Stoichiometry in industry, the environment and society
When a cement company announces how many tonnes of $\text{CO}_2$ it is going to cut, or when people debate whether "green hydrogen" is really clean, the same tool is always behind it: a balanced chemical equation and a calculator. Stoichiometry does not end in the exercise book; it is the basis on which entire factories are designed and their effects on the planet are audited.
From the factory to the environment: the same equation, a different scale
A chemical plant that produces fertilisers buys reactants by the tens of tonnes; if it orders too much or too little natural gas or steam, the financial losses are enormous and the reactor stops. How do engineers calculate the exact quantities of raw materials and emissions on an industrial scale?
Cement factories heat limestone in large kilns: $\text{CaCO}3 \rightarrow \text{CaO} + \text{CO}2$. a) Identify the reactant and products of the reaction. b) Explain why…
Cement factories heat limestone in large kilns: $\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$.
- a) Identify the reactant and products of the reaction.
- b) Explain why a cement plant emits carbon dioxide even if the kiln were heated using only renewable electricity: where does this gas come from?
In a blast furnace, iron ore reacts with carbon monoxide: $\text{Fe}2\text{O}3 + 3\ \text{CO} \rightarrow 2\ \text{Fe} + 3\ \text{CO}2$. a) Identify the reactants and…
In a blast furnace, iron ore reacts with carbon monoxide: $\text{Fe}_2\text{O}_3 + 3\ \text{CO} \rightarrow 2\ \text{Fe} + 3\ \text{CO}_2$.
- a) Identify the reactants and products.
- b) Explain in a sentence what carbon monoxide does to iron oxide: which substance gains its oxygen?
How much CO2 is emitted by burning a fossil fuel
Not all fossil fuels emit the same amount per gram burned: it depends on their proportion of carbon to hydrogen. By comparing their combustion equations you can rank them from least to most polluting per unit of mass, although all three are still sources of $\text{CO}_2$.
A thermal power plant burns coal, which to simplify is carbon: $\text{C} + \text{O}2 \rightarrow \text{CO}2$. Calculate what mass of carbon dioxide is emitted for every…
A thermal power plant burns coal, which to simplify is carbon: $\text{C} + \text{O}_2 \rightarrow \text{CO}_2$. Calculate what mass of carbon dioxide is emitted for every $12\ \text{kg}$ of carbon burned (atomic masses: $\text{C} = 12\ \text{u}$; $\text{O} = 16\ \text{u}$).
In a test, an industrial boiler burns $120\ \text{kg}$ of coal, which can be considered pure carbon: $\text{C} + \text{O}2 \rightarrow \text{CO}2$. Calculate, by…
In a test, an industrial boiler burns $120\ \text{kg}$ of coal, which can be considered pure carbon: $\text{C} + \text{O}_2 \rightarrow \text{CO}_2$. Calculate, by converting through moles or using proportions, the mass of carbon dioxide emitted (atomic masses: $\text{C} = 12\ \text{u}$; $\text{O} = 16\ \text{u}$).
Not all fossil fuels pollute equally. Compare their emissions per gram burned: Methane: $\text{CH}4 + 2\ \text{O}2 \rightarrow \text{CO}2 + 2\ \text{H}2\text{O}$;…
Not all fossil fuels pollute equally. Compare their emissions per gram burned:
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Methane: $\text{CH}_4 + 2\ \text{O}_2 \rightarrow \text{CO}_2 + 2\ \text{H}_2\text{O}$; $16\ \text{g}$ of methane emits $44\ \text{g}$ of $\text{CO}_2$.
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Propane: $\text{C}_3\text{H}_8 + 5\ \text{O}_2 \rightarrow 3\ \text{CO}_2 + 4\ \text{H}_2\text{O}$; $44\ \text{g}$ of propane emits $132\ \text{g}$ of $\text{CO}_2$.
