# How a chemical process works: reactions, separations, catalysts and flowsheets: Reaction basics that decide the economics

Source page: https://www.materialinsights.org/learn/chemicals/how-chemical-processes-work/p2/

[Understanding Chemicals](https://www.materialinsights.org/learn/chemicals/) / [Module 2: How a chemical process works: reactions, separations, catalysts and flowsheets](https://www.materialinsights.org/learn/chemicals/how-chemical-processes-work/) Part 2 of 5

## Reaction basics that decide the economics

A handful of ideas from chemistry decide whether a process makes money: how much raw material the equation demands, how much of the feed reacts, how much of what reacts becomes the right product, where equilibrium lets the reaction stop, how fast it goes, and how much heat it gives off. Each one translates directly into tonnes, equipment size and energy.

### 2.1 Stoichiometry sets the floor on raw material use

Stoichiometry is the bookkeeping of a chemical equation. Atoms are neither created nor destroyed, so the balanced equation fixes the smallest possible amount of each raw material per tonne of product. You can work it out from molar masses, the mass of one mole of each substance.

Take sulphuric acid. Overall, sulphur plus oxygen plus water gives H2SO4. Sulphur weighs 32 per mole and sulphuric acid 98, so one tonne of acid needs at least 32 divided by 98, or 0.327 tonnes of sulphur. Brennan's indicative table gives 0.32 tonnes per tonne, the same figure rounded to two places. Indicative figures are rounded, so small gaps against theory should not be over-read.

Nitric acid is made from ammonia: overall NH3 plus two O2 gives HNO3 plus water. Ammonia weighs 17 and nitric acid 63, so the minimum is 0.270 tonnes of ammonia per tonne of acid. Kent's table of commercial designs gives 0.279 to 0.291 tonnes. Dividing, the plants turn 93 to 97% of their ammonia into acid. The rest is lost mainly as nitrogen gas in the burner, plus a little used to destroy nitrogen oxides in the tail gas.

For acetic acid from methanol and carbon monoxide, CH3OH plus CO gives CH3COOH. Methanol weighs 32 and acetic acid 60, so the floor is 0.534 tonnes of methanol. Brennan's figures of 0.53 and 0.54 match almost exactly, which fits Wittcoff's report of better than 99% selectivity.

The gap between the floor and actual use is the first thing to check in any process. A gap of 3% in a commodity with thin margins is real money.

Data Theoretical versus actual raw material use

| Product | Raw material | Theoretical t per t (from equation) | Reported t per t | Implied efficiency |
|---|---|---|---|---|
| Sulphuric acid | Sulphur | 0.327 | 0.32 (indicative) | matches theory after rounding |
| Nitric acid | Ammonia | 0.270 | 0.279-0.291 | 93-97% |
| Acetic acid | Methanol | 0.534 | 0.53-0.54 | about 99% |
| Acetic acid | Carbon monoxide | 0.466 | 0.47-0.52 | 90-99% |
| Ethylene oxide | Ethylene | 0.637 | 0.88 (indicative) | about 72% |

Theoretical figures and efficiencies are calculated here from the balanced equations; reported figures from the sources.
 Source: Brennan (2020), Ch 4, Tables 4.2 and 4.7; Kent (2012), Ch 22, Table 22.18, Brennan pdf pp. 106-107, 126; Kent pdf p. 915

- Brennan (2020), Ch 4 Operating cost estimation · pdf pp. 106-107, 126
- Kent (2012), Ch 22 Synthetic Nitrogen Products · pdf p. 915
- Wittcoff (2004), Ch 10 Chemicals from methane · pdf p. 391

### 2.2 Conversion, selectivity and yield are three different numbers

Three words get used loosely, and the difference between them is the difference between a good and a bad process.

Conversion is the fraction of a feed that changes into anything at all. Selectivity, as Kent defines it, is the amount of desired product divided by the amount of reactant converted. Yield is the fraction of raw material that ends up as the desired product. Shreve stresses that yield is usually the most important single factor in cost and must not be confused with conversion. Conversion per pass means how much reacts in one trip through the reactor.

Ammonia shows why. Shreve, writing in 1984, gives a yield above 98% but a conversion per pass of only about 14%, held down by equilibrium. So 86% of the gas leaving the converter has not reacted and must be separated and recycled. Kent, in 2012, gives 20 to 30% per pass for modern converters. Either way the plant is mostly a recycle machine. Shreve notes that low conversion makes ammonia and methanol plants four to five times larger than they would be if conversion equalled yield.

Selectivity matters most when a feed can go to several products. Ethylene and oxygen over silver give ethylene oxide, but some ethylene burns to carbon dioxide and water instead. Wittcoff reports that about 75% of the cost of ethylene oxide is ethylene. Early silver catalysts gave 65 to 70% selectivity; improved ones averaged about 82% over their life, and the newest exceed 90% when fresh.

