Exercises: Stoichiometry in industry, the environment and society

Cement factories heat limestone in large kilns: $\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$.

1. a) Identify the reactant and products of the reaction.
2. 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?

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: $\text{C} = 12\ \text{u}$; $\text{O} = 16\ \text{u}$).

The ammonia manufactured in large plants, $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$, is the raw material for fertilisers.

1. a) How many moles of ammonia are obtained, at most, from $1\ \text{mol}$ of nitrogen?
2. b) Explain why this reaction is said to "fix" nitrogen from the air and why it is so important for agriculture.

The production manager of a chemical plant says that their reactor operates "with a yield of $90\ \%$".

1. 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.
2. b) Reason why in practice the yield of an industrial process never reaches exactly $100\ \%$.

So-called green hydrogen is obtained by the electrolysis of water: $2\ \text{H}_2\text{O} \rightarrow 2\ \text{H}_2 + \text{O}_2$.

1. a) What mass of hydrogen is obtained by decomposing $2\ \text{mol}$ of water? (molar mass: $\text{H}_2 = 2\ \text{g/mol}$).
2. b) Explain what condition the electricity used must satisfy for this hydrogen to be called "green".

In a blast furnace, iron ore reacts with carbon monoxide: $\text{Fe}_2\text{O}_3 + 3\ \text{CO} \rightarrow 2\ \text{Fe} + 3\ \text{CO}_2$.

1. a) Identify the reactants and products.
2. b) Explain in a sentence what carbon monoxide does to iron oxide: which substance gains its oxygen?

Car airbags inflate in milliseconds thanks to the decomposition of sodium azide: $2\ \text{NaN}_3 \rightarrow 2\ \text{Na} + 3\ \text{N}_2$.

1. a) How many moles of nitrogen are formed when $2\ \text{mol}$ of azide decomposes?
2. b) Which gas inflates the airbag? Reason why it is desirable for it to be a very unreactive gas.

Some coals contain sulphur as an impurity, which reacts when burned: $\text{S} + \text{O}_2 \rightarrow \text{SO}_2$.

1. a) Calculate what mass of sulphur dioxide is formed when burning $32\ \text{g}$ of sulphur (molar masses: $\text{S} = 32\ \text{g/mol}$; $\text{SO}_2 = 64\ \text{g/mol}$).
2. b) Name the environmental problem associated with emissions of $\text{SO}_2$.

A cement plant feeds its kiln with $500\ \text{kg}$ of calcium carbonate: $\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$, as shown in the kiln diagram.

Knowing that for every $100\ \text{kg}$ of carbonate, $56\ \text{kg}$ of quicklime and $44\ \text{kg}$ of carbon dioxide are obtained, calculate:

1. a) The mass of quicklime ($\text{CaO}$) produced.
2. b) The mass of $\text{CO}_2$ emitted into the atmosphere.

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: $\text{C} = 12\ \text{u}$; $\text{O} = 16\ \text{u}$).

A fertiliser plant feeds its reactor with $140\ \text{kg}$ of nitrogen: $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$. Take into account the proportions from the equation: $28\ \text{g}$ of nitrogen react with $6\ \text{g}$ of hydrogen to yield $34\ \text{g}$ of ammonia. Calculate:

1. a) The mass of hydrogen that the plant needs to buy.
2. b) The mass of ammonia it would produce if the process went to completion.

A blast furnace processes $320\ \text{kg}$ of iron(III) oxide: $\text{Fe}_2\text{O}_3 + 3\ \text{CO} \rightarrow 2\ \text{Fe} + 3\ \text{CO}_2$. The proportions from the equation are: $160\ \text{g}$ of oxide yield $112\ \text{g}$ of iron and $132\ \text{g}$ of carbon dioxide. Calculate:

1. a) The mass of iron obtained.
2. b) The mass of carbon dioxide emitted.

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 photosynthesis, plants manufacture glucose and release oxygen: $6\ \text{CO}_2 + 6\ \text{H}_2\text{O} \rightarrow \text{C}_6\text{H}_{12}\text{O}_6 + 6\ \text{O}_2$. The proportion in the equation is: for every $264\ \text{g}$ of $\text{CO}_2$ absorbed, $192\ \text{g}$ of $\text{O}_2$ are released. It is estimated that the trees in an urban park fix $1\,320\ \text{kg}$ of $\text{CO}_2$ per year, as shown in the figure.

Calculate:

1. a) The mass of oxygen they return to the air in one year.
2. b) Comment on why urban parks are considered the "lungs" of a city.

