The Ksp for AgI is 8.5 x 10-17.
The Ksp for TlI (thallium iodide) is 5.5 x 10-8.
A one litre solution contains 0.035 mol L-1 Ag+ ion and Tl+ ion.
When TlI begins to precipitate, what percentage of Ag+ remains in the solution?
I assume you are adding I^- drop wise.
(Ag^+)(I^-) = 8.5E-17
(Tl^+)(I^-) = 5.5E-8
Adding I^- drop wise will ppt AgI when (I^-) = Ksp/(Ag^+) = 8.5E-17/0.035 = 2.41E-15 M
AgI will continue pptng until Ksp for TlI is exceeded. That will be when
(I^- ) = Ksp/(Ag^+) = 5.5E-8/0.035 = 1.57E-6. This is the (I^-) when TlI first ppts. What is the (Ag^+) at that point?It is
(Ag^+) = Ksp/(I^-) = 8.5E-17/1.57E-6 = 5.41E-11. That is what is left of the 0.035 mols Ag+ from AgI initially.
% Ag^+ remaining = (5.41E-11/0.035)*100 = ?
Check these numbers carefully for typos etc. My calculator is on the blink.
To determine the percentage of Ag+ that remains in the solution when TlI begins to precipitate, we need to compare the solubility product constants (Ksp) of AgI and TlI. Let's break down the steps to solve this problem:
Step 1: Write the balanced chemical equation:
AgI (s) ⇌ Ag+ (aq) + I- (aq)
TlI (s) ⇌ Tl+ (aq) + I- (aq)
Step 2: Determine the maximum concentrations of Ag+ and Tl+ ions in the solution when TlI begins to precipitate.
Since AgI has a lower Ksp value, it will start to precipitate before TlI. Let's assume x mol/L of TlI precipitates. This means x mol/L of Tl+ and I- ions are removed from the solution. Consequently, the concentrations of Ag+ and I- ions in the remaining solution will both be equal to 0.035 - x mol/L.
Step 3: Write the expression for the solubility product constant (Ksp) of AgI using the concentrations from step 2:
Ksp = [Ag+][I-]
Substitute the concentrations: Ksp = (0.035 - x)(0.035 - x) = (0.035 - x)^2
Step 4: Solve for x using the Ksp equation:
Ksp for AgI = 8.5 x 10^-17
8.5 x 10^-17 = (0.035 - x)^2
Take the square root of both sides: sqrt(8.5 x 10^-17) = 0.035 - x
0.935 x 10^-8 = 0.035 - x
Rearrange the equation: x = 0.035 - 0.935 x 10^-8
Step 5: Calculate the percentage of Ag+ that remains in the solution:
To find the concentration of Ag+ remaining in the solution, subtract the concentration of Ag+ that precipitated (x) from the initial concentration of Ag+ (0.035 mol/L). Then, divide the result by the initial concentration and multiply by 100 to get the percentage.
Ag+ remaining = (0.035 - x) / 0.035 * 100
Now, substitute the value of x we found in step 4 and perform the calculation:
Ag+ remaining = (0.035 - (0.035 - 0.935 x 10^-8)) / 0.035 * 100
Simplify the equation and calculate the value to determine the percentage of Ag+ that remains in the solution when TlI begins to precipitate.