Answer:
Making water by electrolysis occurs in the following balanced reaction:
2H2O ---> 2H2 + O2
Therefore there is a 1-to-1 ratio (really 2-to-2, but that's the same) of moles of water to moles of hydrogen gas in the balanced reaction. Therefore the number of moles of hydrogen made is equal to the number of moles of water electrolyzed.
We must do the calculation using moles, not grams or kilograms. The molecular weight of H2 is 2.016 grams per mole. To find the number of moles of H2 in 1 kilogram:
1000 grams ÷ 2.016 grams/mole = 496.081 moles of H2
Because of the 1-to-1 stoichiometry of the balanced reaction, it requires 496.081 moles of water. The molecular weight of water is 18.015 grams/mole. Therefore 496.081 moles of water will weigh:
18.015 grams/mole x 496.081 moles = 8936.80 grams = 8.9368 kilograms
That is also equal to 8.9368 liters of water (exactly if at 4 °C).
See the Related Questions to the left for more information about how to solve this type of stoichiometry problem.