In photography, unexposed silver bromide is removed from film by soaking the film in a solution of sodium thiosulfate, Na2S2O3. Silver ion forms a soluble complex with thiosulfate ion, S2O32-, that has the formula Ag(S2O3)23-, and formation of the complex causes the AgBr in the film to dissolve. The Ag(S2O3)23- complex has Kform= 2.0 x 1013. How many grams of AgBr (Ksp= 5.4 x 10-13) will dissolve in 437 mL of 1.50 M Na2S2O3 solution?

Question

In photography, unexposed silver bromide is removed from film by soaking the film in a solution of sodium thiosulfate, Na2S2O3. Silver ion forms a soluble complex with thiosulfate ion, S2O32-, that has the formula Ag(S2O3)23-, and formation of the complex causes the AgBr in the film to dissolve. The Ag(S2O3)23- complex has Kform= 2.0 x 1013. How many grams of AgBr (Ksp= 5.4 x 10-13) will dissolve in 437 mL of 1.50 M Na2S2O3 solution?

Answer 1

To find the grams of AgBr that will dissolve in the Na2S2O3 solution, we need to determine the concentration of AgBr in the solution. This can be done by using the solubility product constant (Ksp) of AgBr and the concentration of Ag(S2O3)23-.

First, we need to set up the balanced equation for the dissolution of AgBr:
AgBr ⇌ Ag+ + Br-

From the equation, we can see that the concentration of Ag+ ions in the solution will be equal to the concentration of Ag(S2O3)23- complex formed. We also know that the concentration of Br- ions will be equal to the concentration of AgBr dissolved.

Next, we can determine the concentration of Ag(S2O3)23- complex in the solution:
[Ag(S2O3)23-] = Kform * [Ag+]^3

Substituting the given values, we have:
[Ag(S2O3)23-] = (2.0 x 10^13) * ([AgBr] / V)^3

We have the volume of the solution (437 mL), which we convert to liters by dividing by 1000:
V = 437 mL / 1000 = 0.437 L

Now, we can substitute the concentration of Ag(S2O3)23- and solve for [AgBr]:
(2.0 x 10^13) * ([AgBr] / (0.437))^3 = [AgBr]

Substituting the value for Ksp (5.4 x 10^-13) for [AgBr], we have:
(2.0 x 10^13) * ([AgBr] / (0.437))^3 = 5.4 x 10^-13

To solve for [AgBr], we rearrange the equation:
([AgBr] / (0.437))^3 = (5.4 x 10^-13) / (2.0 x 10^13)

Taking the cube root of both sides, we have:
[AgBr] / (0.437) = [(5.4 x 10^-13) / (2.0 x 10^13)]^(1/3)

Now, we can solve for [AgBr]:
[AgBr] = ([(5.4 x 10^-13) / (2.0 x 10^13)]^(1/3)) * (0.437)

Calculating this expression will give us the concentration of AgBr in the solution. Finally, we can multiply the concentration by the volume of the solution to obtain the mass of AgBr dissolved.