The arithmetic is striking. At 70% selectivity a tonne of ethylene oxide needs 0.91 tonnes of ethylene; at 82% it needs 0.78. That 15% saving in ethylene cuts total product cost by roughly 11%, from catalyst chemistry alone.

Data Ethylene oxide: what selectivity does to ethylene use

| Selectivity to ethylene oxide | Ethylene needed per t of product | Context |
|---|---|---|
| 65% | 0.98 t | early silver catalysts (low end) |
| 70% | 0.91 t | early silver catalysts (high end) |
| 72% | 0.88 t | implied by Brennan's indicative figure |
| 82% | 0.78 t | average over catalyst life, early 2000s |
| 90% | 0.71 t | latest catalysts at start of run |

Ethylene per tonne = 28/44 divided by selectivity, calculated here. Selectivity data from Wittcoff (2004).
 Source: Wittcoff (2004), Ch 3 Ethylene oxide; Brennan (2020), Ch 4 Table 4.2, Wittcoff pdf pp. 152-153; Brennan pdf p. 106  Common misreading

#### High conversion is not the goal

It is tempting to think a good reactor converts everything in one pass. Often the opposite is true. In ethylene oxide, pushing conversion higher means more contact between product and oxygen, and the product burns. Wittcoff reports similar trade-offs elsewhere: vapour-phase vinyl acetate runs at about 10% ethylene conversion per pass with 94 to 95% selectivity. Designers accept low conversion and pay for recycle, because unreacted feed can be recovered while feed burned to carbon dioxide is gone for good.

- Shreve (1984), Ch 2 Basic chemical data · pdf p. 25
- Kent (2012), Ch 6 Selectivity · pdf p. 218
- Kent (2012), Ch 22 Ammonia synthesis · pdf p. 902
- Wittcoff (2004), Ch 3 Ethylene oxide and vinyl acetate · pdf pp. 151-153

### 2.3 Equilibrium decides where a reaction wants to stop

Many reactions are reversible: products can turn back into reactants. Left alone, the mixture settles at an equilibrium where both directions run at the same speed and the composition stops changing. The equilibrium constant is a number that summarises where that balance lies at a given temperature. A large constant means the mixture ends up mostly as products.

Le Chatelier's principle says that if you disturb a system at equilibrium, it shifts to oppose the disturbance. Three practical levers follow.

Temperature. For a reaction that releases heat, raising the temperature pushes equilibrium back towards the reactants. Shreve's table for sulphur dioxide oxidation shows the constant falling from 897 at 400 C to 48 at 500 C, 9.5 at 600 C and below 1 at 800 C. Hot is bad for conversion.

Pressure. If the products occupy fewer gas molecules than the reactants, raising pressure favours products. Ammonia is the classic case: four molecules of gas (one nitrogen, three hydrogen) become two of ammonia, so ammonia plants run at 100 to 250 bar according to Kent. Shreve notes that SO2 oxidation also gains from pressure, but only slightly, and a French pressurised acid plant did not deliver the hoped-for savings. Diluting with inert gas such as nitrogen has the opposite effect.

Removing product. If you take product out, the reaction moves forward to replace it. Ammonia plants condense ammonia out of the loop and recycle the rest. Double absorption sulphuric acid plants scrub out sulphur trioxide part way through the converter, then send the gas back over more catalyst. Shreve is explicit that the gain comes from disturbing the equilibrium, not from a better catalyst. Conversion rises from 97 to 98% to over 99.7%.

Data Equilibrium constant for SO2 + 1/2 O2 -> SO3

| Temperature (C) | Kp | Temperature (C) | Kp |
|---|---|---|---|
| 400 | 897 | 800 | 0.915 |
| 500 | 48.1 | 900 | 0.384 |
| 600 | 9.53 | 1000 | 0.1845 |
| 700 | 2.63 | 1100 | 0.0980 |

Pressures in atmospheres. Data originally published in 1905; equilibrium conversion falls steeply as temperature rises.
 Source: Shreve (1984), Ch 19 Sulfur and Sulfuric Acid, Table 19.5, pdf p. 351

- Shreve (1984), Ch 19 Sulfuric acid · pdf pp. 347, 351-354
- Shreve (1984), Ch 18 Synthetic ammonia · pdf pp. 322-323
- Kent (2012), Ch 22 Ammonia synthesis · pdf p. 902

### 2.4 Rate, temperature and heat removal pull in opposite directions

Kinetics is the study of how fast reactions go. Speed matters because it sets equipment size: a slow reaction needs a big reactor or a lot of catalyst to make the same tonnage. Rates usually climb steeply with temperature. Kent gives the Arrhenius equation, which says the rate constant rises exponentially as temperature rises, with the steepness set by the activation energy, the energy barrier molecules must climb to react.

