To gravimetrically analyze the silver content of a piece of jewelry made from an alloy of Ag and Cu, — Solutions Chemistry Question

STEPS:

1. Understand the goal of gravimetric analysis: The primary objective of gravimetric analysis is to determine the amount or percent mass of a target analyte (in this case, silver, $\text{Ag}^+$) by converting it into a solid precipitate of known chemical composition that can be physically isolated, dried, and weighed.
2. Identify the species present in the mixture: Dissolving the jewelry alloy in nitric acid ($\text{HNO}_3$) yields a homogeneous liquid mixture containing dissolved $\text{Ag}^+(aq)$ and $\text{Cu}^{2+}(aq)$ ions. Because both metals are dissolved, they cannot be physically separated in their current state.
3. Determine the method of chemical separation: To isolate the silver from the copper, you must perform a selective precipitation. This requires introducing a specific precipitating reagent (anion) that reacts to form an insoluble solid with only one of the metal ions, while leaving the other metal ion dissolved in the aqueous solution.
4. Identify a suitable chemical reagent: For instance, adding a source of chloride ions (such as $\text{NaCl}(aq)$ or $\text{HCl}(aq)$) introduces $\text{Cl}^-$ ions into the mixture. Because $\text{AgCl}$ is highly insoluble ($K_{sp} = 1.8 \times 10^{-10}$) and $\text{CuCl}_2$ is highly soluble, the chloride selectively precipitates the silver ions as solid silver chloride:
$$\text{Ag}^+(aq) + \text{Cl}^-(aq) \rightarrow \text{AgCl}(s)$$
5. Formulate the next analytical step: By adding an anion that selectively precipitates only one of the metal ions, the student can then easily filter out the solid $\text{AgCl}$ precipitate, wash it, dry it, and weigh it to calculate the original silver content of the jewelry. This corresponds to Option D.

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WHY_OTHERS_WRONG:

• Option A is incorrect: Centrifugation is a laboratory technique used to separate solid precipitate particles from a liquid supernatant based on density. It is completely ineffective at separating individual dissolved, hydrated ions ($\text{Ag}^+$ and $\text{Cu}^{2+}$) from one another.
• Option B is incorrect: Evaporating the water would cause all dissolved solutes in the solution—both silver nitrate, $\text{AgNO}_3$, and copper(II) nitrate, $\text{Cu(NO}_3)_2$—to crystallize out together as a solid mixture. This does not separate the silver from the copper, making gravimetric determination of the silver content impossible.
• Option C is incorrect: Bringing the pH up to 7.0 by adding a base (like $\text{NaOH}$) introduces hydroxide ions ($\text{OH}^-$). Hydroxide ions are not selective and can react with both metal ions to precipitate a mixture of insoluble silver oxide ($\text{Ag}_2\text{O}$) and copper(II) hydroxide ($\text{Cu(OH)}_2$), which fails to separate the metals.