Question

Will Ag₂SO₄ precipitate when 100 mL of a 0.050 M aqueous AgNO₃ solution is mixed with 10 mL of a 5.0 x 10⁻² M aqueous Na₂SO₄ solution? The Ksp for silver sulfate is 1.4 x 10⁻⁵

O Yes, a precipitate will form.
O No, a precipitate will not form.

Answer 1

The reaction quotient (Q) for the mixture of AgNO3 and Na2SO4 exceeds the Ksp for Ag2SO4, indicating that Ag2SO4 will precipitate from the solution.

option a is the correct

Step-by-step explanation:

To determine whether Ag₂SO₄ will precipitate when a 0.050 M aqueous AgNO₃ solution is mixed with a 5.0 x 10⁻² M aqueous Na₂SO₄ solution, we should calculate the reaction quotient (Q) and compare it with the Ksp for silver sulfate.

First, calculate the final concentrations of Ag+ and SO₄2- ions in the mixed solution. For Ag+ from AgNO₃, the concentration is diluted when mixed with the Na₂SO₄ solution:

Final concentration of Ag+ = Initial concentration x (Initial volume / Final volume) = 0.050 M x (100 mL / 110 mL) ≈ 0.0455 M

For SO₄2- from Na₂SO₄, the dilution is also considered:

Final concentration of SO₄2- = Initial concentration x (Initial volume / Final volume) = 5.0 x 10⁻² M x (10 mL / 110 mL) ≈ 4.545 x 10⁻³ M

The reaction quotient (Q) is calculated as:

Q = [Ag+]2 x [SO₄2-] = (0.0455 M)2 x (4.545 x 10⁻³ M) ≈ 9.4 x 10⁻¶

Since Q (9.4 x 10⁻¶) > Ksp (1.4 x 10⁻µ), Ag₂SO₄ will precipitate, indicating a supersaturated solution has been formed and the silver sulfate precipitates until the equilibrium is established with Q equal to Ksp.