Estimate the solubility of TISCN in a solution of which ionic strength is 1.265e-2M at 25 degree and Ksp=1.6e-4.
I do not know why Prof. gives me ionic strength? In the next question, Prof. said " For a sparingly soluble ionic compound of type AB the solubility can be calculated using the following relationship, solubility S= (Ksp) ^(1/2). Si S=(Ksp TISCN) ^(1/2) Give a qualitative explanation for the difference in solubility calculated by both ways. Any help will be greatly appreciated.
what you must do is calculate the solubility of TiSCN as if concn in M is the same as activity. In the other case you want to use ionic strength to calculate activity of Ti and activity of SCN and use that to calculate solubility. Compare the solubility by the two methods.
Thank you DrBob222. My activity of Ti is 0.8661 and SCN is 0.8896. I do not know any equation between activity and solubility. Can you help me with that? Thank you
Note: the first post noted Tl, not Ti.
Ksp = (Tl^+)(SCN^-) and the activity is supposed to be substituted directly; i.e.
Ksp = aTl^+ x aSCN^-. Since you know activity of each(if those numbers are really activities), substitute those and solve for solubility just as you did for the first one.
However, I wonder how you obtained the activity of each without any other date. Since the activity is concn x activity coefficient, I wonder if that 0.8661 and 0.8896 are activity coefficients and not activity. I think they must be activity coefficients. If they are then you do this instead of the above.
Ksp = (Tl^+)(SCN^-)
Ksp = (Tl^+)*0.8661*(SCN^-)*0.8896
Ksp = 0.8661x*0.8896x
and solve for x. If you have further questions please clarify those numbers as to whether they are activities or activity coefficients.
Thank you DrBob222. Yes, 0.8661 and 0.8896 are activity coefficients. That is my bad. Thanks to your suggestion, I already figure out the solubility of TISCN is 0.01425. Besides, the solubility would be 0.01265 if I applied the formula S=Ksp ^(1/2). What makes the big difference between these two numbers? The error between them are kind of big
That's exactly right and I agree with both of the values you have. The profs purpose in assigning a problem like this is to illustrate just how much the solubility increases when one takes into account the activity coefficients. You see when you use molarity by itself you are assuming the activity coefficient is 1.00 so that activity = molarity x 1.00. But when the activity coefficient is not 1.00 (and it is hardly ever 1.00 -- ONLY in VERY dilute solutions is it 1.00) then activity = M x fraction less than 1 which makes the activity less than the molarity. You can see from my bold face work above that the effect of the activity coefficent is to increase Ksp.
Note (Ksp/0.8661*0.8896) = x^2 and that increases x. The error is significant in some cases and not so bad in others. The error is ALWAYS worse in more concentrated solutions because the activity coefficient is smaller. And when you divide Ksp by smaller and smaller numbers the result is larger and larger numbers and that increases x = solubility. So why do we almost never use activities and activity coefficients. Mostly because they are very inconvenient and time consuming AND because determining activity coefficients is not all that easy. In addition they change under normal circumstances and that makes it even more inconvenient. So I think we use the simple method and realize it's a close approximation. The difference usually is not this pronounced but the prof chose an example where Ksp is large already and it makes more difference. If you had something like CuS with Ksp way down there in the 10^-45 or so, I don't think you would see very much difference. Glad to be of help.
To estimate the solubility of TISCN in a solution with an ionic strength of 1.265e-2 M at 25 degrees Celsius and a given Ksp value of 1.6e-4, you can follow these steps:
Step 1: Determine the relationship between ionic strength and the solubility of ions in a solution. Ionic strength, denoted as I, is a measure of the concentration of ions in a solution. For a sparingly soluble ionic compound like TISCN, the solubility can be related to the ionic strength using the following equation:
S = (Ksp)^(1/2)
Where S represents the solubility, Ksp is the solubility product constant, and ^(1/2) denotes square root.
Step 2: Calculate the solubility using the ionic strength provided. Substitute the given Ksp value and calculate the solubility using the equation from step 1:
S = (1.6e-4)^(1/2)
S ≈ 1.26e-2 M (rounded to two significant figures)
So, the estimated solubility of TISCN in the given solution is approximately 1.26e-2 M.
Now, let's address your question about the purpose of the ionic strength and the difference in the calculated solubility.
The ionic strength indicates the concentration of all ionic species present in a solution, not just the TISCN compound. It takes into account the contributions of all ions present, including the solvent itself and any other ions from different sources.
In the case of a sparingly soluble ionic compound like TISCN, the solubility is mainly determined by the concentration of TISCN ions. However, the presence of other ions in the solution affects the activity of TISCN ions and thereby influences its solubility.
By including the ionic strength in the calculation, you are considering the impact of all the ions present in the solution, giving a more accurate estimate of the solubility. The solubility product constant (Ksp) represents the equilibrium constant for the dissolution of the compound and does not account for the influence of any other ions present.
Therefore, calculating the solubility using only the Ksp value neglects the effect of ionic strength, which can lead to a less accurate estimation.
In summary, the difference in solubility calculated by the two methods is due to the consideration of ionic strength, which accounts for the influence of all ions present in the solution, rather than solely relying on the solubility product constant. Including the ionic strength gives a more comprehensive understanding of the solubility behavior in a solution.