Y
ield calculations are first introduced in General Chemistry, but they are put to serious use when
students begin with Organic Chemistry Laboratory. This is where most students are introduced to chemical
synthesis, and when the need for these calculations arises.
There are three calculations which revolve around this topic:
Theoretical Yield – (100%)
Percent Yield – (How you did)
Percent Recovery – (What you got back)
…and they are often confused. The best attack is to review them all at once.
[
T
heoretical Yield. Theoretical Yield is the amount of material you will obtain if the reaction goes
perfectly. Hence “Theoretical Percent Yield” (a parameter which many students want to invoke) would be
100%; that would not be a useful calculation.
To get the correct answer, a three step approach may be applied:
1) Write out the reaction equation, with correct stoiciometry.
Example: The dehydration of cyclohexanol
OH
+
H
+
+
H2O
Organic chemists are afforded the luxury that most organic reactions exhibit 1:1 stoiciometry. However,
this is not always true, so watch out!
2) Determine the limiting reagent.
The limiting reagent is the one that is going to run out. This determines how much product is possible.
(Once any reagent runs out, the reaction stops!)
Example (continued):
Cyclohexanol: 1.422g x 1 mole/100.16g = 0.0142 mole cyclohexanol
LIMITING
H+ (from phosphoric acid): 0.890g x 1 mole/98.08g x 3 mole H+/1 mole H3PO4) = 0.0272 mole H+
The limiting reagent is often the reagent, rather than the organic compound being modified.
3) Determine the theoretical yield by dimensional analysis.
Dimensional analysis is also known as “factor-label method” or “unit factor method.” If you don’t know it
yet, you’ve put it off long enough!
Example (continued further):
0.0142 mole cyclohexanol x 1 mole cyclohexene/1 mole cyclohexanol x 82.15g cyclohexene/mole
= 1.17g cyclohexene
SEVERAL notes:
1) The theoretical yield is typically expressed in GRAMS.
2) Any reagents which are not LIMITING are not used in this calculation.
3) The stoiciometry of the reaction is expressed mathematically.
4) In this case, the theoretical yield is less than the mass of the starting material. This is because the
product has a lower molecular weight than the starting material. When the product has a higher
molecular weight, the theoretical yield will be greater than the mass of the starting material.
5) The theoretical yield is STILL NOT A PERCENT!
\
P
ercent Yield. The percent yield is how you did, and completing this calculation is the usual reason for
doing the theoretical yield. This calculation is simply:
Actual Yield
x 100 = percent yield
Theoretical Yield
Example: If, in the above calculation, the final product you obtained was 0.90g cyclohexene, then:
0.90g cyclohexene/1.17g cyclohexene x 100 = 76.9% yield
]
P
ercent Recovery. Yield calculations are conducted on syntheses; when you are turning one molecule
into another one. RECOVERY calculations are conducted when no transformation occurs. When you start
with a specific species and end with the same species, then you will be calculating a recovery. In this case:
Final Amount
x 100 = percent recovery
Starting Amount
The usual time for a calculation of this sort is when you are purifying a product. In a recrystallization
experiment, you start with a specific product, and isolate the same product, only more pure.
Example: If our product from the dehydration reaction which we were analyzing showed evidence of
unreacted starting material (red color in the ammonium cerium (IV) nitrate test), we could purify it by
distillation. If we recover 0.73g of purified cyclohexene from the original 0.90g, then:
0.73g cyclohexene/0.90g cyclohexene x 100 = 81.1% recovery
^
H
ence, there are three different calculations that are typically conducted in organic chemistry. Keeping
them straight is the key to getting the correct answers. And remember, we organic chemists pride ourselves
on having adequate mathematical ability to count to four, so this can’t be too hard!