# 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.

Feb 8, 2016

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://socratic.org/questions/how-does-a-diels-alder-reaction-work

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://socratic.org/questions/why-is-maleic-anhydride-a-good-dienophile

The molar masses are:

$\text{MM"_"Cyclopentadiene" = 5*12.011 + 6*1.0079 = "66.1024 g/mol}$

$\text{MM"_"Maleic anhydride" = 4*12.011 + 3*15.999 + 2*1.0079 = "98.0568 g/mol}$

$\text{MM"_"Product" = 9*12.011 + 3*15.999 + 8*1.0079 = "164.1592 g/mol}$

The masses we have in $\text{mol}$s are therefore:

$\text{n"_"Cyclopentadiene" = "0.200" cancel"g"xx "1 mol"/("66.1024" cancel"g") = "0.00303 mols}$

$\text{n"_"Maleic anhydride" = "0.300" cancel"g"xx "1 mol"/("98.0568" cancel"g") = "0.00306 mols}$

$\text{n"_"Product" = "0.375" cancel"g"xx "1 mol"/("164.1592" cancel"g") = "0.00228 mols}$

Therefore, we know that:

1. Cyclopentadiene is the limiting reagent by a small margin.
2. A 100% theoretical yield should be $\text{0.00303 mols}$ of product since cyclopentadiene gets fully consumed first.
3. The actual yield is $\text{0.00228 mols}$.
4. The percent yield is "Actual"/"Theoretical"xx100%.

Therefore, the percent yield is "0.00228 mols"/"0.00303 mols" = color(blue)("75.5% yield")