Shreve calls the clash between rate and equilibrium frequently the major design problem. Conditions that speed a reaction often lower the conversion it can reach. Sulphur dioxide oxidation reacts 10 to 100 times faster at 500 C than at 400 C, yet equilibrium is far better at 400 C. The contact process answers this in stages. Gas enters the first catalyst bed at about 425 to 440 C. The reaction releases heat, so the gas warms itself and reacts fast until, near 600 C, it approaches equilibrium with 60 to 70% converted. The gas is then cooled in a boiler or exchanger to no more than about 430 C before the next bed, where it reacts slowly but almost to completion.

Heat of reaction is the heat released (exothermic) or absorbed (endothermic) per mole. Shreve gives minus 46 kJ per mole of ammonia, minus 298 kJ for burning sulphur, minus 98 kJ for oxidising SO2 and minus 130 kJ for absorbing SO3 into water. That heat must be removed or it will overheat the catalyst and damage the vessel. Ammonia converters inject cold feed gas between beds, a method called quenching. The heat is also an asset: recovered as steam, it can earn money.

Pressure costs money too. Compressing gas takes power, and thick-walled vessels cost more. Shreve notes that raising pressure improves ammonia and methanol yields but increases operating and equipment costs.
 Worked example

#### How much heat does an acid plant release?

Adding Shreve's three heats of reaction gives 527 kJ per mole of sulphuric acid. One tonne of acid is about 10,200 moles (1,000,000 g divided by 98), so the plant releases about 5.4 GJ per tonne. Kent gives the thermal capacity of a 1,000 tonne-per-day plant as about 63 MW. Multiply by 86,400 seconds in a day and divide by 1,000 tonnes: 5.4 GJ per tonne again. The two sources, written 28 years apart, agree. That heat is either a disposal problem or a product, depending on design.

- Shreve (1984), Ch 1 and Ch 19 · pdf pp. 21, 25, 349-352
- Shreve (1984), Ch 18 · pdf pp. 322-326
- Kent (2012), Ch 6 Kinetics · pdf pp. 221-223
- Kent (2012), Ch 25 Sulfur and Sulfuric Acid · pdf p. 1017

### See it in the table
[H₂O Water](https://www.materialinsights.org/commodities/water/)[Ag Silver](https://www.materialinsights.org/commodities/silver/)[H2SO4 Sulphuric acid](https://www.materialinsights.org/chemicals/sulphuric_acid/)[HNO3 Nitric acid](https://www.materialinsights.org/chemicals/nitric_acid/)[H2 Hydrogen](https://www.materialinsights.org/chemicals/hydrogen/)[O2 Oxygen](https://www.materialinsights.org/chemicals/oxygen/)[N2 Nitrogen gas](https://www.materialinsights.org/chemicals/nitrogen_gas/)[CO2 Carbon dioxide](https://www.materialinsights.org/chemicals/carbon_dioxide/)[NH3 Ammonia](https://www.materialinsights.org/chemicals/ammonia/)[C2H4 Ethylene](https://www.materialinsights.org/chemicals/ethylene/)[MeOH Methanol](https://www.materialinsights.org/chemicals/methanol/)[AcOH Acetic acid](https://www.materialinsights.org/chemicals/acetic_acid/)[EO Ethylene oxide](https://www.materialinsights.org/chemicals/ethylene_oxide/)

### Check your understanding

An ammonia plant has a yield above 98% but converts only about 14% of its gas per pass. How is that possible?
 Conversion per pass is limited by equilibrium, but the recycle loop returns unreacted hydrogen and nitrogen until nearly all of it becomes ammonia. The price is a much bigger plant.

Why does a double absorption sulphuric acid plant reach higher conversion than a single absorption plant?
 Shreve states the gain is not from catalyst efficiency. Taking product out lets the reaction go further in the last beds, by Le Chatelier's principle.

Raising ethylene oxide selectivity from 70% to 82% cuts ethylene use per tonne by about:
 Ethylene needed falls from 0.91 to 0.78 tonnes per tonne, about 15%. With ethylene at 75% of cost, total cost falls by roughly 11%.

[← Part 1: The anatomy of a chemical plant](https://www.materialinsights.org/learn/chemicals/how-chemical-processes-work/p1/)[Mark read · Part 3: Catalysts: what they change and what they cannot →](https://www.materialinsights.org/learn/chemicals/how-chemical-processes-work/p3/)

## Other sections

- [Module overview](https://www.materialinsights.org/learn/chemicals/how-chemical-processes-work/index.md)
- [The anatomy of a chemical plant](https://www.materialinsights.org/learn/chemicals/how-chemical-processes-work/p1/index.md)
- [Catalysts: what they change and what they cannot](https://www.materialinsights.org/learn/chemicals/how-chemical-processes-work/p3/index.md)
- [Unit operations, their energy bills, and batch versus continuous](https://www.materialinsights.org/learn/chemicals/how-chemical-processes-work/p4/index.md)
- [Reading a flowsheet, and safety as a design input](https://www.materialinsights.org/learn/chemicals/how-chemical-processes-work/p5/index.md)
- [Key terms, quiz and sources](https://www.materialinsights.org/learn/chemicals/how-chemical-processes-work/review/index.md)