E-factor and process mass intensity come from the same data you already record in a batch sheet: every mass that goes in and the mass of isolated product. PMI is total input mass divided by product mass; the complete E-factor is total waste mass divided by product mass, which is simply PMI minus one. The work is not the arithmetic, it is deciding what counts as input: water, solvent for washes, recovered solvent, the catalyst, the nitrogen. The conventions you choose decide whether your number can be compared with anyone else's.
The formulas
PMI
= total mass of all inputs / mass of isolated product. The ACS GCI Pharmaceutical Roundtable adopted PMI as its primary mass metric because it is a ratio of positive quantities and aggregates cleanly over several steps.
Complete E-factor
= total mass of waste / mass of product = PMI − 1. Waste is everything in that did not end up as product.
Simple E-factor
counts only reagents, substrates and catalysts, leaving out water and process solvent. It is useful for comparing chemistry, misleading for comparing processes, because in fine chemicals solvent usually dominates.
Report which one you used. A simple E-factor of 0.4 and a complete E-factor of 15 can describe the same step.
A worked single step
A batch step producing 11.5 kg of isolated product. All masses are from the batch record.
| Input | Mass (kg) |
|---|---|
| Starting material | 10.0 |
| Reagent | 6.2 |
| Catalyst | 0.15 |
| Toluene (reaction and wash) | 80.0 |
| Water (quench and wash) | 50.0 |
| Brine | 12.0 |
| Heptane (crystallisation) | 30.0 |
| Total input | 188.35 |
- PMI = 188.35 / 11.5 = 16.4 kg per kg
- Complete E-factor = (188.35 − 11.5) / 11.5 = 15.4 kg waste per kg
- Simple E-factor = (10.0 + 6.2 + 0.15 − 11.5) / 11.5 = 0.42
The two E-factors differ by a factor of 37, and the reason is visible in the table: solvent and aqueous phases are 172 of the 188 kg. Any serious reduction starts there, not with the reagent stoichiometry.
What solvent recovery does to the number
Recover 85 % of the toluene, that is 68 kg, and feed it back to the next batch:
PMI = (188.35 − 68) / 11.5 = 10.5 kg per kg, a 36 % reduction, with no change to the chemistry.
Two conventions matter here, and both must be stated:
1. Is recovered solvent counted as input? If recovery happens inside your process and the material is reused, subtracting it is defensible and widely done. If it is sold or incinerated for energy, it is still waste. 2. Does the energy of recovery count? Mass metrics ignore it. A distillation that halves PMI and doubles the energy demand looks like an improvement and may not be one. That is why PMI should be reported next to an energy figure, not alone.
Several steps: do not average
For a linear sequence, PMI aggregates on the basis of the final product. For each step, express the inputs per kilogram of final product, taking the yields of all downstream steps into account, and add them up. Averaging the per-step PMI values understates the total, because early steps carry the losses of every later step.
A short example. Three steps, each with PMI 15 on its own product, each at 80 % yield by mass. One kilogram of final product needs 1.25 kg of intermediate 2, which needs 1.56 kg of intermediate 1. The cumulative PMI is 15 × 1.56 + 15 × 1.25 + 15 × 1.00 = 57, not 15.
This is also why a yield improvement in a late step reduces PMI more than a solvent reduction in the first step, which is often counterintuitive to the lab.
Where the metrics help, and where they stop
They help when you need to decide between routes, to find the step worth working on, or to report a defensible number to a customer or in a sustainability report. They are cheap: the data exist.
They stop at everything that is not mass:
- Hazard and toxicity. Replacing 80 kg of dichloromethane with 80 kg of 2-methyltetrahydrofuran leaves PMI unchanged and the risk profile transformed. Use the ICH Q3C classes and a solvent selection guide alongside the mass metrics.
- Energy and carbon. Not in PMI. A cryogenic step and a room-temperature step look identical.
- Water scarcity, land use, end of life. Outside mass metrics entirely; these need a life cycle assessment.
- Equipment occupancy and cost. A low-PMI route that needs three extra unit operations may be worse on every commercial measure.
Limits of the statement
- PMI and E-factor are only comparable when the boundaries match. State whether water, recovered solvent, cleaning solvent and analytical samples are inside the boundary.
- Isolated product mass must be defined: wet, dry, assay-corrected. An assay correction changes PMI by whatever the purity is.
- Reported values across companies are rarely on the same basis. Treat external benchmarks as orientation, not as a target.
Frequently asked questions
How do you calculate PMI?
Divide the total mass of all inputs to the step or process by the mass of isolated product. In the worked example, 188.35 kg of input and 11.5 kg of product give a PMI of 16.4 kg per kg.
What is the difference between the simple and the complete E-factor?
The simple E-factor counts only substrates, reagents and catalysts; the complete E-factor counts every input including water and solvent. In the example they are 0.42 and 15.4 for the same step, because solvent and aqueous phases dominate the mass.
Is PMI the same as the E-factor?
They differ by exactly one: complete E-factor = PMI − 1. PMI is a mass ratio of input to product, the E-factor a ratio of waste to product.
Does recovered solvent count in PMI?
It depends on the convention you state. Solvent recovered and reused inside the process is commonly subtracted from the input; solvent incinerated or sold is not. Always state the convention, because it can change the number by a third or more.
What do green metrics not tell you?
Anything that is not mass: hazard, toxicity, energy, carbon footprint, water scarcity, cost and equipment time. A solvent swap at equal mass can change the risk profile completely without moving PMI.