Question

As sodium chloride solution is added to a solution of silver nitrate, a white precipitate forms. Ammonia is added to the mixture and the precipitate dissolves. When potassium bromide solution is then added, a pale yellow precipitate appears. When a solution of sodium thiosulfate is added, the yellow precipitate dissolves. Finally, potassium iodide is added to the solution and a yellow precipitate forms. Write equations for all the changes mentioned above. What conclusions can you draw concerning the sizes of the \(K_{\mathrm{sp}}\) values for \(\mathrm{AgCl}, \mathrm{AgBr}\), and \(\mathrm{AgI}\) ?

Short answer

The reactions involved are as follows: 1. AgNO3 (aq) + NaCl (aq) -> AgCl (s) + NaNO3 (aq) 2. AgCl (s) + 2NH3 (aq) -> [Ag(NH3)2]+ (aq) + Cl- (aq) 3. [Ag(NH3)2]+ (aq) + KBr (aq) -> AgBr (s) + 2NH3 (aq) + K+ (aq) 4. AgBr (s) + 2Na2S2O3 (aq) -> Na3[Ag(S2O3)2] (aq) + NaBr (aq) 5. Na3[Ag(S2O3)2] (aq) + KI (aq) -> AgI (s) + 2K+ (aq) + 2S2O3^2- (aq) + Na+ (aq) Based on the solubility of the precipitates, we can infer the following trend in the Ksp values: \(K_{\mathrm{sp}}(\mathrm{AgI}) < K_{\mathrm{sp}}(\mathrm{AgBr}) < K_{\mathrm{sp}}(\mathrm{AgCl})\)

Step-by-step solution

Identify the Reactions

First, let's identify the reactions happening at each step of the exercise: 1. Sodium chloride (NaCl) solution is added to silver nitrate (AgNO3) solution. 2. Ammonia (NH3) is added to the mixture. 3. Potassium bromide (KBr) solution is added to the mixture. 4. Sodium thiosulfate (Na2S2O3) is added to the mixture. 5. Potassium iodide (KI) is added to the mixture.

Write Equations for Each Reaction

Now let's write the equations for each reaction: 1. AgNO3 (aq) + NaCl (aq) -> AgCl (s) + NaNO3 (aq) 2. AgCl (s) + 2NH3 (aq) -> [Ag(NH3)2]+ (aq) + Cl- (aq) 3. [Ag(NH3)2]+ (aq) + KBr (aq) -> AgBr (s) + 2NH3 (aq) + K+ (aq) 4. AgBr (s) + 2Na2S2O3 (aq) -> Na3[Ag(S2O3)2] (aq) + NaBr (aq) 5. Na3[Ag(S2O3)2] (aq) + KI (aq) -> AgI (s) + 2K+ (aq) + 2S2O3^2- (aq) + Na+ (aq)

Analyze the Precipitates and Ksp Values

Now let's analyze the formation and dissolution of the precipitates: 1. AgCl forms a white precipitate, indicating it has a low solubility in water. The low solubility means that its Ksp value is likely to be small. 2. AgBr forms a pale yellow precipitate, indicating that it is less soluble than AgCl. Based on this observation, its Ksp value is likely to be smaller than that of AgCl. 3. AgI forms a yellow precipitate, but we do not have enough information to directly compare its solubility to that of AgCl or AgBr. However, based on the general trend in the halides, it is likely that AgI has the lowest solubility (smallest Ksp value) among the three. In conclusion, the sizes of the Ksp values for AgCl, AgBr, and AgI can be inferred as: \(K_{\mathrm{sp}}(\mathrm{AgI}) < K_{\mathrm{sp}}(\mathrm{AgBr}) < K_{\mathrm{sp}}(\mathrm{AgCl})\)

Key concepts

Precipitate Formation

When two solutions containing ions that can form an insoluble compound are mixed together, a process called precipitation occurs. Precipitate formation involves the creation of a solid from a solution when the concentration of these ions exceeds their solubility limit. In reaction to this process, the insoluble compound, which is the precipitate, separates from the solution.

This concept was exemplified in the exercise with the addition of sodium chloride to silver nitrate, resulting in the formation of a white precipitate, silver chloride (AgCl). The process can be described as a reaction where the product's solubility is so low that it cannot dissolve in the solvent and thus falls out of the solution as a solid. Precipitation is essential in many areas of chemistry, including qualitative analysis and purification processes.
When ammonia was added, however, the precipitate dissolved, highlighting the distinctive nature of chemical equilibria. Substances like ammonia can shift the equilibrium by forming complexes, which alter the solubility and allow the precipitate to dissolve back into the solution. This is reflected by the production of a complex ion, [Ag(NH3)2]+, when AgCl reacts with ammonia.

Solubility Rules

Solubility rules are guidelines used to predict whether a given ionic compound is soluble in water, and they are crucial for understanding the outcomes of chemical reactions in aqueous solutions. For instance, most nitrates and alkali metal salts are soluble, while many silver salts are not, except when they form complexes, as seen with ammonia in the exercise.

These rules assist in forecasting the occurrence of precipitate formation in a reaction. According to solubility rules, silver chloride (AgCl) is not soluble in water, which is why it precipitated out when sodium chloride was added to silver nitrate. Later, when ammonia was introduced, it interacted with the silver ion, forming a complex ion that is soluble, leading to the dissolution of the precipitate.
Moreover, when evaluating the formation of different silver halides, the rules suggest a decreasing solubility from chloride to bromide to iodide, guiding the expectation regarding the size of their respective Ksp values, and coincides with the observations from the textbook exercise.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions, where the reactants are shown on the left and the products on the right. They provide valuable insights into the stoichiometry of the reactions, indicating the relative amounts of substances involved. For proper understanding and communication, it's essential that these equations be balanced, with the same number of each atom on both sides of the equation.

In the given exercise, a series of balanced chemical equations were written out to describe the sequential reactions occurring in the mixture. These equations grant a clear understanding of the processes, such as the formation and dissolution of precipitates and the eventual reformation of a new precipitate. The careful examination of these equations allows students to deduce the comparative solubility of different compounds by observing the pattern of precipitate formation and dissolution. This is particularly demonstrated in the exercise by the addition of potassium bromide, which led to the formation of sparingly soluble silver bromide (AgBr), and then sodium thiosulfate, which dissolved that precipitate, indicating a complexation reaction. These reactions progress until finally, potassium iodide was added, resulting in the precipitation of the least soluble compound, silver iodide (AgI), according to the solubility rules.