How do you calculate limiting reagent and theoretical yield?

You identify the limiting reactant by calculating the moles of product that can be formed from each reactant.

Then you calculate the theoretical yield of product from the amount of the limiting reactant.

EXAMPLE

Aspirin is prepared by the reaction between acetic anhydride and salicylic acid.

##"acetic anhydride + salicylic acid → aspirin + acetic acid"##

##"C"_4"H"_6"O"_3 + "C"_7"H"_7"O"_3 → "C"_9"H"_8"O"_4 + "C"_2"H"_4"O"_2##

##color(white)(mm)"A"color(white)(ml) +color(white)(m) "B"color(white)(mm) →color(white)(mll) "C"color(white)(mll) +color(white)(ml) "D"##

What is the theoretical yield of aspirin (##"C"##) if you reacted 4.32 g of acetic anhydride (##"A"##) with 2.00 g of salicylic acid (##"B"##)?

Solution

The molar masses are

Acetic anhydride = ##"A" = "C"_4"H"_6"O"_3 = "102.1 g/mol"##

Salicylic acid = ##"B" = "C"_7"H"_6"O"_3 = "138.1 g/mol"##

Aspirin = ##"C" = "C"_9"H"_8"O"_4 = "180.2 g/mol"##

Identify the limiting reactant

We calculate the moles of each reactant and then use the molar ratios from the balanced equation to calculate the moles of aspirin.

##"Moles of aspirin from A" = 4.32 cancel("g A") × (1 cancel("mol A"))/(102.1 cancel("g A")) × "1 mol C"/(1cancel("mol A")) = "0.0423 mol C"##

##"Moles of aspirin from B" = 2.00 cancel("g B") × (1 cancel("mol B"))/(138.1 cancel("g B")) × "1 mol C"/(1 cancel("mol B")) = "0.0145 mol C"##

##"B"## gives the smaller amount of aspirin, so ##"B"## is the limiting reactant.

Calculate the theoretical yield

##0.0145 cancel("mol C") × "180.2 g C"/(1 cancel("mol C")) = "2.61 g C"##