Starting with 200 mg of cyclopentadiene, 300 mg of maleic anhydride and 375 mg of cycloadduct anhydride is obtained, what is the limiting reagent? Calculate the % yield for the anhydride.

Question

Starting with 200 mg of cyclopentadiene, 300 mg of maleic anhydride and 375 mg of cycloadduct anhydride is obtained, what is the limiting reagent?  Calculate the % yield for the anhydride.

Ella Allen · Accepted Answer

A Diels-Alder reaction (or a [4+2]cycloaddition reaction) yields a cycloaddition product---the cycloadduct anhydride. The stoichiometric coefficients are all 1:1:1. You can read up on the Diels-Alder reaction here and see the mechanism at the top:
https://tutor.hix.ai From there, the mechanism is very similar to any other Diels-Alder reaction. The challenge is really the visualization of it during the bond formation.  I've discussed this particular reaction in detail here if you wish to understand more about why the endo product is the major product under mild conditions:
https://tutor.hix.ai The molar masses are: #"MM"_"Cyclopentadiene" = 5*12.011 + 6*1.0079 = "66.1024 g/mol"# #"MM"_"Maleic anhydride" = 4*12.011 + 3*15.999 + 2*1.0079 = "98.0568 g/mol"# #"MM"_"Product" = 9*12.011 + 3*15.999 + 8*1.0079 = "164.1592 g/mol"# The masses we have in #"mol"#s are therefore: #"n"_"Cyclopentadiene" = "0.200" cancel"g"xx "1 mol"/("66.1024" cancel"g") = "0.00303 mols"# #"n"_"Maleic anhydride" = "0.300" cancel"g"xx "1 mol"/("98.0568" cancel"g") = "0.00306 mols"# #"n"_"Product" = "0.375" cancel"g"xx "1 mol"/("164.1592" cancel"g") = "0.00228 mols"# Therefore, we know that: Therefore, the percent yield is #"0.00228 mols"/"0.00303 mols" = color(blue)("75.5% yield")#

Paisley Boney · Answer

undefined To determine the limiting reagent, we need to compare the amount of product obtained from each reactant.

Given:
- Cyclopentadiene (Cp): 200 mg
- Maleic anhydride (MA): 300 mg
- Cycloadduct anhydride: 375 mg

From the reaction, one molecule of cyclopentadiene reacts with one molecule of maleic anhydride to produce one molecule of the cycloadduct anhydride.

1. Calculate the theoretical yield of the cycloadduct anhydride from each reactant:

From cyclopentadiene:
Theoretical yield = (molar mass of cycloadduct anhydride / molar mass of cyclopentadiene) * mass of cyclopentadiene
= (375 mg / 1 mole) * (1 mole / 1 mole) * (200 mg / 66.04 mg/mol)
= 601.2 mg

From maleic anhydride:
Theoretical yield = (molar mass of cycloadduct anhydride / molar mass of maleic anhydride) * mass of maleic anhydride
= (375 mg / 1 mole) * (1 mole / 1 mole) * (300 mg / 98.06 mg/mol)
= 1146.0 mg

2. Compare the theoretical yields:

Theoretical yield from cyclopentadiene = 601.2 mg
Theoretical yield from maleic anhydride = 1146.0 mg

Since the theoretical yield from maleic anhydride is higher, it is the limiting reagent.

3. Calculate the percent yield:

Actual yield = mass of cycloadduct anhydride obtained = 375 mg

Percent yield = (actual yield / theoretical yield from limiting reagent) * 100%
= (375 mg / 1146.0 mg) * 100%
= 32.7%