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Calculations
This page provides instructions for three common lab calculations: converting volume to mass, calculating molar equivalents, and calculating % yield. It also provides instructions for a "green chemistry" calculation that is slowly gaining acceptance among chemists: the E-factor.
Whichever calculation you perform, preserve insignificant figures throughout the intermediate states of your calculation. Do not round off anything until you obtain your final result.
Convert volume (in mL) to mass (in g)
Liquid reagents are normally measured by volume. You can convert volume to number of moles if you know how to convert volume to mass.
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weight = DV
Sometimes you have a different problem: you know what weight (in g) you need, and you want to calculate the volume (in mL) that will give this weight. In this case, repeat step 1 and calculate the required volume using:
V = weight / D
Some laboratory instructions state reagent amounts as "XXX molar equivalents". To interpret these instructions correctly, you must pay attention to their context.
In most cases, the instruction is preceded by another instruction that stipulates the amount of another reagent, and it is this other reagent that tells you what is needed.
An example will help make this clear. Let's assume that you obtained 10 g of compound A from an earlier experiment, and now you want to combine A with compound B to make compound P. Suppose too that a catalyst, compound Z, is required and the reaction stoichiometry is given by:
The instructions for this procedure might read: "Combine A from the previous experiment with B (1.1 molar equivalents) and Z (0.01 molar equivalents)."
You should interpret these instructions as follows:
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In other words, the instruction "molar equivalents" (or sometimes just "equivalents") refers to the amount of compound A measured in moles. The instructions are intended to guarantee that the compounds are used in the following molar ratio:
A : B : Z = 1 : 1.1 : 0.01
% yield compares the amount of product you actually obtain from an experiment with the amount that theoretically could have been obtained had every molecule of the limiting reactant been used to make product. It is defined as:
% yield = 100% (#moles product obtained) / max. #moles product possible
The yield can vary from 0% (no product obtained) to 100% (theoretically, the maximum amount possible).
To calculate "% yield" you must know:
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Most reactions give one molecule of product for every molecule of reactant. If this is the case, the maximum number of moles of product that can be obtained is identical to the number of moles of limiting reactant used (call this R). If you obtain only P moles of product, then:
% yield = (P / R) x 100%
Some reactions give one molecule of product for every two molecules of limiting reactant. In this case, the yield is defined as:
% yield = (2P / R) x 100%
E-factors compare the amount of product you actually obtain with the amount of waste that must be discarded after the experiment. The E-factor is a measure of the wastefulness of a preparative experiment.
E-factors are expressed as a mass ratio:
E-factor = total mass discarded / mass product
A larger E-factor represents a more wasteful process. Although the ideal E-factor, zero, is extremely hard to reach, it has been estimated that E-factors in the oil refining industry are less than one tenth (< 0.1), which is pretty impressive. E-factors for pharmaceuticals, on the other hand, are much higher (25-100). This is probably not surprising since more processing steps are required to make a pharmaceutical.
Unfortunately, it is difficult to calculate accurate E-factors because it is very hard to identify all of the disposables in any given experiment. In addition, we do not ask you to weigh the material that you throw away. However, you can estimate the combined mass of the material that must be discarded as follows:
1) Assume that everything you use (consume) during an experiment eventually is discarded (except for the product). Therefore,
total mass discarded = total mass consumed - mass product
2) When estimating your total mass consumed, make several simplifying (but questionable) assumptions:
Ignore water
Ignore fuel that is consumed to produce energy
Ignore coolants (ice, dry ice)
Ignore items like filter paper, rubber tubing, pH paper, disposable pipets, broken glassware, and the like
Ignore items that are used to monitor the reaction (TLC plates, etc.) or characterize the product (NMR solvent, etc.)
Include aqueous reagents (but not the weight of the water itself), e.g., count the dissoved NaCl in a saturated brine solution
Include dry ice if it is used a chemical reagent
Include all solvents (but not water)
Include your starting materials and reagent
Include silica gel used for preparative columns
Remember, after you total up everything you have consumed, subtract the mass of your product from the total (your product is valuable, it is not waste).
Also, do not worry about having accurate masses. You can convert (estimated) volumes to masses, either by looking up the reagent's density, or, when really desparate, assuming an appropriate density.
