Question

You know that an unlabeled bottle contains a solution of one of the following: \(\mathrm{AgNO}_{3}, \mathrm{CaCl}_{2}\), or \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3} .\) A friend suggests that you test a portion of the solution with \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\) and then with \(\mathrm{NaCl}\) solutions. Explain how these two tests together would be sufficient to determine which salt is present in the solution.

Short answer

By testing the unknown solution first with \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\) and then with \(\mathrm{NaCl}\), we can identify the salt present. If a white precipitate forms in the first test, the unknown solution contains \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\). If no precipitate forms in the first test but forms in the second test, the unknown solution contains \(\mathrm{AgNO}_{3}\). If no precipitate forms in either test, the unknown solution contains \(\mathrm{CaCl}_{2}\).

Step-by-step solution

Consider the reactions with \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\)

Let's first analyze what will happen if the unknown solution reacts with \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\). If the unknown solution contains: 1. \(\mathrm{AgNO}_{3}\): \(\mathrm{AgNO}_{3} + \mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2} \rightarrow \mathrm{Ba}\left[\mathrm{NO}_{3}\right]_{2} + \mathrm{AgNO}_{3}\) (No visible reaction) 2. \(\mathrm{CaCl}_{2}\): \(\mathrm{CaCl}_{2} + \mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2} \rightarrow \mathrm{BaCl}_{2} + \left[\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\right]\) (No visible reaction) 3. \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\): \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3} + 3\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2} \rightarrow 3\mathrm{Ba}\left[\mathrm{SO}_{4}\right] + 2\mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}\) (Production of a white precipitate of barium sulfate) If a white precipitate forms, we can conclude that the unknown solution contains \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\). Otherwise, it can be either \(\mathrm{AgNO}_{3}\) or \(\mathrm{CaCl}_{2}\).

Consider the reactions with \(\mathrm{NaCl}\)

Now let's analyze what will happen if the unknown solution reacts with \(\mathrm{NaCl}\). If the unknown solution contains: 1. \(\mathrm{AgNO}_{3}\): \(\mathrm{AgNO}_{3} + \mathrm{NaCl} \rightarrow \mathrm{AgCl} + \mathrm{NaNO}_{3}\) (Formation of a white precipitate of silver chloride) 2. \(\mathrm{CaCl}_{2}\): \(\mathrm{CaCl}_{2} + 2\mathrm{NaCl} \rightarrow 2\mathrm{NaCl} + \mathrm{CaCl}_{2}\) (No visible reaction) 3. \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) (already ruled out in the previous test as we assume that there was no precipitation): \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3} + 6\mathrm{NaCl} \rightarrow 2\mathrm{AlCl}_{3} + 3\mathrm{Na}_{2}\mathrm{SO}_{4}\) (No visible reaction) If a white precipitate forms in this reaction, we can conclude that the unknown solution contains \(\mathrm{AgNO}_{3}\). If not, it must contain \(\mathrm{CaCl}_{2}\)

Combine the results of the two tests to identify the unknown solution

We have now established the reactions and outcomes for each test. To determine the salt present in the unknown solution, we can use the results of the two tests as follows: 1. If a white precipitate is formed in the first test (with \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\)), the unknown solution contains \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\). 2. If no precipitate is formed in the first test but a white precipitate is formed in the second test (with \(\mathrm{NaCl}\)), the unknown solution contains \(\mathrm{AgNO}_{3}\). 3. If no precipitate is formed in either test, the unknown solution contains \(\mathrm{CaCl}_{2}\). These two tests together are sufficient to identify the salt present in the solution.

Key concepts

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, are transformed into different substances, called products. In the context of solutions, chemical reactions often involve ions exchanging partners to form new products. A balanced chemical equation represents such a reaction and showcases how reactants combine and convert, ensuring the conservation of mass and charge.

Let’s consider how these reactions manifest with our unknown solution example. When \( \mathrm{Ba(NO}_{3})_{2} \) or \( \mathrm{NaCl} \) is added to the unknown solution, they interact differently depending on the original salt present. The balanced chemical equations provide crucial insights into these interactions. These interactions reveal whether or not a visible product, like a precipitate, is formed.

The key to understanding reactions in this setting is recognizing which ions will form an insoluble compound. This is often guided by solubility rules—guidelines for predicting whether a compound will dissolve in water or not.

Precipitation

Precipitation is a specific type of chemical reaction where two solutions combine, and an insoluble solid forms. This solid, known as a precipitate, appears because the new compound formed doesn't dissolve in the solvent (usually water).

In our example, adding \( \mathrm{Ba(NO}_{3})_{2} \) to the unknown solution might form a white precipitate if \( \mathrm{Al}_{2}(\mathrm{SO}_{4})_{3} \) is present. This happens because \( \mathrm{Ba}^{2+} \) ions from \( \mathrm{Ba(NO}_{3})_{2} \) combine with \( \mathrm{SO}_{4}^{2-} \) ions in \( \mathrm{Al}_{2}(\mathrm{SO}_{4})_{3} \) to form \( \mathrm{BaSO}_{4} \), which is insoluble in water.

Similarly, when \( \mathrm{NaCl} \) is added, \( \mathrm{AgNO}_{3} \) forms \( \mathrm{AgCl} \), a precipitate, if present. Recognizing these reactions helps identify the original compound based on whether a precipitate forms, confirming the presence of specific ions.

Identifying Compounds in Solution

Identifying compounds in a solution involves understanding which chemicals react together to form noticeable products, like precipitates, gases, or color changes. This is often achieved through systematic tests known as qualitative analysis.

In the discussed exercise, the solution's contents were narrowed down using two specific tests:

• Adding \( \mathrm{Ba(NO}_{3})_{2} \) to check for \( \mathrm{Al}_{2}(\mathrm{SO}_{4})_{3} \)
• Adding \( \mathrm{NaCl} \) to test for \( \mathrm{AgNO}_{3} \)

These tests rely on observing reactions that result in precipitate formation, which is easily noticeable and provides clear identification of the unknown compound. By matching observed outcomes with expected ones from balanced equations, the compound in solution is identified successfully. This approach ensures accuracy and efficiency in recognizing chemical substances within a solution.