Aluminum is obtained by electrolysis of its dissolved oxide: $2\ \text{Al}_2\text{O}_3 \rightarrow 4\ \text{Al} + 3\ \text{O}_2$. The ratio is: $204\ \text{g}$ of oxide yields $108\ \text{g}$ of aluminum.

1. a) Calculate the mass of aluminum produced from an electrolytic cell charged with $204\ \text{kg}$ of aluminum oxide.
2. b) Electrolysis consumes a huge amount of electricity. Explain why recycling aluminum cans saves as much energy as advertised.

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:

1. a) The mass of oxygen consumed.
2. b) The mass of water vapour formed.

(molar masses: $\text{H}_2 = 2\ \text{g/mol}$; $\text{O}_2 = 32\ \text{g/mol}$; $\text{H}_2\text{O} = 18\ \text{g/mol}$).

A cement factory buys $1\,000\ \text{kg}$ of limestone with a calcium carbonate purity of $90\ \%$ (the rest are inert impurities) and calcinates it completely: $\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$.

1. a) What mass of calcium carbonate does the batch contain?
2. b) Calculate the mass of quicklime ($\text{CaO}$) obtained.
3. c) Calculate the mass of $\text{CO}_2$ emitted solely by the chemical reaction.

(ratio: $100\ \text{kg}$ of $\text{CaCO}_3$ yields $56\ \text{kg}$ of $\text{CaO}$ and $44\ \text{kg}$ of $\text{CO}_2$).

A boiler burns $60\ \text{kg}$ of coal with a carbon purity of $80\ \%$ (the rest does not burn): $\text{C} + \text{O}_2 \rightarrow \text{CO}_2$.

1. a) What mass of carbon is actually burned?
2. b) Calculate the mass of carbon dioxide emitted (atomic masses: $\text{C} = 12\ \text{u}$; $\text{O} = 16\ \text{u}$).
3. c) Explain why companies must know the purity of their fuel to declare their emissions, and why simply weighing the coal they buy is not enough.

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 $60\ \%$.

1. a) Calculate the theoretical mass of ammonia that would be obtained with a 100% yield.
2. b) Calculate the mass that is actually produced.
3. 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.

Not all fossil fuels pollute equally. Compare their emissions per gram burned:

• Methane: $\text{CH}_4 + 2\ \text{O}_2 \rightarrow \text{CO}_2 + 2\ \text{H}_2\text{O}$; $16\ \text{g}$ of methane emits $44\ \text{g}$ of $\text{CO}_2$.

• 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 $\text{CO}_2$.

• Coal (carbon): $\text{C} + \text{O}_2 \rightarrow \text{CO}_2$; $12\ \text{g}$ of carbon emits $44\ \text{g}$ of $\text{CO}_2$.

1. a) Calculate the grams of $\text{CO}_2$ emitted per gram of fuel in all three cases (round to one decimal place if necessary).
2. b) Order them from least to most polluting per gram.
3. 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.

An airbag needs to inflate with $3\ \text{mol}$ of nitrogen. The reaction supplying it is $2\ \text{NaN}_3 \rightarrow 2\ \text{Na} + 3\ \text{N}_2$.

1. a) How many moles of sodium azide must decompose?
2. b) Calculate the mass of azide that the airbag canister must contain (molar masses: $\text{NaN}_3 = 65\ \text{g/mol}$).
3. c) Explain why it is important for the manufacturer to know this calculation precisely: what would happen if the canister contained much less or much more azide than calculated?

To treat an acidic spill from a factory, slaked lime (calcium hydroxide) is used, which neutralises sulfuric acid: $\text{Ca(OH)}_2 + \text{H}_2\text{SO}_4 \rightarrow \text{CaSO}_4 + 2\ \text{H}_2\text{O}$. The tank contains $392\ \text{kg}$ of sulfuric acid. Calculate, using moles or proportions, the mass of calcium hydroxide that needs to be ordered to neutralise it completely (molar masses: $\text{Ca(OH)}_2 = 74\ \text{g/mol}$; $\text{H}_2\text{SO}_4 = 98\ \text{g/mol}$).

In the environmental accounting of a cement plant, two sources of $\text{CO}_2$ must be distinguished: the chemical reaction of the stone, $\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$, 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.

1. a) Explain why improving the kiln insulation and the efficiency of its burners reduces only one of the two sources.
2. 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 $220\ \text{kg}$ 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 $\text{CaO}$).

1. a) Calculate what mass of lime would be needed to capture that $220\ \text{kg}$ of $\text{CO}_2$.
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?
3. c) Propose other options being studied for this gas (other materials that fix it or its storage) and briefly assess the idea.