[Thresh]

Here is my question:  How many grams of La(IO3)3 can be dissolved in 500mL of a 0.100M KIO3 solution at 25degrees C? Use activities in your calculation.                                 IO3- activity=0.80  La3+ activity=0.18.  How would you solve this?

[Thresh]

 This is how I have been trying to solve this problem.
  1.0 * 10^-11 = x [0.18 ](0.775)^3 (0.100 + 3x)^3   I assume that the 3x << 0.1 and
solve without the 3x then go and continue with successive approximations until
the answers of two consecutive trials are the same. I can't seem to get it.  Would my molarity just be the x value?

[Borek]

Why do you want to use iterations? It makes sense if you have to calculate ionic strength and activity coefficients by yourself, but you are given these.

[Thresh]

 Iteration=success of approximation correct? This is the way our professor taught it in lecture. He really stressed this process. I just got the correct answer using this method.

I had to find the activities by myself. Sorry I didn't make that clear.

[Borek]

Iteration=success of approximation correct?

Any process in which result from previous calculation is used as input for the next step is called iteration.

I had to find the activities by myself. Sorry I didn't make that clear.

You have listed them in your original question, it wasn't obvious where you got them from.