Question

Which one of the following solutions can be used to separate the cations in an aqueous solution in which \(\left[\mathrm{Ba}^{2+}\right]=\left[\mathrm{Ca}^{2+}\right]=0.050 \mathrm{M}: 0.10 \mathrm{M} \mathrm{NaCl}(\mathrm{aq}), 0.05 \mathrm{M}\) \(\mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq}),\) \(0.001 \mathrm{M}\) \(\mathrm{NaOH}(\mathrm{aq}),\) or \(0.50 \mathrm{M}\) \(\mathrm{Na}_{2} \mathrm{CO}_{3}(\text { aq }) ?\) Explain why.

Short answer

The solution that can separate \(Ba^{2+}\) and \(Ca^{2+}\) ions is 0.05 M \(Na_2SO_4\). This is because Barium forms an insoluble sulfate, allowing it to be precipitated out of the solution, whereas Calcium sulfate remains soluble.

Step-by-step solution

Understand the Solubility Rules

The solubility rules state that all sulfates are soluble, with the exception of Barium sulfate, which is insoluble. This means that when a sulfate solution, like Sodium sulfate (\(Na_2SO_4\)), interacts with a solution containing Barium cations, it will form an insoluble precipitate leaving behind only the soluble cations.

Apply the Solubility Rules to the Problem

Given the solubility rules from Step 1, let's apply these to the solutions given in the exercise. Of these, only Sodium sulfate (\(Na_2SO_4\)) can react to selectively precipitate Barium cations from the solution because \(BaSO_4\) is insoluble while \(CaSO_4\) remains soluble.

Confirm the Correct Solution

Therefore, by adding Sodium sulfate (\(Na_2SO_4\)) to the solution, one can easily separate out Barium cations because Barium sulfate will not dissolve, while all other ions, including Calcium ions, will stay in solution. So, 0.05 M \(Na_2SO_4\) can be used to separate the cations in the given solution.

Key concepts

Precipitation Reactions

Precipitation reactions are a type of chemical reaction where two aqueous solutions combine to form an insoluble solid, called a precipitate. This solid separates from the remaining solution, making it possible to isolate certain ions or compounds. These reactions typically occur when the product of the concentrations of the ions involved exceeds the solubility product ( K_{sp} ) of the compound that forms.

In the context of the provided exercise, we are particularly interested in the reaction of barium ( Ba^{2+} ) ions with sulfate ( SO_4^{2-} ) ions. When these two ions meet in a solution, they form barium sulfate ( BaSO_4 ), which is insoluble in water. The formation of this white solid precipitate signifies a precipitation reaction has occurred. As a result, barium cations can be separated from other ions that remain dissolved. This principle can be applied for selective ion removals, which is essential in processes like water softening and metal purification.

Cation Separation

Cation separation involves distinguishing and isolating positive ions from a mixture of ions in a solution. This process often leverages differences in chemical properties such as solubility.

In the exercise, we have a mixture containing barium ( Ba^{2+} ) and calcium ( Ca^{2+} ) ions. To separate these cations, we exploit the fact that barium sulfate is insoluble in water.

• The addition of sodium sulfate ( Na_2SO_4 ) to the solution results in barium cations reacting with sulfate anions to form an insoluble barium sulfate precipitate.
• This precipitate can then be removed by filtration or other means of physical separation, leaving the calcium ions in the aqueous phase.

By choosing the appropriate reagent, in this case, sodium sulfate, cation separation can be achieved effectively even in complex mixtures. This is critical in many laboratory and industrial processes where pure samples of specific ions are required.

Barium Sulfate

Barium sulfate ( BaSO_4 ) is a chemical compound known for its low solubility in water. It is formed when barium ions ( Ba^{2+} ) in a solution encounter sulfate ions ( SO_4^{2-} ). Because of its insolubility, barium sulfate is a common precipitate in chemical processes that separate ions.

This compound is particularly important in the medical and industrial fields. In medicine, it is used as a radiocontrast agent for X-ray imaging and other diagnostic procedures because it is opaque to X-rays. Its ability to form a distinct precipitate with barium makes it effective for use in various chemical analyses and purification processes.

• Barium sulfate's formation is governed by the solubility product ( K_{sp} ), which is very low, indicating it will precipitate out of solution under typical conditions.
• Its low reactivity and insolubility make it safe for use in many applications where pure separation of barium is necessary.

Understanding the properties of barium sulfate helps chemists predict and manipulate its formation in chemical reactions, facilitating its use in both laboratory and industrial settings.