Question #27862

You're dealing with a synthesis reaction in which aluminium metal, #"Al"#, reacts with chlorine gas, #"Cl"_2#, to form aluminium chloride, #"AlCl"_3#.

The balanced chemical equation that describes this reaction looks like this

#2"Al"_ ((s)) + color(red)(3)"Cl"_ (2(g)) -> color(blue)(2)"AlCl"_(3(s))#

Notice that you have a #color(red)(3):color(blue)(2)# mole ratio between chlorine gas and aluminium chloride. This tells you that for every #color(red)(3)# moles of chlorine gas that take part in the reaction, the reaction produces #color(blue)(2)# moles of aluminium chloride.

In other words, the reaction will consume #color(red)(3)/color(blue)(2)# times more moles of chlorine gas than the number of moles of aluminium chloride it will produce.

The problem tells you that the reaction produced #3# moles of aluminium chloride. This means that the reaction must have consumed

#3 color(red)(cancel(color(black)("moles AlCl"_3))) * (color(red)(3)color(white)(a)"moles Cl"_2)/(color(blue)(2)color(red)(cancel(color(black)("moles AlCl"_3)))) = color(green)(|bar(ul(color(white)(a/a)"4.5 moles Cl"_2color(white)(a/a)|)))#

As a conclusion, the stoichiometric coefficients listed in the balanced chemical equation can be used as mole ratios between the chemical species that take part in a given reaction.