Redox Titration Confusion

[mdk2]

I am a bit confused about a question in my textbook involving redox titrations. This is actually a sample problem that has been fully worked through in the book, so I am not trying to get its answer. However, I am confused about one particular step. Here is the question:

A group of students prepares to standardize a Na₂S₂O₃ solution. 32 mL of the Na₂S₂O₃ solution is titrated into 50 mL of a 0.01 M KIO₃ solution to reach the equivalence point. They first titrate the KIO₃solution until it loses color, then add a starch indicator until the reaction is complete. The reaction proceeds in these two steps:

IO₃^-+ I^-+ H⁺ ----->   I₃^-+ H₂O

I₃^-+ S₂O₃^2-  -----> I^-+ S₄O₆^2-

Determine the concentration of the sodium thiosulfate solution at the beginning of the experiment.##

 

I think I understand the basic logic here: We know that when we titrate a 32 mL solution of Na₂S₂O₃  (unknown concentration) into 50 mL of 0.01 M KIO₃ , we reach the equivalence point. To find the concentration of Na₂S₂O_{3 ,} we find the total number of moles IO₃ at the equivalence point and then multiply it by the stoichiometric ratios to find the total moles of Na₂S₂O₃ and then divide by the volume of Na₂S₂O_3.

I realize that the two reactions must be balanced. The textbook notes that it is essential that students not fall into the trap of balancing the first equation as follows: 

IO₃^-+ 2I^-+ 6H⁺  -----> I₃^-+ 3H₂O

I realize that this wrong because the charges don't add up correctly. However, the textbook just follows this up by telling us the correct balance: 

IO₃^-+ 8I^-+ 6H⁺  -----> 3I₃^-+ 3H₂O.            and

I₃^-+ 2S₂O₃^2-  -----> 3I^-+ S₄O₆^2-     

What I don't understand is how we are supposed to figure out how to achieve this balance. I find myself trying to keep track of two different sets of variables (the stoichiometric balance and the charge balance) and can't conceive of a strategy for doing so that makes any sense. 

I have a two part question. First, generally speaking, is there a strategy/approach for achieving this balance? In stoichiometric atom balancing, we generally save Hs to last, for example. Is there a roadmap one can apply for balancing when we have to balance atoms and charges? 

And second, this question follows shortly after the textbook's discussion of balancing half reactions. However, I am struggling to see how this reaction links to half-reactions. Are the two equations above half reactions? Should I be balancing them as half reactions? (E.g. adding water to balance Os, adding H+s to balance Hs?) Or is that not at all the way I should be thinking about this?

So, in sum, I am trying to figure out (a) how to keep track of balancing atoms and charges, (b) whether balancing the half-reactions is the answer, (c) if so, how, and (d) if not, what in the world half reactions have to do with any of this! 

Thank you so much!

(PS: I know that the answer to this problem is 0.094 M -- I promise I'm not trying to get the answer! Just trying to understand the process!)

 

 

Edited May 1, 2020 by mdk2