What is the Ksp of a compound A3B2 (molar mass 288 g/mol) that has a solubility of 3.6x10^-17 g/L?
I thought A3B2 dissociates into 3A +2B
so Ksp = (3x^3)(2x^2) = 36x^5
So, Ksp = 36(3.6x10^-17)^5
= 2.18x10^-81.
But that's such a SMALL number so I think I did it wrong. Help please! :)
Maybe it has something to do with they gave the solubility in g/L instead of mol/L.
I thought A3B2 dissociates into 3A +2B
so Ksp = (3x^3)(2x^2) = 36x^5
So, Ksp = 36(3.6x10^-17)^5
= 2.18x10^-81.
But that's such a SMALL number so I think I did it wrong. Help please! :)
Maybe it has something to do with they gave the solubility in g/L instead of mol/L.
-
Yes - it has something to do with the mol/L aspect. But, beyond that, you’ve made an error in the calculation.
Assuming the compound ionizes/ dissociates as you suggested …
A3B2 <=====> 3 A2+ + 2 B3-
… so …
Ksp = [A 2+]^3 [B 3-]^2
The solubility of A2B3 is 3.6 x 10^-17 g/L, which I think comes to 1.25 x 10^-19 mol/L. For every mole of A2B3 that dissolves, we obtain 3 mol A2+ and 3 mol B3-. Therefore, in a saturated solution of A3B2 we have ….
[A 2+] = 3.75 x 10^-19 mol/L
[B 3-] = 2.50 x 10^-19 mol/L
So Ksp = (3.75 x 10^-19 mol/L)^3 x (2.50 x 10^-19 mol/L)^2
= 3.3 x 10^-93 mol^5/L^5
---------------------------
And you thought 2.18x10^-81 was small!!!
Check my calculations: I may have made some careless mistake. But , on the face of it, based on the data you supplied, this would appear to be the value of Ksp. Glancing down the list of Ksp values in the CRC Handbook, the lowest one I can see is 4 x 10^-53, for HgS. Whether this hypothetical A3B2 actually exists, I don’t know. The obvious question I ask myself is, if the solubility is purportedly only 3.6 x 10^-17 g/L, how could anyone ever have measured it? Are you sure the solubility figure is correct?
Anyway, I hope this answer is of some use to you.
Assuming the compound ionizes/ dissociates as you suggested …
A3B2 <=====> 3 A2+ + 2 B3-
… so …
Ksp = [A 2+]^3 [B 3-]^2
The solubility of A2B3 is 3.6 x 10^-17 g/L, which I think comes to 1.25 x 10^-19 mol/L. For every mole of A2B3 that dissolves, we obtain 3 mol A2+ and 3 mol B3-. Therefore, in a saturated solution of A3B2 we have ….
[A 2+] = 3.75 x 10^-19 mol/L
[B 3-] = 2.50 x 10^-19 mol/L
So Ksp = (3.75 x 10^-19 mol/L)^3 x (2.50 x 10^-19 mol/L)^2
= 3.3 x 10^-93 mol^5/L^5
---------------------------
And you thought 2.18x10^-81 was small!!!
Check my calculations: I may have made some careless mistake. But , on the face of it, based on the data you supplied, this would appear to be the value of Ksp. Glancing down the list of Ksp values in the CRC Handbook, the lowest one I can see is 4 x 10^-53, for HgS. Whether this hypothetical A3B2 actually exists, I don’t know. The obvious question I ask myself is, if the solubility is purportedly only 3.6 x 10^-17 g/L, how could anyone ever have measured it? Are you sure the solubility figure is correct?
Anyway, I hope this answer is of some use to you.