Sodium sulfate is slowly added to a solution containing 0.0500 M Ca^2+ (aq) and 0.0390 M Ag^+ (aq). What will be the concentration of Ca^2+ (aq) when Ag2SO4(s) begins to precipitate?
What percentage of the Ca^2+ (aq) can be separated from the Ag^+ (aq) by selective precipitation?
ksp for CaSO4 is 4.93*10^-5
ksp for Ag2SO4 is 1.20*10^-5
The concentration of Ca^2+ is 9.86*10^-4. Is this correct?
How do you find the percentage?
No although you got part way home with that answer. I do the following.
Ksp CaSO4 = (Ca^2+)(SO4^2-) = 4.93E-5
What must SO4 be to ppt CaSO4?
(SO4^2-) = (4.93E-5/0.05) = 9.86E-4M.
Ksp Ag2SO4 = (Ag^+)^2(SO4^2-) = 1.2E-5
What must SO4 be to ppt Ag2SO4. That's
(SO4^2-) = [1.2E-5/(0.039)^2] = 7.89E-3 M.
Now this is where the chemical reasoning comes in.
If you have a solution as described in the problem and you add tiny crystals of Na2SO4 (or liquid) a bit at a time, the first salt that exceeds Ksp will ppt first. The above calculation shows CaSO4 requires LESS SO4 than Ag2SO4; therefore, CaSO4 will start pptng first and it will continue pptng as more Na2SO4 is added UNTIL Ksp for Ag2SO4 is exceeded. When will that occur? When the SO4 gets up to where? 7.89E-3 of course. (That's the point at which Ag^2)^2(SO4^2-) > 1.2E-3. So we take 7.89E-3, plug that into CaSO4 Ksp for SO4 and solve for (Ca^2+). Check my work but I obtained about 0.006 and that's approximate at that. That's the answer to part a.
b. Therefore you can obtain pure CaSO4 until Ksp for Ag2SO4 is exceeded but not after that. At that point, you start getting the two mixed sulfates. At that point, Ca^2+ = 0.006M, you had 0.05 to start so you must have pptd 0.05-0.006 = about (remember this is approximate) 0.044. Percent recovery = about (0.044/0.05)*100 = ? about a little less than 90%.
Well, let's calculate it step by step, shall we?
First, we need to find out the concentration of sulfate ions (SO4^2-) in the solution. Since sodium sulfate dissociates completely into two sulfate ions, the concentration of sulfate ions will be equal to the concentration of sodium sulfate added.
Now, let's find the initial concentrations of Ca^2+ and Ag^+ ions in the solution. We know that they are 0.0500 M and 0.0390 M, respectively.
Now, when Ag2SO4(s) precipitates, it will consume 2 moles of Ag^+ ions for every 1 mole of SO4^2- ions. So, if 'x' moles of SO4^2- ions react, '2x' moles of Ag^+ ions will be consumed.
The remaining concentrations of Ca^2+ and Ag^+ ions will be 0.0500 - x and 0.0390 - 2x, respectively.
At the point of precipitation, the concentrations of Ca^2+ and SO4^2- ions will be equal to the solubility product constant (Ksp) of CaSO4.
So, for Ca^2+ ions, we have (0.0500 - x)(x) = 4.93x10^-5
Solving this equation will give us the value of 'x' which represents the concentration of SO4^2- ions, and thus the concentration of Ca^2+ ions when precipitation starts.
Now, let's calculate the percentage of Ca^2+ ions that can be separated from Ag^+ ions by selective precipitation.
The initial concentration of Ca^2+ ions is 0.0500 M, and the concentration when precipitation begins is determined as above.
The percentage of Ca^2+ ions that can be separated is given by:
(Initial conc. - conc. when precipitation begins) / Initial conc. * 100
So, we can substitute the values into the equation and calculate the percentage.
Hope that clarifies things! If you need any further assistance, feel free to ask!
To determine the concentration of Ca^2+ when Ag2SO4 begins to precipitate, we need to compare the solubility product constant (Ksp) values for CaSO4 and Ag2SO4.
