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#)

1 Answer
Jul 3, 2016

Answer:

Quite probably.

Explanation:

We need to work out the ion product for the following reaction, under the given conditions:

#2Ag^(+) + SO_4^(2-) rightleftharpoonsAg_2SO_4(s)darr#

#Q_"the ion product"=[Ag^+]^2[SO_4^(2-)]#

And now, we must determine the individual 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"#

Please don't trust my arithmetic. The approach I took (I think) was sound; we had to add volumes and recalculate concentrations.

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?