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Chemistry Question 56 – JEE-MAIN 2025

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If equal volumes of AB2 and XY (both are salts) aqueous solutions are mixed, which of the following combination will give a precipitate of AY2 at 300 K ? (Given Ksp (at 300 K) for AY2=5.2×10−7)

A precipitate forms when the ion product (Qsp) exceeds the solubility product constant (Ksp).

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Ninja Strategy•Order of Magnitude Estimation

Quickly estimate the order of magnitude of Qsp for each option by approximating concentrations to powers of 10 and comparing with Ksp to identify the most plausible answer.

● Video Walkthrough
Step 1: Determine initial ion concentrations after mixing✦ Active

When equal volumes of AB2 and XY solutions are mixed, the concentration of each ion is halved. The relevant ions for AY2 precipitation are A2+ from AB2 and Y− from XY. Let the initial concentrations of AB2 and XY be CAB2 and CXY respectively. After mixing, the concentrations of the ions will be:

[A2+]=CAB22
[Y−]=CXY2
Step 2: Calculate the Ion Product (Qsp) for each option○ Expand

The solubility product expression for AY2 is Ksp=[A2+][Y−]2. We need to calculate the ion product Qsp using the diluted concentrations for each option. Precipitation occurs if Qsp>Ksp.

Qsp=(CAB22)(CXY2)2=CAB2⋅CXY28

Given Ksp=5.2×10−7.

Option 1: CAB2=2.0×10−2 M, CXY=2.0×10−2 M

Qsp=(2.0×10−2)×(2.0×10−2)28=2.0×10−2×4.0×10−48=8.0×10−68=1.0×10−6

Option 2: CAB2=1.5×10−4 M, CXY=1.5×10−3 M

Qsp=(1.5×10−4)×(1.5×10−3)28=1.5×10−4×2.25×10−68=3.375×10−108≈4.2×10−11

Option 3: CAB2=2.0×10−4 M, CXY=0.8×10−3 M

Qsp=(2.0×10−4)×(0.8×10−3)28=2.0×10−4×0.64×10−68=1.28×10−108=1.6×10−11

Option 4: CAB2=3.6×10−3 M, CXY=5.0×10−4 M

Qsp=(3.6×10−3)×(5.0×10−4)28=3.6×10−3×25.0×10−88=90×10−118≈1.1×10−10
💡 Teacher's Secret Hint

Ensure correct handling of exponents and the dilution factor of 8 in the denominator.

Step 3: Compare Qsp with Ksp○ Expand

Compare the calculated Qsp values with the given Ksp=5.2×10−7:

Option 1: Qsp=1.0×10−6. Since 1.0×10−6>5.2×10−7, precipitation will occur.

Option 2: Qsp≈4.2×10−11. Since 4.2×10−11<5.2×10−7, no precipitation.

Option 3: Qsp=1.6×10−11. Since 1.6×10−11<5.2×10−7, no precipitation.

Option 4: Qsp≈1.1×10−10. Since 1.1×10−10<5.2×10−7, no precipitation.

Therefore, only the combination in Option 1 will result in a precipitate of AY2.

💡 Teacher's Secret Hint

Remember that precipitation occurs only when the ion product exceeds the solubility product constant.

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