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Coal (carbon): $\text{C} + \text{O}_2 \rightarrow \text{CO}_2$; $12\ \text{g}$ of carbon emits $44\ \text{g}$ of $\text{CO}_2$.
- a) Calculate the grams of $\text{CO}_2$ emitted per gram of fuel in all three cases (round to one decimal place if necessary).
- b) Order them from least to most polluting per gram.
- c) Explain, looking at the composition of each fuel, why natural gas is considered the "least dirty" fossil fuel, and clarify whether this means it does not contribute to climate change.
The real yield of an industrial process
In the laboratory you carefully measure out the reactants to obtain exactly $10{,}0\ \text{g}$ of white precipitate, but after filtering and drying the solid, the balance reads only $8{,}5\ \text{g}$. Why in practice do you never collect the exact mass predicted by the calculation on paper?
The production manager of a chemical plant says that their reactor operates "with a yield of $90\ \%$". a) Explain in your own words what this figure means, thinking…
The production manager of a chemical plant says that their reactor operates "with a yield of $90\ \%$".
- a) Explain in your own words what this figure means, thinking about the difference between what the balanced equation predicts and what actually comes out of the reactor.
- b) Reason why in practice the yield of an industrial process never reaches exactly $100\ \%$.
An ammonia plant feeds its reactor with $140\ \text{kg}$ of nitrogen: $\text{N}2 + 3\ \text{H}2 \rightarrow 2\ \text{NH}3$. The equation predicts that $28\ \text{g}$ of…
An ammonia plant feeds its reactor with $140\ \text{kg}$ of nitrogen: $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$. The equation predicts that $28\ \text{g}$ of nitrogen yield $34\ \text{g}$ of ammonia, but the reactor operates with a percentage yield of $60\ \%$.
- a) Calculate the theoretical mass of ammonia that would be obtained with a 100% yield.
- b) Calculate the mass that is actually produced.
- c) Plants recirculate unreacted gases back into the reactor over and over again. Explain what they achieve by doing this and how it relates to the percentage yield and the cost of the process.
Fixing nitrogen and producing green hydrogen
The ammonia manufactured in large plants, $\text{N}2 + 3\ \text{H}2 \rightarrow 2\ \text{NH}3$, is the raw material for fertilisers. a) How many moles of ammonia are…
The ammonia manufactured in large plants, $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$, is the raw material for fertilisers.
- a) How many moles of ammonia are obtained, at most, from $1\ \text{mol}$ of nitrogen?
- b) Explain why this reaction is said to "fix" nitrogen from the air and why it is so important for agriculture.
So-called green hydrogen is obtained by the electrolysis of water: $2\ \text{H}2\text{O} \rightarrow 2\ \text{H}2 + \text{O}2$. a) What mass of hydrogen is obtained by…
So-called green hydrogen is obtained by the electrolysis of water: $2\ \text{H}_2\text{O} \rightarrow 2\ \text{H}_2 + \text{O}_2$.
- a) What mass of hydrogen is obtained by decomposing $2\ \text{mol}$ of water? (molar mass: $\text{H}_2 = 2\ \text{g/mol}$).
- b) Explain what condition the electricity used must satisfy for this hydrogen to be called "green".
Some rocket stages burn liquid hydrogen: $2\ \text{H}2 + \text{O}2 \rightarrow 2\ \text{H}2\text{O}$. In a ground test, $12\ \text{g}$ of hydrogen is burned. Calculate,…
Some rocket stages burn liquid hydrogen: $2\ \text{H}_2 + \text{O}_2 \rightarrow 2\ \text{H}_2\text{O}$. In a ground test, $12\ \text{g}$ of hydrogen is burned. Calculate, using moles:
- a) The mass of oxygen consumed.
- b) The mass of water vapour formed.
(molar masses: $\text{H}_2 = 2\ \text{g/mol}$; $\text{O}_2 = 32\ \text{g/mol}$; $\text{H}_2\text{O} = 18\ \text{g/mol}$).
