Chemistry question

Question

A solution is made by combining 75.0 mL of 0.0040 M Na2SO4 and 25.0 mL of 0.080 M AgNO3. Calculate the final concentrations of all four ions in solution. The Ksp of Ag2SO4 is 1.5 x 10^-5.

Answer 1

The balanced equation:

2AgNO3 (aq)+ Na2SO4 (aq) -----> 2Ag2SO4 (s) + 2Na²⁺⁽aq) + 2(NO3)^1- (aq)

The total volume after combining the solutions is 100 mL (0.1 L). The number of moles of AgNO3 is 0.080 moles/L x 25/1000 = 0.002 moles. The number of moles of Na2SO4 is 0.0040 moles /L x 75/1000 = 0.0001 moles. 

Since every mole of Na2SO4 produces 2 moles of Na2+ ions, the concentration of Na2+ will be

2 x 0.0001moles x 1000 mL/L /100mL = 0.002 M.

Since 2 moles of AgNO3 produces 2 moles of (NO3)^1- ions, the moles of (NO3)^1- will be equal to the initial number of moles of  AgNO3. Therefore, the final concentration of (NO3)^1- ions will be

0.002 moles x 1000 mL/L / 100 mL = 0.02 M.

As Ag2SO4 is only slightly soluble, it dissociates as Ag2SO4 -à 2Ag¹⁺ + SO4^2- and obeys the equation Ksp = [Ag1+]² [SO4^2-]. Let X be the concentration of SO4^2- ions, then 2X is the concentration of Ag¹⁺ ions. Substituting into the Ksp equation yields (2X)² x X = 1.5 x 10^-5.

4X² x X = 4 X³ = 1.5 x 10^-5.

X = {(1.5 x 10^-5)/4}^1/3. X is the cube root of {(1.5 x 10^-5)/4} = 1.6 x 10^-2 M = SO4^2- concentration, and 3.2 x 10^-2 = Ag¹⁺ concentration. (2 sig figs)

The balanced equation:

2AgNO3 (aq)+ Na2SO4 (aq) -----à 2Ag2SO4 (s) + 2Na²⁺⁽aq) + 2(NO3)^1- (aq)

The total volume after combining the solutions is 100 mL (0.1 L). The number of moles of AgNO3 is 0.080 moles/L x 25/1000 = 0.002 moles. The number of moles of Na2SO4 is 0.0040 moles /L x 75/1000 = 0.0001 moles. 

Since every mole of Na2SO4 produces 2 moles of Na2+ ions, the concentration of Na2+ will be

2 x 0.0001moles x 1000 mL/L /100mL = 0.002 M.

Since 2 moles of AgNO3 produces 2 moles of (NO3)^1- ions, the moles of (NO3)^1- will be equal to the initial number of moles of  AgNO3. Therefore, the final concentration of (NO3)^1- ions will be

0.002 moles x 1000 mL/L / 100 mL = 0.02 M.

As Ag2SO4 is only slightly soluble, it dissociates as Ag2SO4 -à 2Ag¹⁺ + SO4^2- and obeys the equation Ksp = [Ag1+]² [SO4^2-]. Let X be the concentration of SO4^2- ions, then 2X is the concentration of Ag¹⁺ ions. Substituting into the Ksp equation yields (2X)² x X = 1.5 x 10^-5.

4X² x X = 4 X³ = 1.5 x 10^-5.

X = {(1.5 x 10^-5)/4}^1/3. X is the cube root of {(1.5 x 10^-5)/4} = 1.6 x 10^-2 M = SO4^2- concentration, and 3.2 x 10^-2 = Ag¹⁺ concentration. (2 sig figs)

Please check all math.