1. Write out the balanced chemical equation for the precipitation reaction:
Ca^2+(aq) + SO4^2-(aq) → CaSO4(s)
2. Determine the common ion that affects the solubility of both salts. In this case, it is the sulfate ion (SO4^2-).
3. Find the concentration of the sulfate ion in the solution. It can be calculated by multiplying the molarity of sodium sulfate (Na2SO4) by the ratio of sulfate ions in the compound. Since Na2SO4 dissociates into 2 Na+ ions and 1 SO4^2- ion, the concentration of the sulfate ion is (0.0500 M Sodium sulfate) * (1 SO4^2- / 2 Na+).
Concentration of SO4^2- = (0.0500 M) * (1 / 2) = 0.0250 M
4. Compare the ion product (Qsp) with the solubility product constant (Ksp) values to determine if precipitation will occur.
Qsp = [Ca^2+][SO4^2-] = (0.0500 M Ca^2+)(0.0250 M SO4^2-) = 1.25 * 10^-3
For Ag2SO4 to begin precipitating, Qsp must exceed the Ksp of Ag2SO4 but be less than or equal to the Ksp of CaSO4.
Ksp(Ag2SO4) = 1.20 * 10^-5
Ksp(CaSO4) = 4.93 * 10^-5
Therefore, precipitation occurs when Qsp > Ksp(Ag2SO4) and Qsp <= Ksp(CaSO4).
1.20 * 10^-5 < 1.25 * 10^-3 <= 4.93 * 10^-5
So, Ag2SO4 will precipitate when [Ca^2+] reaches a concentration of 1.25 * 10^-3 M.
To find the percentage of Ca^2+ that can be separated from Ag^+, we need to determine the ratio of moles of Ca^2+ to moles of Ag^+ using the balanced equation.
1 mole of Ca^2+ reacts with 1 mole of SO4^2- to form 1 mole of CaSO4 (s), and 2 moles of Ag^+ react with 1 mole of SO4^2- to form 1 mole of Ag2SO4 (s).
So, the ratio of moles of Ca^2+ to Ag^+ is 1:2.
If we assume that all the Ca^2+ present before precipitation can be separated, the percentage of Ca^2+ that can be separated is given by:
Percentage of Ca^2+ separated = (1/3) * 100 = 33.33% (rounded to two decimal places)
Therefore, you cannot separate 100% of the Ca^2+ from the Ag^+ by selective precipitation.
Lastly, the concentration of Ca^2+ you provided (9.86 * 10^-4 M) is not correct. To find the concentration of Ca^2+ when Ag2SO4 begins to precipitate, you need to follow the steps outlined above.
To determine the concentration of Ca^2+ when Ag2SO4(s) begins to precipitate, we need to determine the solubility product (Ksp) for Ag2SO4 and compare it to the concentrations of Ca^2+ and Ag^+ ions in the solution.
1. Write the balanced chemical equation for the precipitation reaction:
Ca^2+(aq) + SO4^2-(aq) -> CaSO4(s)
2. Use the given Ksp values to calculate the equilibrium concentrations of Ca^2+ and SO4^2- ions when Ag2SO4(s) begins to precipitate.
For Ag2SO4:
Ksp = [Ag^+]^2 * [SO4^2-]
1.20*10^-5 = (0.0390)^2 * [SO4^2-]
[SO4^2-] = (1.20*10^-5) / (0.0390)^2
3. Since the molar ratio of Ca^2+ to SO4^2- in the balanced equation is 1:1, the concentration of Ca^2+ when Ag2SO4 begins to precipitate will be equal to [SO4^2-], i.e., (1.20*10^-5) / (0.0390)^2.
Now, to find the percentage of Ca^2+ that can be separated from Ag^+ by selective precipitation, we need to determine the maximum amount of Ca^2+ that can remain in solution when Ag2SO4 precipitates.
4. Calculate the initial concentration of Ca^2+:
Given the concentration of Ca^2+ = 0.0500 M
5. Subtract the concentration of Ca^2+ at the point of precipitation from the initial concentration:
Ca^2+ remaining in solution = Initial concentration - Concentration when Ag2SO4(s) begins to precipitate
Finally, to find the percentage:
6. Calculate the percentage remaining by dividing the remaining concentration of Ca^2+ by the initial concentration and multiplying by 100:
Percentage remaining = (Ca^2+ remaining in solution / Initial concentration) * 100
You mentioned that the concentration of Ca^2+ is 9.86*10^-4, but without the initial concentration, it is not possible to determine the percentage remaining.
Please provide the initial concentration of Ca^2+ in order to find the percentage.