Solutions of sodium thiosulfate are used to dissolve unexposed AgBr (Ksp = 5.0 10-13) in the developing process for black-and-white film. What mass of AgBr can dissolve in 1.40 L of 0.425 M Na2S2O3? Ag+ reacts with S2O32- to form a complex ion.
Ag+(aq) + 2 S2O32-(aq)--> Ag(S2O3)23-(aq) K = 2.9 10^13
To determine the mass of AgBr that can dissolve in the given solution, we need to use the solubility product constant (Ksp) and the reaction equation provided.
First, let's write the equation of dissolution for AgBr:
AgBr (s) ⇌ Ag+ (aq) + Br- (aq)
From the equation, we can see that the concentration of Ag+ ions produced by the dissolution of AgBr is the same as the concentration of AgBr that dissolves.
Now, we can use the Ksp expression to relate the concentration of Ag+ ions to the concentration of AgBr:
Ksp = [Ag+][Br-]
Since the concentration of Br- ions is not given, we need to find it using the reaction equation for the complex formation between Ag+ and S2O32- ions:
Ag+ (aq) + 2 S2O32- (aq) → Ag(S2O3)23- (aq)
We can see that the molar ratio between Ag+ and S2O32- is 1:2. Therefore, when the reaction is at equilibrium, the concentration of Ag+ ions is twice that of S2O32- ions:
[Ag+] = 2[S2O32-]
Now, let's substitute this relationship into the Ksp expression:
Ksp = (2[S2O32-])([Br-])
We are given the concentration of Na2S2O3 solution, which contains the S2O32- ions. The concentration of S2O32- is therefore 0.425 M.
Now we can solve for the concentration of Br- using the Ksp value:
Ksp = (2 × S2O32-)([Br-])
5.0 × 10^-13 = (2 × 0.425)([Br-])
Now, solve for [Br-]:
[Br-] = (5.0 × 10^-13)/(0.85)
[Br-] = 5.88 × 10^-13 M
Since the concentration of Br- ions is the same as the concentration of dissolved AgBr, the concentration of AgBr is also 5.88 × 10^-13 M.
Finally, to calculate the mass of AgBr, we need to convert the concentration from moles per liter to grams per liter, and then multiply by the volume of the solution:
Mass of AgBr = (0.425 M) × (1.40 L) × (187.77 g/mol of AgBr)
Mass of AgBr = 112.9 g
Therefore, 112.9 grams of AgBr can dissolve in 1.40 L of 0.425 M Na2S2O3 solution.