid.
• Forming a precipitate often involves an insoluble salt. For example, when \(\text{Pb}^{2+}\) ions combine with \(\text{Br}^-\) ions, they form insoluble \(\text{PbBr}_2\).
• Precipitation reactions are vital for identifying specific ions in solutions, as seen in our exercise, helping us deduce the presence of \(\text{Pb}^{2+}\).

Knowing the outcome of such reactions can help analytical chemists determine the composition of unknown mixtures, aiding in experiments or industry applications.

Cation Analysis

Cation analysis involves determining specific positively charged ions (cations) present in a solution. This is crucial for identifying unknown substances, where step-by-step examination can provide clarity.

• First, understand the potential cations: \(\text{K}^+\), \(\text{Pb}^{2+}\), \(\text{Ba}^{2+}\).
• Cations react with specific anions to form precipitates based on solubility rules. For instance, \(\text{Pb}^{2+}\) forms a precipitate with \(\text{Br}^-\), \(\text{SO}_4^{2-}\), and \(\text{OH}^-\).
• An iterative process helps test reactions with common anions to determine soluble or insoluble outcomes.

Cation analysis is essential in a laboratory setting, guiding chemists toward understanding solution contents and ensuring correct identifications.

Chemistry Problem Solving

Chemistry problem solving requires critical thinking to apply scientific principles and rules to unravel exercises and draw conclusions effectively. This is exemplified by tackling complex precipitation and solubility questions.

• The key is analyzing problem details, such as identifying compounds, and checking interactions between cations and anions.
• Use foundational knowledge about solubility to hypothesize which reactions occur. For example, knowing which ions form precipitates under given circumstances nabs the solution, as exemplified by identifying \(\text{Pb}^{2+}\).
• Troubleshooting involves checking interim results against known rules, ensuring consistent and logical deductions.

Effective chemistry problem solving is about connecting theoretical understanding with practical application, enhancing clear and logical thinking fresh from hypothesis to conclusion.