This is NOT an easy question to answer, so I will assist you. The reaction referred to in the question is a redox reaction that takes place in an alkaline battery. I believe the product of the reaction is ZnO, not Zn(OH)2, which is insoluble. Perhaps your teacher is using the first half reaction below and assuming that ZnO + H2O -->Zn(OH)2. The half reactions are:
Zn(s) + 2OH−(aq) ==> ZnO(s) + H2O(l) + 2e−
2MnO2(s) + H2O(l) + 2e− ==> Mn2O3(s) + 2OH−(aq)
The overal reaction is:
Zn(s) + 2MnO2(s) <==> ZnO(s) + Mn2O3(s) This is the balanced equation. Now for calculation of limiting reactant and mass of ZnO. (If you need Zn(OH)2, you'll have to re-submit after being sure that's what is needed).
moles Zn = 17.5 g x 1 mole/ 65.4g = 0.268 moles
moles MnO2 = 27.5 g x 1 mole/86.9 g = 0.316 moles
Limiting reactant = MnO2 since stoichiometric mole ratio is 2 moles MnO2 :1 mole Zn. MnO2 will run out first.
Mass of product produced (either ZnO or Zn(OH)2) will depend on moles MnO2 only.
2 moles MnO2 produces 1 mole of ZnO as determined from the overal reaction.
moles ZnO produced = 0.316 moles MnO2 x 1 mole ZnO/2 moles MnO2 = 0.158 moles ZnO produced
mass ZnO produced = 0.158 moles x 81.4 g/mole = 12.9 grams
NOTE: I think you can follow this approach using Zn(OH)2 as the product, but I'm not sure how that product is arrived at. Unless, as stated in the beginning the ZnO reacts with water to produce Zn(OH)2. Most oxides do react with water to produce the metal hydroxide, so you may want to rework the problem using that approach.
Alexandr K.
02/03/18