Exercises: Stoichiometry in industrial processes

A fertilizer plant synthesizes ammonia via the Haber process: $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$.

1. a) How many moles of ammonia are obtained, at most, from $5\ \text{mol}$ of nitrogen?
2. b) How many moles of hydrogen are consumed in that case?

In the Haber process, $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$, the molar masses are $M(\text{N}_2) = 28\ \text{g/mol}$, $M(\text{H}_2) = 2\ \text{g/mol}$ and $M(\text{NH}_3) = 17\ \text{g/mol}$.

1. a) Calculate the mass of ammonia obtained from $28\ \text{g}$ of nitrogen with sufficient hydrogen.
2. b) Calculate the mass of hydrogen consumed and check that the law of conservation of mass is satisfied.

In the blast furnace, the main ore reduction reaction is $\text{Fe}_2\text{O}_3 + 3\ \text{CO} \rightarrow 2\ \text{Fe} + 3\ \text{CO}_2$.

1. a) How many moles of iron are obtained from $2\ \text{mol}$ of iron(III) oxide?
2. b) Given that $M(\text{Fe}) = 56\ \text{g/mol}$, calculate the mass of iron obtained from $1\ \text{mol}$ of iron(III) oxide.

A cement plant decomposes limestone in its kiln: $\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$, with molar masses $M(\text{CaCO}_3) = 100\ \text{g/mol}$, $M(\text{CaO}) = 56\ \text{g/mol}$ and $M(\text{CO}_2) = 44\ \text{g/mol}$. $100\ \text{g}$ of pure calcium carbonate is loaded.

1. a) Calculate the mass of quicklime ($\text{CaO}$) obtained.
2. b) Calculate the mass of carbon dioxide released.
3. c) Check that the sum of the masses of the products equals the mass of the reactant.

In the manufacture of sulfuric acid, the key stage is the oxidation of sulfur dioxide: $2\ \text{SO}_2 + \text{O}_2 \rightarrow 2\ \text{SO}_3$.

1. a) How many moles of sulfur trioxide are obtained from $4\ \text{mol}$ of sulfur dioxide?
2. b) How many moles of oxygen are consumed in that transformation?

On a trip you prepare sandwiches: each one has exactly $2$ slices of bread and $1$ slice of ham. You have $10$ slices of bread and $4$ slices of ham. The available ingredients are shown in the figure.

1. a) How many complete sandwiches can you prepare?
2. b) Which ingredient is left over and in what quantity?
3. c) In chemistry, the reactant that is used up first and limits the amount of product is called the limiting reactant: state which ingredient plays that role here.

A cement plant calculates that, according to stoichiometry, its kiln should produce $100\ \text{t}$ of lime per day, but the actual production is $92\ \text{t}$.

1. a) Calculate the yield of the kiln, as a percentage.
2. b) State two reasons why a real industrial process might not reach the theoretical yield of $100\ \%$.

Major chemical processes have an environmental impact: blast furnaces and cement manufacturing emit $\text{CO}_2$, and the hydrogen consumed in the Haber process is usually obtained today from natural gas.

1. a) Explain what global environmental problem is associated with carbon dioxide emissions.
2. b) Explain why manufacturing hydrogen by water electrolysis powered by renewable energy ("green hydrogen") would reduce the environmental footprint of ammonia.

In industry, the kilomole ($1\ \text{kmol} = 1000\ \text{mol}$) is often used: the mass of one kilomole in kilograms is numerically equal to the molar mass in $\text{g/mol}$. For the Haber process, $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$, we have $M(\text{N}_2) = 28\ \text{kg/kmol}$, $M(\text{H}_2) = 2\ \text{kg/kmol}$ and $M(\text{NH}_3) = 17\ \text{kg/kmol}$. A plant consumes $140\ \text{t}$ of nitrogen per day.

1. a) Express that mass of nitrogen in kmol.
2. b) Calculate the metric tons of ammonia that the plant produces per day.
3. c) Calculate the metric tons of hydrogen it needs daily.

Industry obtains hydrochloric acid by direct synthesis from the elements: $\text{H}_2 + \text{Cl}_2 \rightarrow 2\ \text{HCl}$. A reactor is loaded with $3\ \text{mol}$ of hydrogen and $2\ \text{mol}$ of chlorine. The reactor feed is represented using the particle model:

1. a) Determine which reactant is the limiting reactant, justifying your answer using stoichiometry.
2. b) Calculate the moles of $\text{HCl}$ formed.
3. c) Calculate the moles of excess reactant remaining unreacted and the mass of $\text{HCl}$ obtained ($M(\text{HCl}) = 36.5\ \text{g/mol}$).

