JEE Main · 2021 · Shift-IIhardIEQ-057

A solution is 0.1 M in Cl- and 0.001 M in CrO42-. Solid AgNO3 is gradually added to it. [Ksp(AgCl) = 1.7 10-10\ M2;\…

Ionic Equilibrium · Class 11 · JEE Main Previous Year Question

Question

A solution is 0.1 M in Cl−\mathrm{Cl^-} and 0.001 M in CrO42−\mathrm{CrO_4^{2-}}. Solid AgNO3\mathrm{AgNO_3} is gradually added to it.

[Ksp(AgCl)=1.7×10−10 M2; Ksp(Ag2CrO4)=1.9×10−12 M3][K_{sp}(\mathrm{AgCl}) = 1.7 \times 10^{-10}\ \mathrm{M^2};\ K_{sp}(\mathrm{Ag_2CrO_4}) = 1.9 \times 10^{-12}\ \mathrm{M^3}]

Select the correct statement:

Options
  1. a

    AgCl precipitates first because its KspK_{sp} is high

  2. b

    Ag2CrO4\mathrm{Ag_2CrO_4} precipitates first as its KspK_{sp} is low

  3. c

    Ag2CrO4\mathrm{Ag_2CrO_4} precipitates first because the amount of Ag+\mathrm{Ag^+} needed is low

  4. d

    AgCl will precipitate first as the amount of Ag+\mathrm{Ag^+} needed to precipitate is low

    ✓
Correct Answerd

AgCl will precipitate first as the amount of Ag+\mathrm{Ag^+} needed to precipitate is low

Detailed Solution

Step 1 — Find [Ag+][\mathrm{Ag^+}] needed to start precipitation of each:

For AgCl: [Ag+]=Ksp(AgCl)[Cl−]=1.7×10−100.1=1.7×10−9 M[\mathrm{Ag^+}] = \frac{K_{sp}(\mathrm{AgCl})}{[\mathrm{Cl^-}]} = \frac{1.7 \times 10^{-10}}{0.1} = 1.7 \times 10^{-9}\ \mathrm{M}

For Ag2CrO4\mathrm{Ag_2CrO_4}: [Ag+]2=Ksp(Ag2CrO4)[CrO42−]=1.9×10−120.001=1.9×10−9[Ag+]=1.9×10−9≈4.36×10−5 M[\mathrm{Ag^+}]^2 = \frac{K_{sp}(\mathrm{Ag_2CrO_4})}{[\mathrm{CrO_4^{2-}}]} = \frac{1.9 \times 10^{-12}}{0.001} = 1.9 \times 10^{-9} [\mathrm{Ag^+}] = \sqrt{1.9 \times 10^{-9}} \approx 4.36 \times 10^{-5}\ \mathrm{M}

Step 2 — Compare:

  • AgCl needs [Ag+]=1.7×10−9[\mathrm{Ag^+}] = 1.7 \times 10^{-9} M (much smaller)
  • Ag2CrO4\mathrm{Ag_2CrO_4} needs [Ag+]=4.36×10−5[\mathrm{Ag^+}] = 4.36 \times 10^{-5} M (larger)

AgCl precipitates first (needs less Ag+\mathrm{Ag^+})

Answer: Option (4) — AgCl precipitates first

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A solution is 0.1 M in Cl- and 0.001 M in CrO42-. Solid AgNO3 is gradually added to it. [Ksp(AgCl)… (JEE Main 2021) | Canvas Classes