Mole Ratio Stoichiometry

Q.
How many moles of hydrogen gas are produced when 0.1 moles of sodium reacts with 0.1 moles of water?
[2Na(s) + 2H2O (l)>>>> H2(g) + 2NaOH(aq)]?
A.
2 moles of Na react with 2 moles of H2O, producing 1 mole of H2 as the chemical equation shows.
Based on the coefficients of the chemical equation, the ratio of (2 : 2 : 1) is the same as
(1 : 1 : 0.5) or (0.1 : 0.1 : 05)
2Na + 2H2O ---> H2 + 2NaOH
1Na + 1H2O ---> 0.5H2 + 1NaOH
0.1Na + 0.1H2O --->0.05H2 + 0.1NaOH

All three chemical equations show the same ratio with different coefficients. The last one has the answer to your question.
A more formal solution using “conversion factors” is:

(0.1 mole Na)(1 mol H2 / 2 mol Na) = 0.05 mol H2
or
(0.1 mole H2O)(1 mol H2 / 2 mol H2O) = 0.05 mol H2

If the last two solutions were not the same, you should have taken the smaller one since that one is automatically based on the “limiting reagent”. In this case both calculation both solutions give the same answer since Na and H2O are used at the same ratio as the one shown in the chemical equation.
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