Balanced equation
#"4 Al(s) + 3O"_2("g")"##rarr##"2Al"_2"O"_3("s")#
This is a limiting reagent question. We need to determine the mass of aluminum oxide #("Al"_2"O"_3")# the given mass of each reactant can produce. The maximum mass of aluminum oxide that can be produced is the amount the limiting reagent can produce.
Mass of aluminum oxide produced by 30.4 g Al
Determine moles Al by dividing its given mass by its molar mass #("26.982 g/mol")#. Since molar mass is a fraction #("g"/"mol")#, we can divide by multiplying by the reciprocal of the molar mass #("mol"/"g")#.
#30.4color(red)cancel(color(black)("g Al"))xx(1"mol Al")/(26.982color(red)cancel(color(black)("g Al")))="1.1267 mol Al"#
(I am leaving some extra digits to reduce rounding errors. The final answer will be rounded to three significant figures.)
Determine moles #"Al"_2"O"_3"# by multiplying mol Al by the mol ratio between #"Al"_2"O"_3"# and #"O"_2"# in the balanced equation. Make sure #"Al"_2"O"_3"# is in the numerator.
#1.1267color(red)cancel(color(black)("mol Al"))xx(2"mol Al"_2"O"_3)/(4color(red)cancel(color(black)("mol Al")))="0.56335 mol Al"_2"SO"_3#
Multiply mol #"Al"_2"O"_3"# by its molar mass #("101.961 g/mol")#.
#0.56335color(red)cancel(color(black)("mol Al"_2"O"3))xx(101.961"g Al"_2"O"_3)/(1color(red)cancel(color(black)("mol Al"_2"O"_3)))="57.4 g Al"_2"O"_3"# (rounded to three significant figures)
#"30.4 g Al"# will produce #"57.4 g Al"_2"O"_3"#
Mass of aluminum oxide produced by 30.4 g oxygen gas
We can put all three steps into one equation.
#30.4color(red)cancel(color(black)("g O"_2))xx(1color(red)cancel(color(black)("mol O"_2)))/(31.998color(red)cancel(color(black)("g O"_2)))xx(2color(red)cancel(color(black)("mol Al"_2"O"_3)))/(3color(red)cancel(color(black)("mol O"_2)))xx(101.961"g Al"_2"O"_3)/(1color(red)cancel(color(black)("mol Al"_2"O"_3)))="64.6 g Al"_2"O"_3"# (rounded to three significant figures)
#"30.4 g O"_2"# will produce #"64.6 g Al"_2"O"_3"#.
The limiting reagent is aluminum, and the maximum amount of aluminum oxide that can be produced in this reaction is #"57.4 g"#,
