# Question 19e95

Jan 25, 2014

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

#### Explanation:

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.

$\text{acetic anhydride + salicylic acid → aspirin + acetic acid}$

${\text{C"_4"H"_6"O"_3 + "C"_7"H"_7"O"_3 → "C"_9"H"_8"O"_4 + "C"_2"H"_4"O}}_{2}$

$\textcolor{w h i t e}{m m} \text{A"color(white)(ml) +color(white)(m) "B"color(white)(mm) →color(white)(mll) "C"color(white)(mll) +color(white)(ml) "D}$

What is the theoretical yield of aspirin ($\text{C}$) if you reacted 4.32 g of acetic anhydride ($\text{A}$) with 2.00 g of salicylic acid ($\text{B}$)?

Solution

The molar masses are

Acetic anhydride = $\text{A" = "C"_4"H"_6"O"_3 = "102.1 g/mol}$

Salicylic acid = $\text{B" = "C"_7"H"_6"O"_3 = "138.1 g/mol}$

Aspirin = $\text{C" = "C"_9"H"_8"O"_4 = "180.2 g/mol}$

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.

$\text{Moles of aspirin from A" = 4.32 cancel("g A") × (1 cancel("mol A"))/(102.1 cancel("g A")) × "1 mol C"/(1cancel("mol A")) = "0.0423 mol C}$

$\text{Moles of aspirin from B" = 2.00 cancel("g B") × (1 cancel("mol B"))/(138.1 cancel("g B")) × "1 mol C"/(1 cancel("mol B")) = "0.0145 mol C}$

$\text{B}$ gives the smaller amount of aspirin, so $\text{B}$ 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"#