# Question 40c54

Dec 22, 2017

The theoretical yield of glutaric acid is 182 g.

#### Explanation:

Step 1. Calculate the mass of γ-butyrolactone

$\text{Mass" = 105 color(red)(cancel(color(black)("mL"))) × "1.13 g"/(1 color(red)(cancel(color(black)("mL")))) = "118.6 g}$

Step 2. Calculate the moles of ${\text{C"_4"H"_6"O}}_{2}$

The equation for the reaction is

underbrace("C"_4"H"_6"O"_2)_color(red)("γ-butyrolactone") + "KCN" + "2HCl" + "2H"_2"O" → underbrace("C"_5"H"_8"O"_4)_color(red)("glutaric acid") + "NH"_4"Cl" + "KCl"#

${\text{Moles of C"_4"H"_6"O"_2 = 118.6 color(red)(cancel(color(black)("g C"_4"H"_6"O"_2))) × (1 "mol C"_4"H"_6"O"_2)/(86.09 color(red)(cancel(color(black)("g C"_4"H"_6"O"_2)))) = "1.378 mol C"_4"H"_6"O}}_{2}$

Step 3. Calculate the moles of ${\text{C"_5"H"_8"O}}_{4}$

${\text{Moles of C"_5"H"_8"O"_4 = 1.378 color(red)(cancel(color(black)("mol C"_4"H"_6"O"_2))) × (1 "mol C"_5"H"_8"O"_4)/(1 color(red)(cancel(color(black)("mol C"_4"H"_6"O"_2)))) = "1.378 mol C"_5"H"_8"O}}_{4}$

Step 4. Calculate the mass of ${\text{C"_5"H"_8"O}}_{4}$

${\text{Mass of C"_5"H"_8"O"_4 = 1.378 color(red)(cancel(color(black)("mol C"_5"H"_8"O"_4))) × ("132.11 g C"_5"H"_8"O"_4)/(1 color(red)(cancel(color(black)("mol C"_5"H"_8"O"_4)))) = "182 g C"_5"H"_8"O}}_{4}$

The theoretical yield of glutaric acid is 182 g.