Question

The solubility product constant, Ksp, for Ag2SO4 is 1.2 x 10-5 at 25o C. Find [Ag ] and [SO4 2-] after 0.755 g of AgNO3 are added to a 500.0 mL saturated solution of Ag2SO4 and equilibrium is established. Assume that the total volume of the solution remains the same and the final temperate is 25o C.

Answer 1

Answer:

[Ag+] = 0.032 M

[SO42-] = 0.0116 M

Explanation:

• AgNO3 ↔       Ag+      +       NO3-

      8.89E-3 M   8.89E-3 M      8.89E-3 M

∴ mass AgNO3 = 0.755 g

∴ mm AgNO3 = 169.87 g/mol

⇒ mol AgNO3 = (0.755 g)(mol /169.87 g) = 4.44 E-3 mol

⇒ M AgNO3 = 4.44 E-3 mol/0.500 L = 8.89 E-3 M

• Ag2SO4 ↔        2Ag+         +     SO42-

           S               2S + 8.89E-3             S

⇒ 1.2 E-5 = (2S + 8.89E-3)²(S)

⇒ 1.2 E-5 = (4S² + 0.036S + 7.903 E-5)(S)

⇒ 1.2 E-5 = 4S³ + 0.036S² + 7.903 E-5S

⇒ S³ + 9 E-3S² + 1.976 E-5S - 3 E-6 = 0

⇒ S = 0.0116 M

⇒ [Ag+] = 2(0.0116) + 8.89 E-3 = 0.032 M

⇒ [SO42-] = S = 0.0116 M