If 2.5mL of 0.30M #AgNO_3# is mixed with 7.5mL of 0.015M #Na_2SO_4#, should a precipitate of #Ag_2SO_4# form? (Ksp = #1.2x10^-5#)

Question

Noah Aldrich · Accepted Answer

Quite probably.

Given the following conditions, we must determine the ion product for the following reaction: #2Ag^(+) + SO_4^(2-) rightleftharpoonsAg_2SO_4(s)darr# #Q_"the ion product"=[Ag^+]^2[SO_4^(2-)]# We now need to ascertain each person's concentrations: #[Ag^+]# #=# #(2.5xx10^(-3)*Lxx0.30*mol*L^-1)/((2.5+7.5)xx10^-3L)# #=# #7.50xx10^-2*mol*L^-1#. #[SO_4^(2-)]# #=# #(7.5xx10^(-3)*Lxx0.015*mol*L^-1)/((2.5+7.5)xx10^-3L)# #=# #1.13xx10^-2*mol*L^-1#. #Q_"the ion product"=(7.50xx10^-2)^(2)(1.13xx10^-2) = 6.4xx10^-5#. Since #Q_"the ion product"=6.4xx10^-5>K_"sp"=1.2xx10^-5#, precipitation of silver sulfate should occur until equilibrium is satisfied, and #Q=K_"sp"# I believe the method I used was sound, but we had to add volumes and recalculate concentrations, so please don't trust my math. Temperature was not referred to in this question; we would assume room temperature for #K_"sp"#. At higher temperatures, how would you expect #K_"sp"# to evolve? Would solubility of silver sulfate increase or decrease?

Cooper Anderson · Answer

undefined Yes, a precipitate of Ag2SO4 should form as the ion product exceeds the Ksp for Ag2SO4 (1.2x10^-5). The ion product for the given concentrations is 3.375x10^-5.