JEE Main · 2025 · Shift-IhardIEQ-088

If equal volumes of AB2 and XY (both are salts) aqueous solutions are mixed, which of the following combination will…

Ionic Equilibrium · Class 11 · JEE Main Previous Year Question

Question

If equal volumes of \ceAB2\ce{AB2} and \ceXY\ce{XY} (both are salts) aqueous solutions are mixed, which of the following combination will give a precipitate of \ceAY2\ce{AY2} at 300 K? (Given KspK_{sp} for \ceAY2=5.2×10−7\ce{AY2} = 5.2 \times 10^{-7})

Options
  1. a

    3.6×10−33.6 \times 10^{-3} M \ceAB2\ce{AB2}, 5.0×10−45.0 \times 10^{-4} M \ceXY\ce{XY}

  2. b

    2.0×10−42.0 \times 10^{-4} M \ceAB2\ce{AB2}, 0.8×10−30.8 \times 10^{-3} M \ceXY\ce{XY}

  3. c

    2.0×10−22.0 \times 10^{-2} M \ceAB2\ce{AB2}, 2.0×10−22.0 \times 10^{-2} M \ceXY\ce{XY}

    ✓
  4. d

    1.5×10−41.5 \times 10^{-4} M \ceAB2\ce{AB2}, 1.5×10−31.5 \times 10^{-3} M \ceXY\ce{XY}

Correct Answerc

2.0×10−22.0 \times 10^{-2} M \ceAB2\ce{AB2}, 2.0×10−22.0 \times 10^{-2} M \ceXY\ce{XY}

Detailed Solution

Step 1 — Dissolution: \ceAY2−>A2++2Y−\ce{AY2 -> A^{2+} + 2Y^-}; Ksp=[\ceA2+][\ceY−]2=5.2×10−7K_{sp} = [\ce{A^{2+}}][\ce{Y^-}]^2 = 5.2 \times 10^{-7}

Precipitation when Qsp>KspQ_{sp} > K_{sp}. Mixing equal volumes halves each concentration.

Step 2 — Check option (c)

[\ceA2+]mix=2.0×10−22=1.0×10−2[\ce{A^{2+}}]_{\text{mix}} = \frac{2.0 \times 10^{-2}}{2} = 1.0 \times 10^{-2} M

[\ceY−]mix=2.0×10−22=1.0×10−2[\ce{Y^-}]_{\text{mix}} = \frac{2.0 \times 10^{-2}}{2} = 1.0 \times 10^{-2} M

Qsp=(10−2)(10−2)2=10−6>5.2×10−7Q_{sp} = (10^{-2})(10^{-2})^2 = 10^{-6} > 5.2 \times 10^{-7} ✓ Precipitation occurs

Step 3 — Verify other options give Qsp<KspQ_{sp} < K_{sp}

(a) Qsp=(1.8×10−3)(2.5×10−4)2=1.1×10−10<KspQ_{sp} = (1.8 \times 10^{-3})(2.5 \times 10^{-4})^2 = 1.1 \times 10^{-10} < K_{sp} ✗

(b) Qsp=(10−4)(4×10−4)2=1.6×10−11<KspQ_{sp} = (10^{-4})(4 \times 10^{-4})^2 = 1.6 \times 10^{-11} < K_{sp} ✗

(d) Qsp=(7.5×10−5)(7.5×10−4)2=4.2×10−11<KspQ_{sp} = (7.5 \times 10^{-5})(7.5 \times 10^{-4})^2 = 4.2 \times 10^{-11} < K_{sp} ✗

Answer: Option (c)

Key Points to Remember:

  • Precipitation: Qsp>KspQ_{sp} > K_{sp}
  • Equal volume mixing halves each concentration
  • For \ceAY2\ce{AY2}: Qsp=[\ceA2+][\ceY−]2Q_{sp} = [\ce{A^{2+}}][\ce{Y^-}]^2

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