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Answer 1 · 2017-05-15T17:32:56

#0.246"mol of H"_2#

To use Dimensional Analysis (the Factor-Label Method), you begin by writing the given quantity over 1:

#(0.123"mol of O"_2)/1#

We observe that two moles of hydrogen are need for 1 mole of oxygen, therefore we multiply by that conversion factor:

#(0.123"mol of O"_2)/1(2"mol of H"_2)/(1"mol of O"_2)#

Please observe how the units cancel:

#(0.123cancel("mol of O"_2))/1(2"mol of H"_2)/(1cancel("mol of O"_2))#

We may stop and perform the multiplication, because the only unit that remain are the desired units:

#(0.123cancel("mol of O"_2))/1(2"mol of H"_2)/(1cancel("mol of O"_2)) = 0.246"mol of H"_2#