A solution contains three anions with the following concentrations: 0.20 M CrO4^2-, 0.10 M CO3^2-, and 0.010 M Cl-. If a dilute AgNO3 solution is slowly added to the solution, what is the first compound to precipitate: Ag2CrO4 (Ksp = 1.2 * 10^-12), Ag2CO3 (Ksp = 8.1 * 10^-12), or AgCl (Ksp = 1.8 * 10^-10)?

Verified step by step guidance

Step 1: Identify the relevant chemical reactions for the precipitation of each compound: Ag2CrO4, Ag2CO3, and AgCl. Write the balanced equations for each reaction.

Step 2: Use the solubility product constant (Ksp) expressions for each compound to determine the concentration of Ag+ required to initiate precipitation. For example, for Ag2CrO4, the Ksp expression is Ksp = [Ag+]^2[CrO4^2-].

Step 3: Calculate the minimum concentration of Ag+ needed to start precipitation for each compound using the given Ksp values and the initial concentrations of the anions. Rearrange the Ksp expression to solve for [Ag+].

Step 4: Compare the calculated [Ag+] values for each compound. The compound with the lowest [Ag+] required for precipitation will be the first to precipitate.

Step 5: Conclude which compound precipitates first based on the comparison of the [Ag+] values calculated in the previous step.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the solubility of ionic compounds. It quantifies the extent to which a compound can dissolve in water, expressed as the product of the molar concentrations of its ions, each raised to the power of their coefficients in the balanced equation. A lower Ksp value indicates a less soluble compound, which is crucial for predicting which compound will precipitate first when ions are added to a solution.

Precipitation Reaction

A precipitation reaction occurs when two soluble salts react in solution to form an insoluble compound, or precipitate. This process is driven by the formation of a solid that is less soluble than the ions in solution. In the context of the question, as AgNO3 is added, silver ions (Ag+) will react with the anions present to form precipitates, and the order of precipitation depends on the Ksp values of the resulting compounds.

Ion Product (Q)

The ion product (Q) is a measure of the current concentration of ions in solution compared to the Ksp of a compound. It is calculated similarly to Ksp but uses the actual concentrations of the ions present at any given moment. When Q exceeds Ksp for a particular compound, precipitation occurs. In this scenario, calculating Q for each potential precipitate as AgNO3 is added will help determine which compound precipitates first.

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