Stoichiometry in industrial processes

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.

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 ($M(\text{HCl}) = 36,5\ \text{g/mol}$).

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.

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 $100\ \%$.

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.

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.

A steelworks 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.

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 tonnes.
4. d) Calculate the actual production with the specified yield.
5. e) Calculate the tonnes 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 tonne of steel are higher than calculated in d) and cite a technological pathway to reduce them.

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.

Copper can be obtained via two routes: A) $\text{CuO} + \text{H}_2 \rightarrow \text{Cu} + \text{H}_2\text{O}$; B) $\text{Fe} + \text{CuSO}_4 \rightarrow \text{Cu} + \text{FeSO}_4$ ($M(\text{CuO}) = 80\ \text{g/mol}$; $M(\text{H}_2) = 2\ \text{g/mol}$; $M(\text{CuSO}_4) = 160\ \text{g/mol}$; $M(\text{Fe}) = 56\ \text{g/mol}$; $M(\text{Cu}) = 64\ \text{g/mol}$). The atom economy of a route is the percentage represented by the mass of the desired product over the total mass of the reactants.

1. a) Calculate the atom economy of each route.
2. b) Decide which is "greener" according to that criterion and justify your answer.
3. c) State two additional factors (economic, energetic or environmental) that a company would consider before choosing a route and comment on why the less atom-efficient route might end up being used.

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 "grey 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.