Chemistry

Chemistry

Problem

A 250  mL250\;\text{mL} sample of 2.0×10−5  M2.0\times10^{-5}\;\text{M} AgNO3\mathrm{AgNO_3} is to be treated with solid NaCl\mathrm{NaCl} to produce the first trace of AgCl\mathrm{AgCl} precipitate at 25∘C25^\circ\text{C}. Ignoring any change in volume, what mass of NaCl\mathrm{NaCl} (in mg) must be added? (Ksp(AgCl)=1.8×10−10K_{sp}(\mathrm{AgCl})=1.8\times10^{-10}; molar mass NaCl=58.44  g mol−1\mathrm{NaCl}=58.44\;\text{g mol}^{-1}) a) 0.20 mg0.20\ \text{mg} b) 1.3 mg1.3\ \text{mg} c) 0.13 mg0.13\ \text{mg} d) 0.013 mg0.013\ \text{mg}
Intuitive explanation

The key is recognizing that "first trace of precipitate" means you've reached the solubility product threshold—the point where [Ag+][Cl−]=Ksp[Ag^+][Cl^-] = K_{sp}. Since you know the initial [Ag+][Ag^+] and KspK_{sp}, you can calculate the exact [Cl−][Cl^-] needed to trigger precipitation. Then convert that concentration to the moles and mass of NaCl\mathrm{NaCl} required, using the solution volume.

Intuitive explanation

The key is recognizing that "first trace of precipitate" means you've reached the solubility product threshold—the point where [Ag+][Cl−]=Ksp[Ag^+][Cl^-] = K_{sp}. Since you know the initial [Ag+][Ag^+] and KspK_{sp}, you can calculate the exact [Cl−][Cl^-] needed to trigger precipitation. Then convert that concentration to the moles and mass of NaCl\mathrm{NaCl} required, using the solution volume.

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