Cleaning flue gases, capturing CO2 and the limits of these technologies
A similar idea would make it possible to capture the $\text{CO}_2$ directly from a cement works' chimney by making it react with lime: $\text{CO}_2 + \text{CaO} \rightarrow \text{CaCO}_3$. But that same stoichiometry reveals an awkward limit: if you compare the mass of $\text{CO}_2$ emitted by the kiln with the mass of lime it produces (both calculated with the same decomposition equation), you discover that a cement works cannot capture all of its emissions using only its own product. It would need "extra" lime, brought in from elsewhere, with its own cost and its own carbon footprint.
Some coals contain sulphur as an impurity, which reacts when burned: $\text{S} + \text{O}2 \rightarrow \text{SO}2$. a) Calculate what mass of sulphur dioxide is formed…
Some coals contain sulphur as an impurity, which reacts when burned: $\text{S} + \text{O}_2 \rightarrow \text{SO}_2$.
- a) Calculate what mass of sulphur dioxide is formed when burning $32\ \text{g}$ of sulphur (molar masses: $\text{S} = 32\ \text{g/mol}$; $\text{SO}_2 = 64\ \text{g/mol}$).
- b) Name the environmental problem associated with emissions of $\text{SO}_2$.
To clean the flue gases from a thermal power station, the smoke is passed through a bed of limestone, which traps the sulfur dioxide:…
To clean the flue gases from a thermal power station, the smoke is passed through a bed of limestone, which traps the sulfur dioxide: $\text{SO}_2 + \text{CaCO}_3 \rightarrow \text{CaSO}_3 + \text{CO}_2$. The power station emits $128\ \text{kg}$ of $\text{SO}_2$ per day. Calculate, using moles or proportions, the mass of calcium carbonate needed daily to trap all of it (molar masses: $\text{SO}_2 = 64\ \text{g/mol}$; $\text{CaCO}_3 = 100\ \text{g/mol}$).
In the environmental accounting of a cement plant, two sources of $\text{CO}2$ must be distinguished: the chemical reaction of the stone,…
In the environmental accounting of a cement plant, two sources of $\text{CO}_2$ must be distinguished: the chemical reaction of the stone, $\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$, which emits $44\ \text{kg}$ of $\text{CO}_2$ for every $56\ \text{kg}$ of lime produced, and the fuel burned to heat the kiln.
- a) Explain why improving the kiln insulation and the efficiency of its burners reduces only one of the two sources.
- b) Explain what would need to change to reduce the other source: would using renewable electricity work? What about capturing the gas before it leaves the chimney?
A cement plant is studying capturing the $\text{CO}2$ from its chimney by reacting it again with lime: $\text{CO}2 + \text{CaO} \rightarrow \text{CaCO}3$. Its kiln emits…
A cement plant is studying capturing the $\text{CO}_2$ from its chimney by reacting it again with lime: $\text{CO}_2 + \text{CaO} \rightarrow \text{CaCO}_3$. Its kiln emits $220\ \text{kg}$ of $\text{CO}_2$ when producing $280\ \text{kg}$ of quicklime (ratio: $44\ \text{kg}$ of $\text{CO}_2$ react with $56\ \text{kg}$ of $\text{CaO}$).
- a) Calculate what mass of lime would be needed to capture that $220\ \text{kg}$ of $\text{CO}_2$.
- b) Compare the result with the lime produced by the factory and explain the conclusion: can a cement plant capture all of its $\text{CO}_2$ using only its own product?
- c) Propose other options being studied for this gas (other materials that fix it or its storage) and briefly assess the idea.
Back to the beginning: Hydrogen is only "green" if the electricity used to split water by electrolysis comes entirely from renewable sources; otherwise, the stoichiometry of the power station shows that as much indirect $\text{CO}_2$ is emitted as is saved, or even more.