If equal volumes of \(\mathrm{AB}_2\) and XY (both are salts) aqueous solutions are mixed, which of the…

If equal volumes of \(\mathrm{AB}_2\) and XY (both are salts) aqueous solutions are mixed, which of the following combination will give a precipitate of \(\mathrm{AY}_2\) at 300 K ?
(Given \(\mathrm{K}_{\mathrm{sp}}\) (at 300 K) for \(\mathrm{AY}_2=5.2 \times 10^{-7}\))
  1. \(3.6 \times 10^{-3} \mathrm{M}~ \mathrm{AB}_2, 5.0 \times 10^{-4} \mathrm{M}~ \mathrm{XY}\)
  2. \(2.0 \times 10^{-4} \mathrm{M}~ \mathrm{AB}_2, 0.8 \times 10^{-3} \mathrm{M}~ \mathrm{XY}\)
  3. \(2.0 \times 10^{-2} \mathrm{M}~ \mathrm{AB}_2, 2.0 \times 10^{-2} \mathrm{M}~ \mathrm{XY}\)
  4. \(1.5 \times 10^{-4} \mathrm{M}~ \mathrm{AB}_2, 1.5 \times 10^{-3} \mathrm{M}~ \mathrm{XY}\)

Solution

When equal volumes are mixed molarity reduce to half.
For precipitation \(\mathrm{Q}_{\mathrm{SP}}=\left[\mathrm{A}^{+2}\right]\left[\mathrm{Y}^{-}\right]^2 \gt \mathrm{K}_{\mathrm{SP}}\)
(1) \(\mathrm{Q}_{\mathrm{SP}}=\left(1.8 \times 10^{-3}\right)\left(\frac{5}{2} \times 10^{-4}\right)^2 \lt \mathrm{K}_{\mathrm{sP}}\)
(2) \(\mathrm{Q}_{\mathrm{SP}}=\left(10^{-4}\right)\left(0.4 \times 10^{-3}\right)^2 \lt \mathrm{K}_{\mathrm{sp}}\)
(3) \(\mathrm{Q}_{\mathrm{SP}}=\left(10^{-2}\right)\left(10^{-2}\right)^2 \gt \mathrm{K}_{\mathrm{sP}}\)
(4) \(\mathrm{Q}_{\mathrm{SP}}=\left(\frac{1.5}{2} \times 10^{-4}\right)\left(\frac{1.5}{2} \times 10^{-3}\right)^2 \lt \mathrm{K}_{\mathrm{sP}}\)

Asked in: JEE Main 2025 (02 Apr Shift 1)

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