A steel mill receives an iron ore with $80\ \%$ by mass of iron(III) oxide; the rest is inert gangue that does not react. In the blast furnace: $\text{Fe}_2\text{O}_3 + 3\ \text{CO} \rightarrow 2\ \text{Fe} + 3\ \text{CO}_2$, with $M(\text{Fe}_2\text{O}_3) = 160\ \text{kg/kmol}$ and $M(\text{Fe}) = 56\ \text{kg/kmol}$. $1000\ \text{kg}$ of ore is loaded.

1. a) Calculate the mass of iron(III) oxide that actually enters the furnace.
2. b) Calculate the maximum mass of iron that could be obtained.
3. c) State what mass of gangue must be removed as waste.

A lime kiln decomposes $200\ \text{g}$ of pure calcium carbonate: $\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$, with $M(\text{CaCO}_3) = 100\ \text{g/mol}$ and $M(\text{CaO}) = 56\ \text{g/mol}$.

1. a) Calculate the theoretical mass of quicklime that should be obtained.
2. b) If the actual yield of the kiln is $90\ \%$, calculate the mass of lime obtained in practice.
3. c) Suggest a reason why the kiln does not reach the theoretical yield.

The manufacture of sulfuric acid from sulfur occurs in three stages: $\text{S} + \text{O}_2 \rightarrow \text{SO}_2$; $2\ \text{SO}_2 + \text{O}_2 \rightarrow 2\ \text{SO}_3$; $\text{SO}_3 + \text{H}_2\text{O} \rightarrow \text{H}_2\text{SO}_4$. The sequence of transformations is shown schematically in the figure:

1. a) By following the sulfur atoms through the three equations, deduce how many moles of sulfuric acid are obtained per mole of initial sulfur.
2. b) With $M(\text{S}) = 32\ \text{kg/kmol}$ and $M(\text{H}_2\text{SO}_4) = 98\ \text{kg/kmol}$, calculate the metric tons of acid produced by a plant from $32\ \text{t}$ of sulfur.

Titanium for the aerospace industry is obtained via the Kroll process: $\text{TiCl}_4 + 2\ \text{Mg} \rightarrow \text{Ti} + 2\ \text{MgCl}_2$, with molar masses $M(\text{TiCl}_4) = 190\ \text{g/mol}$, $M(\text{Mg}) = 24\ \text{g/mol}$ and $M(\text{Ti}) = 48\ \text{g/mol}$. A reactor is loaded with $190\ \text{g}$ of titanium tetrachloride and $36\ \text{g}$ of magnesium.

1. a) Determine the limiting reactant.
2. b) Calculate the mass of titanium obtained.
3. c) Calculate the moles of excess reactant remaining unreacted.

In the Haber process, $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$, only part of the gas is converted on each pass through the reactor. $10\ \text{mol}$ of nitrogen is introduced with excess hydrogen, and the conversion per pass is $40\ \%$ ($M(\text{NH}_3) = 17\ \text{g/mol}$).

1. a) Calculate the theoretical mass of ammonia if all the nitrogen reacted.
2. b) Calculate the mass of ammonia actually obtained on one pass.
3. c) Explain what is done industrially with the gas that leaves the reactor unreacted and why this decision improves the overall utilization of nitrogen.

The calcination of limestone in cement manufacturing is $\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$, with $M(\text{CaCO}_3) = 100\ \text{kg/kmol}$ and $M(\text{CO}_2) = 44\ \text{kg/kmol}$. A cement plant calcines $1000\ \text{kg}$ of pure limestone per day.

1. a) Calculate the mass of carbon dioxide generated each day by the chemical reaction itself.
2. b) Calculate the tons emitted per year if the plant operates for $300$ days.
3. c) The kiln is heated by burning fuel: explain why the plant's actual carbon footprint exceeds the calculated value and why cement is listed among the highest-emitting materials.

An ammonia plant, $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$, daily has $28\ \text{t}$ of nitrogen and $8\ \text{t}$ of hydrogen available, and operates with a yield of $95\ \%$ ($M(\text{N}_2) = 28\ \text{kg/kmol}$; $M(\text{H}_2) = 2\ \text{kg/kmol}$; $M(\text{NH}_3) = 17\ \text{kg/kmol}$).

1. a) Express both masses in kmol.
2. b) Determine the limiting reactant.
3. c) Calculate the theoretical daily production of ammonia, in metric tons.
4. d) Calculate the actual production with the specified yield.
5. e) Calculate the metric tons of hydrogen left over each day and explain what should be done with them in the plant.

A blast furnace processes $1000\ \text{kg}$ of ore with $80\ \%$ of $\text{Fe}_2\text{O}_3$ according to $\text{Fe}_2\text{O}_3 + 3\ \text{CO} \rightarrow 2\ \text{Fe} + 3\ \text{CO}_2$, with a yield of $90\ \%$ ($M(\text{Fe}_2\text{O}_3) = 160\ \text{kg/kmol}$; $M(\text{Fe}) = 56\ \text{kg/kmol}$; $M(\text{CO}_2) = 44\ \text{kg/kmol}$).

