The first step to this question is finding the balanced chemical reaction.
H₂+1/2O₂⇒H₂O
Then you need to find the limiting reagent by finding the moles of each reactant then finding how much product each amount of reactants will form. The reactant that produces the least amount of product is the limiting reagent.
moles of H₂:
1g/(1g/mol)=1mol
moles of O₂:
10g/32g/mol=0.3125mol
moles of H₂O formed with amount of H₂:
1molH₂x(1molH₂O/1molH₂O)=1molH₂O
moles of H₂O formed with amount of O₂:
0.3125molO₂x(1molH₂O/0.5molO₂)=0.625molH₂O
Since less water is produced with the amount of oxygen given, oxygen is the limiting reagent and the moles of water formed from the oxygen is the moles of H₂O we will use to find the amount of H₂O produced.
0.625molH₂Ox18g/mol=11.25g H₂O