A solution contains 0.002 M Ag+ and 1.6 x 10-5 M Zn2+, and the ions need to be separated. For this purpose begin mathsize 11px style CO subscript 3 superscript 2 minus end superscript end style is added to the solution so that both Ag2CO3 (Ksp = 8.1 x 10-12) and ZnCO3 (Ksp = 1.0 x 10-10) can precipitate from the solution. What will the concentration of begin mathsize 11px style CO subscript 3 superscript 2 minus end superscript end stylebe just before the first salt starts to precipitate.
Please explain
Well, it seems like this solution has some silver ions (Ag+) and zinc ions (Zn2+) that need to be separated. To do this, CO32- ions are added to the solution to form precipitates of Ag2CO3 and ZnCO3.
The question asks what the concentration of CO32- ions will be just before the first salt starts to precipitate.
Let's start by considering the solubility product constant (Ksp) for each salt. The Ksp for Ag2CO3 is 8.1 x 10-12, and for ZnCO3 it is 1.0 x 10-10.
When a salt precipitates, it means that the concentration of the ions in the solution has reached the point where the product of their concentrations exceeds the solubility product constant.
Since Ag2CO3 has a smaller Ksp than ZnCO3, it will precipitate first. To find the concentration of CO32- ions just before Ag2CO3 starts to precipitate, we can set up an equilibrium expression for Ag2CO3:
[Ag+]^2 * [CO32-] = Ksp
Since the concentration of Ag+ is given as 0.002 M, we can substitute this value into the equation:
(0.002)^2 * [CO32-] = 8.1 x 10-12
Simplifying the equation, we can solve for [CO32-]:
[CO32-] = (8.1 x 10-12) / (0.002)^2
Calculating this, we find [CO32-] to be approximately 2.025 x 10-10 M.
Therefore, just before the first salt (Ag2CO3) starts to precipitate, the concentration of CO32- ions in the solution will be approximately 2.025 x 10-10 M.
Hope this clears things up! Remember, precipitation can be a bit "salt-ty"!
To find the concentration of CO3^2- just before the first salt starts to precipitate, we need to compare the Ksp values for Ag2CO3 and ZnCO3.
First, let's write the balanced equations and the expressions for the Ksp values for both salts:
Ag2CO3 (s) ⇌ 2Ag+ (aq) + CO3^2- (aq)
Ksp(Ag2CO3) = [Ag+]^2[CO3^2-]
ZnCO3 (s) ⇌ Zn^2+ (aq) + CO3^2- (aq)
Ksp(ZnCO3) = [Zn^2+][CO3^2-]
Since both Ag2CO3 and ZnCO3 can precipitate, the concentration of CO3^2- would be the same just before the first salt starts to precipitate.
Let's assume 'x' as the concentration of CO3^2- at equilibrium.
Therefore, the concentration of Ag+ would be x, and the concentration of Zn^2+ would be x as well.
Substituting these values in the expressions for Ksp, we can write:
Ksp(Ag2CO3) = x^2
Ksp(ZnCO3) = x * x = x^2
Since both Ksp values are given, we can set up the following equation:
8.1 x 10^-12 = 1.0 x 10^-10
Simplifying the equation, we get:
x^2 = 1.24 x 10^-2
Taking the square root of both sides:
x = √(1.24 x 10^-2)
x ≈ 0.111 M (rounded to three decimal places)
Therefore, the concentration of CO3^2- just before the first salt starts to precipitate is approximately 0.111 M.
To determine the concentration of CO32- just before the first salt starts to precipitate, we need to compare the solubility product constants (Ksp) of the two salts, Ag2CO3 and ZnCO3, with their initial concentrations in the solution.
The Ksp expression for Ag2CO3 is:
Ag2CO3 ⇌ 2Ag+ + CO32-
The Ksp expression for ZnCO3 is:
ZnCO3 ⇌ Zn2+ + CO32-
Since the ions Ag+ and Zn2+ are already present in the solution, we need to focus on the common ion CO32- to determine its concentration just before the precipitation.
Let's consider two scenarios:
1. Ag2CO3 precipitates first:
In this case, the maximum amount of Ag2CO3 can precipitate from the solution. This means that all the Ag+ ions will react with CO32-, which is equal to 0.002 M.
So, the concentration of CO32- would be 0.002 M.
2. ZnCO3 precipitates first:
In this scenario, the maximum amount of ZnCO3 can precipitate from the solution. This means that all the Zn2+ ions will react with CO32-, which is equal to 1.6 x 10-5 M.
So, the concentration of CO32- would be 1.6 x 10-5 M.
Since we need to find the concentration just before the first salt starts to precipitate, the lower value between the two scenarios is the correct answer. Therefore, the concentration of CO32- just before the first salt starts to precipitate is 1.6 x 10-5 M.
Your post is hard to read because of the "mathsize" and all that follows. Apparently you are trying to communicate carbonate ion which is written as CO3^2-. Technically that isn't right, of course, but everybody understands that the 3 is a subscript and the 2- is a superscript. Anyway, what you have here is a solution of two salts. You want to know what the CO3^2- must be to ppt the first salt. The plan is to calculate (CO3^2-) required to ppt each salt. The one requiring the smallest amount of CO3^2- will be the one that ppts first.
.......................ZnCO3 ==> Zn^2+ + CO3^2-
I......................solid...............0..............0
C.....................solid...............x..............x
E......................solid...............x..............x
Ksp = (Zn^2+)(CO3^2-)
You know Ksp and Zn^2+ from the problem. Calculate (CO3^-); i.e., the minimum amount necessary to ppt the first molecule of ZnCO3.
Now you do the same thing for Ag2CO3. You know (Ag^2+) from the problem. You calculate the minimum amount of CO3^2- needed to start precipitating Ag2CO3. The salt that requires the smallest amount of CO3^2- will be the one that is ready to ppt when the next CO3^2- ion is added.
Post your work if you get stuck.