There are 11.7 g of ethane and 30.5 g of oxygen that will undergo combustion
If 4.5 mol of ethane, C2H6, undergo combustion according to the unbalanced equation the amount of O2 is the same that amount of ethane.
C2H6 + O2 ----> CO2 + H2O, so it is 4.5 mol of O2
But when it is balanced equation the amount of O2 is next,
C2H6 + 7/2 O2 ----> 2CO2 + 3H2O
4.5 mol* 7/2 = 15.72 mol
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