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Always with this these types of questions you want to make sure your chemical equation is balanced (the same amount of each element on each side of the arrow). The equation you provided is balanced so we can move on. I always set up dimensional analysis to solve these types of problems. Start with the given amount in the question, set up a mole to mole ratio using your coefficients from your balanced equation, make sure your old unit cancels out and you are left with your wanted unit.
1 mol FeTiO3 x ``= 1 mol TiO2
You already have a balanced chemical equation and the coefficients before each reactant and product tell you the moles of each substance in the reaction.
Ilmenite is FeTiO3 and rutile is TiO2, so for every 4 moles of ilmenite you start with you end up with 4 moles of rutile. In other words, it is a 1:1 ratio, so for each mole of ilmenite, you get 1 mole of rutile plus 1/2 mole of iron oxide.
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