Question

\(\mathrm{AgNO}_{3}\) is added slowly to a solution that contains \(0.1 \mathrm{M}\) each of \(\mathrm{Br}^{-}, \mathrm{CO}_{3}^{2-},\) and \(\mathrm{SO}_{4}^{2-}\) ions. What compound will precipitate first and what compound will precipitate last?

Short answer

AgBr precipitates first, Ag2SO4 precipitates last.

Step-by-step solution

Determine the Solubility Product Constants

Know that different anions will form precipitates with silver ions at different thresholds given by their respective solubility products \( K_{sp} \). The \( K_{sp} \) values are typically found in reference tables: \( \text{AgBr} = 5.0 \times 10^{-13} \), \( \text{Ag}_2\text{CO}_3 = 8.1 \times 10^{-12} \), \( \text{Ag}_2\text{SO}_4 = 1.2 \times 10^{-5} \).

Write the Formation Reactions

Write the reaction equations for the formation of each precipitate: - \( \text{Ag}^+ + \text{Br}^- \rightarrow \text{AgBr(s)} \)- \( 2\text{Ag}^+ + \text{CO}_3^{2-} \rightarrow \text{Ag}_2\text{CO}_3(s) \)- \( 2\text{Ag}^+ + \text{SO}_4^{2-} \rightarrow \text{Ag}_2\text{SO}_4(s) \)

Calculate Ion Product for Precipitation

For the ion \( \text{Br}^- \), we find when \( [Ag^+] \) meets the solubility requirement: \( [Ag^+] \cdot [Br^-] = K_{sp} = 5.0 \times 10^{-13} \). Since \( [Br^-] = 0.1 \), \([Ag^+] = \frac{5.0 \times 10^{-13}}{0.1} = 5.0 \times 10^{-12} \).

Calculate Ion Product for Carbonate

For \( \text{CO}_3^{2-} \), we have \( [Ag^+]^2 \cdot [CO_3^{2-}] = K_{sp} = 8.1 \times 10^{-12} \).Solve for \([Ag^+]\): \( [Ag^+]^2 = \frac{8.1 \times 10^{-12}}{0.1} \Rightarrow [Ag^+] = \sqrt{8.1 \times 10^{-11}} = 9.0 \times 10^{-6} \).

Calculate Ion Product for Sulfate

For \( \text{SO}_4^{2-} \), the condition \( [Ag^+]^2 \cdot [SO_4^{2-}] = K_{sp} = 1.2 \times 10^{-5} \) applies.Solve for \([Ag^+]\): \( [Ag^+]^2 = \frac{1.2 \times 10^{-5}}{0.1} \Rightarrow [Ag^+] = \sqrt{1.2 \times 10^{-4}} = 0.011 \).

Compare and Conclude

Since \([Ag^+]\) required to start precipitation for each is different, compare them:- \( \text{AgBr} \) precipitates first because it requires the least \( [Ag^+] \).- \( \text{Ag}_2\text{SO}_4 \) precipitates last since it requires the highest \( [Ag^+] \).

Key concepts

Precipitation Reactions

Precipitation reactions are fascinating chemical processes that occur when two solutions containing soluble salts are mixed, resulting in the formation of an insoluble compound called a precipitate. This occurs when the product of the concentrations of the reacting ions exceeds the solubility product constant ( K_{sp} ) of the compound formed.
When we talk about precipitation reactions, it's important to note that they are generally observed as a solid forming or appearing when solutions are mixed.
Key factors in these reactions include the concentration of the ions in solution and the K_{sp} of the possible products.

The understanding of precipitation reactions is crucial in various fields:

• Water treatment to remove unwanted ions.
• Mining, to extract metals from ores.
• Qualitative chemical analysis to identify ions in a solution.

By analyzing these reactions, we can predict which compounds will precipitate first from a solution when a certain reactant is continuously added, such as a silver nitrate solution. This allows for the selective separation of ions depending on their solubility.

Ionic Reactions

Ionic reactions involve the making and breaking of ionic bonds, leading to the formation of new products. These occur exclusively in ionic compounds and are often fast and spontaneous.
The primary driving force for a reaction between ions is the pursuit of stability, often achieved by forming less soluble compounds. One common aspect of ionic reactions is the exchange of ions between reactants to produce one or more insoluble products, often observed as precipitation.

When thinking about ionic reactions, one often encounters terms like spectral ions and net ionic equations:

• **Spectator Ions**: These ions remain unchanged throughout the reaction and therefore do not participate in the reaction.
• **Net Ionic Equation**: It includes only those compounds and ions that undergo a chemical change in a reaction in an aqueous solution.

While running ionic reactions, especially in an academic setting, it is essential to differentiate between spectator ions and those part of the precipitating compound. This distinction helps us simplify the process to understanding which ions are actively participating in forming different compounds.

Silver Nitrate Solution

Silver nitrate ( AgNO_3 ) is a versatile compound frequently used in laboratory settings because it readily reacts with many other compounds to form precipitates.
For instance, when added to a solution containing halide ions like Br^-, chloride or iodide ion, silver nitrate forms precipitates such as silver bromide (AgBr), which is extensively studied in precipitation reactions.

Silver nitrate solution has a variety of applications:

• Used in chemical synthesis and analytical chemistry.
• Sterilizing agent due to its antimicrobial properties.
• In photography, particularly in the production of silver-based photographic films.

When it comes to reactions with AgNO_3 , such as adding it to a solution with various anions, we use the solubility product constants to predict which silver salt will form a precipitate first. This is particularly significant in analytical processes where knowledge about precise precipitation points aids in separating and identifying ions.

Solubility Rules

Solubility rules help predict whether a compound will dissolve in water or form a precipitate. These rules are empirical guidelines derived from experimental data and are crucial for chemists working with ionic solutions.
Understanding solubility rules involves knowing which ionic compounds are generally soluble and which are not. For instance:

• **Most nitrate salts ( NO_3^- ) are soluble.**
• **Most salts containing Ag^+ are insoluble, except those of nitrates and acetates.**
• **Common halides (chlorides, bromides, iodides) are soluble, except when paired with Ag^+ , Pb^{2+}, Hg_2^{2+}**.

Utilizing solubility rules can dramatically simplify the prediction of which salts might precipitate in a reaction. They help in understanding which ions will behave as reactants and which as products, thus providing insight into managing reaction pathways effectively during chemical synthesis and separation processes.