1. a) Calculate the mass of iron(III) oxide contained in the feed.
2. b) Calculate the theoretical mass of iron.
3. c) Calculate the actual mass of iron with the furnace's yield.
4. d) Calculate the mass of carbon dioxide generated by the reduction reaction.
5. e) The process also uses coke (carbon) as a fuel and as a source of $\text{CO}$: explain why total emissions per metric ton of steel are higher than calculated in d) and cite a technological pathway to reduce them.

Many sulfuric acid plants start from pyrite, an ore of $\text{FeS}_2$. The first stage is roasting: $4\ \text{FeS}_2 + 11\ \text{O}_2 \rightarrow 2\ \text{Fe}_2\text{O}_3 + 8\ \text{SO}_2$; then, $\text{SO}_2$ is oxidized to $\text{SO}_3$ and this is hydrated to $\text{H}_2\text{SO}_4$ ($M(\text{FeS}_2) = 120\ \text{kg/kmol}$; $M(\text{H}_2\text{SO}_4) = 98\ \text{kg/kmol}$; $M(\text{Fe}) = 56\ \text{kg/kmol}$). $1000\ \text{kg}$ of ore with $60\ \%$ pyrite content is processed.

1. a) Calculate the kmol of $\text{FeS}_2$ processed.
2. b) Using the sulfur atoms, verify that each mole of $\text{FeS}_2$ leads to $2\ \text{mol}$ of $\text{H}_2\text{SO}_4$, and calculate the mass of acid obtained.
3. c) The iron(III) oxide generated during roasting can be sent to a blast furnace: calculate the mass of recoverable iron and comment on the economic and environmental advantage of integrating two processes in this way.

A cement plant loads $1000\ \text{kg}$ of limestone with $90\ \%$ of $\text{CaCO}_3$ (the rest being inert impurities) into its kiln. The reaction is $\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$, with $M(\text{CaCO}_3) = 100\ \text{kg/kmol}$, $M(\text{CaO}) = 56\ \text{kg/kmol}$ and $M(\text{CO}_2) = 44\ \text{kg/kmol}$, and the yield of the kiln is $95\ \%$.

1. a) Calculate the mass of calcium carbonate contained in the feed.
2. b) Calculate the theoretical mass and actual mass of quicklime obtained.
3. c) Calculate the mass of carbon dioxide generated by the reaction.
4. d) Propose two technological measures to reduce the carbon footprint of cement manufacturing and briefly justify each one.

A plant wants to produce $480\ \text{kg}$ of titanium via the Kroll process: $\text{TiCl}_4 + 2\ \text{Mg} \rightarrow \text{Ti} + 2\ \text{MgCl}_2$ ($M(\text{TiCl}_4) = 190\ \text{kg/kmol}$; $M(\text{Mg}) = 24\ \text{kg/kmol}$; $M(\text{Ti}) = 48\ \text{kg/kmol}$).

1. a) Calculate the mass of titanium tetrachloride required.
2. b) Calculate the theoretical mass of magnesium and the mass that must be loaded if working with an excess of $25\ \%$.
3. c) Explain why it is advantageous to work with excess magnesium even if it increases the cost of the process, and why the plant subsequently electrolyzes the $\text{MgCl}_2$ obtained to recover the magnesium.

The hydrogen consumed by the Haber process is mostly obtained from methane; the overall process can be written as $\text{CH}_4 + 2\ \text{H}_2\text{O} \rightarrow \text{CO}_2 + 4\ \text{H}_2$ ($M(\text{CO}_2) = 44\ \text{g/mol}$; $M(\text{NH}_3) = 17\ \text{g/mol}$). In the synthesis, $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$.

1. a) Calculate the moles of hydrogen required for each mole of ammonia.
2. b) Calculate the moles of carbon dioxide emitted in obtaining that hydrogen per mole of ammonia.
3. c) Calculate the kilograms of $\text{CO}_2$ emitted per kilogram of ammonia manufactured using this "gray hydrogen".
4. d) With green hydrogen (water electrolysis using renewable electricity), state what that direct emission would be and comment on what other indirect emissions might still exist in ammonia manufacturing.

In a Haber plant operating at high pressure and about $450\ \celsius$, only $15\ \%$ of the nitrogen reacts on each pass through the reactor. $100\ \text{kmol}$ of $\text{N}_2$ enters with sufficient hydrogen ($M(\text{NH}_3) = 17\ \text{kg/kmol}$).

1. a) Calculate the kmol of ammonia obtained in one pass and its mass.
2. b) The unreacted gas is recirculated to the reactor: explain why, as a result, the overall nitrogen utilization approaches $100\ \%$ even though the conversion per pass is low.
3. c) Relate recirculation to the economic and environmental efficiency of the process (raw material and energy per metric ton of product).
4. d) The process is exothermic but requires compressing the gases and maintaining the temperature: comment on what these conditions mean for the plant's energy consumption and why industry seeks more effective catalysts.