Quick Question about theory in solving Ksp?

[RoboNerd]

Homework Statement

[/B]
Lead chromate, PbCrO4, is a yellow pigment used in paints. Suppose 0.50 L of a 1.0 x 10-5 M Pb(C2H3O2) and 0.50 L of a 1.0 x 10-3 M K2CrO4 solution are mixed. Calculate the equilibrium concentration of Pb+2 ion remaining in the solution after PbCrO4 precipitates. What is the percentage of Pb+2 remaining in solution after the precipitation has occurred. (The Ksp for PbCrO4 is 1.8 x 10-14)I have a little question regarding theory about how a website solved this problem.

Homework Equations

The solution is here on page 21 of the document.
http://faculty.icc.edu/bcook/chem132NT/acid_base_eq.pdf

The Attempt at a Solution

My question is this: is it really necessary to assume initially that this is a limiting reagent problem and have the reaction of Pb2+ and CrO42- go to completion to form the salt and then do the ICE chart calculation for the solubility, or is it OK if I just go and do the ice chart straight away?

I tried both methods, and both gave the same numerical answer, but which approach is more "legit"?

Thanks in advance.

 

[Bystander]

"ICE?" If you have to use it to satisfy "OC" types, do so. Otherwise, plug it in and grind it out.