The Ksp of Ag2CrO4, AgCl, AgBr and AgI are respectively, 1.1 × 10–12, 1.8 × 10–10, 5.0 × 10–13, 8.3 × 10–17. Which one of the following salts will precipitate last if AgNO3 solution is added to the solution containing equal moles of NaCl, NaBr, NaI and Na2CrO4 ?

To determine which silver salt will precipitate last when adding AgNO3 to a solution containing equal moles of NaCl, NaBr, NaI, and Na2CrO4, we first need to understand how precipitation occurs based on the solubility product constant (Ksp). The salts you mentioned, along with their Ksp values, dictate the order in which they will form solid precipitates when silver ions (Ag+) are introduced into the solution.

Understanding Ksp Values

The Ksp, or solubility product constant, indicates how much of a compound can dissolve in water before it starts to precipitate. A lower Ksp value means that the salt is less soluble, meaning it will precipitate out of solution at a lower concentration of ions.

Analyzing the Ksp Values

• Ag2CrO4: Ksp = 1.1 × 10^–12
• AgCl: Ksp = 1.8 × 10^–10
• AgBr: Ksp = 5.0 × 10^–13
• AgI: Ksp = 8.3 × 10^–17

Precipitation Order

When AgNO3 is added to the mixed solution, silver ions will react with the anions to form precipitates. The order of precipitation is determined by the Ksp values, as follows:

Calculating Ion Concentrations for Precipitation

To find out which salt will precipitate last, we can use the Ksp expression for each salt. For a generic salt, the Ksp is given by:

Ksp = [Ag⁺]^m [X^n-]^n

where "X" is the anion. We can rearrange this to find the concentration of Ag⁺ needed for precipitation:

[Ag⁺] = Ksp / [X^n-]^n

Calculating for Each Salt

Assuming equal concentrations of the anions in the solution:

• For Ag2CrO4: [Ag⁺] = 1.1 × 10^–12 / [CrO4^2-]²
• For AgCl: [Ag⁺] = 1.8 × 10^–10 / [Cl^–]
• For AgBr: [Ag⁺] = 5.0 × 10^–13 / [Br^–]
• For AgI: [Ag⁺] = 8.3 × 10^–17 / [I^–]

Determining the Precipitation Sequence

Since we are adding equal moles of NaCl, NaBr, NaI, and Na2CrO4, the anion concentrations will be equal. Therefore, we can compare the Ksp values directly to determine which salt will precipitate last, indicating that it requires the highest concentration of Ag⁺ to start precipitating:

• AgI has the lowest Ksp, which means it will precipitate first.
• Ag2CrO4 has the highest Ksp, meaning it will precipitate last.

Final Decision

Based on the Ksp values and the analysis, Ag2CrO4 will precipitate last when AgNO3 is added to the solution containing equal moles of the four salts. This is because it requires a higher concentration of silver ions to reach its solubility limit compared to the others.