You must react 5.3 g H_2 to produce 47 g H_2O.
Step 1. Calculate the moles of H_2O
Moles of H_2O = 47 g H_2O × (1 mol H_2O/18.02 g H_2O) =2.61 mol H_2O
Step 2. Calculate the moles of H_2
Moles of H_2 = 2.61 mol H_2O × (2mol H_2/2 mol H_2O) = 2.61 mol H_2
Step 3. Calculate the mass of H_2
Mass of H_2 = 2.61 mol H_2 × (2.016 g H_2/1 mol H_2) = 5.3 g H_2