Stoichiometry and Gases

Silicon carbide, $\mathrm{SiC}$, is produced industrially by a high-temperature reaction between silicon dioxide and elemental carbon according to the unbalanced chemical equation:

$$\mathrm{SiO_2(s) + C(s) \rightarrow SiC(s) + CO(g)}$$

For an initial charge of $150.0\,\text{g}$ of silicon dioxide with a purity of $80.0\,\%$ by mass and sufficient carbon:

1. a) Balance the chemical equation by inspection.
2. b) Calculate the mass of $\mathrm{SiC}$, in grams, that would theoretically be obtained if the reaction proceeds with a yield of $100\,\%$.

Data: Atomic masses: $\mathrm{C} = 12.01$; $\mathrm{O} = 16.00$; $\mathrm{Si} = 28.09$.

In the lab, the synthesis of an insoluble precipitate is planned by mixing two aqueous solutions stored in separate containers, as outlined below:

Container 1 holds $150.0\,\text{mL}$ of aqueous barium chloride solution, $\mathrm{BaCl_2}$, of concentration $0.200\,\text{M}$. Container 2 holds $250.0\,\text{mL}$ of aqueous sodium sulfate solution, $\mathrm{Na_2SO_4}$, of concentration $0.160\,\text{M}$. When both contents are poured completely into the same beaker, quantitative precipitation of barium sulfate, $\mathrm{BaSO_4(s)}$, takes place according to the equation:

$$\mathrm{BaCl_2(aq) + Na_2SO_4(aq) \rightarrow BaSO_4(s) + 2\,NaCl(aq)}$$

1. a) Identify, with justification, the limiting reagent.
2. b) Calculate the mass of $\mathrm{BaSO_4(s)}$ that precipitates and the molar concentration of the excess reagent remaining dissolved in the final mixture (assume additive volumes).

Data: Relative atomic masses: $\mathrm{O} = 16.00$; $\mathrm{Na} = 22.99$; $\mathrm{S} = 32.06$; $\mathrm{Cl} = 35.45$; $\mathrm{Ba} = 137.33$.

Metallic titanium is obtained by the Kroll process, by reacting gaseous titanium tetrachloride with liquid magnesium according to the balanced equation:

$$\mathrm{TiCl_4(g) + 2\,Mg(l) \rightarrow Ti(s) + 2\,MgCl_2(l)}$$

$379.4\,\text{g}$ of $\mathrm{TiCl_4}$ and excess magnesium are placed in a reactor. Once the process is complete and the mixture has cooled, $81.4\,\text{g}$ of pure metallic titanium is isolated experimentally.

1. a) Calculate the theoretical amount of titanium, in grams, that should have been obtained.
2. b) Determine the percent yield of the process.

Data: Relative atomic masses: $\mathrm{Cl} = 35.45$; $\mathrm{Ti} = 47.87$; $\mathrm{Mg} = 24.31$.

Impure calcium carbide reacts with liquid water to produce acetylene gas (ethyne, $\mathrm{C_2H_2}$) and calcium hydroxide according to:

$$\mathrm{CaC_2(s) + 2\,H_2O(l) \rightarrow C_2H_2(g) + Ca(OH)_2(aq)}$$

A sample of $12.50\,\text{g}$ of calcium carbide with inert impurities is available, and its purity is to be determined. When it is treated with excess water at a temperature of $22.0\,^{\circ}\text{C}$ and under a constant pressure of $0.980\,\text{atm}$, a volume of $4.15\,\text{L}$ of acetylene is collected, after drying and assuming ideal gas behavior, with the reaction proceeding at a yield of $92.0\,\%$.

1. a) Calculate the moles of acetylene that would theoretically have been generated if the yield had been $100\,\%$.
2. b) Determine the percentage purity in $\mathrm{CaC_2}$ of the initial sample analyzed.

Data: Relative atomic masses: $\mathrm{C} = 12.01$; $\mathrm{Ca} = 40.08$. $R = 0.082\,\text{atm}\times\text{L}/(\text{mol}\times\text{K})$.

A closed, rigid container of capacity $10.0\,\text{L}$ contains $0.650\,\text{mol}$ of nitrogen gas, $\mathrm{N_2}$, at a temperature of $25.0\,^{\circ}\text{C}$.

1. a) Determine the pressure exerted by the gas inside the container, in atmospheres and in pascals.
2. b) If the container is heated to a temperature of $120.0\,^{\circ}\text{C}$, calculate the new pressure of the nitrogen in atmospheres, assuming ideal gas behavior.

Data: Universal ideal gas constant $R = 0.082\,\text{atm}\times\text{L}/(\text{mol}\times\text{K}) = 8,314\,\text{J}/(\text{mol}\times\text{K})$; $1\,\text{atm} = 101325\,\text{Pa}$.

A rigid container of capacity $5.00\,\text{L}$ contains at $300\,\text{K}$ a gas mixture made up of $4.40\,\text{g}$ of propane, $\mathrm{C_3H_8}$, and $11.20\,\text{g}$ of argon gas, $\mathrm{Ar}$ (inert). Then $16.00\,\text{g}$ of oxygen, $\mathrm{O_2}$, is injected into the container and complete combustion of the hydrocarbon is initiated by an electric spark, producing carbon dioxide and water vapor according to:

$$\mathrm{C_3H_8(g) + 5\,O_2(g) \rightarrow 3\,CO_2(g) + 4\,H_2O(g)}$$

After combustion has finished, the temperature of the chamber is adjusted to $450\,\text{K}$, with all substances remaining in the gas phase.

1. a) Identify the limiting reagent of the combustion.
2. b) Determine the partial pressure of the argon and the total pressure of the final gas mixture in the container at $450\,\text{K}$.

Data: Relative atomic masses: $\mathrm{H} = 1,008$; $\mathrm{C} = 12.01$; $\mathrm{O} = 16.00$; $\mathrm{Ar} = 39.95$. $R = 0.082\,\text{atm}\times\text{L}/(\text{mol}\times\text{K})$.

A rigid reactor of $8.20\,\text{L}$ initially contains at $500\,\text{K}$ a mixture with $0.400\,\text{mol}$ of carbon monoxide, $\mathrm{CO}$, $0.300\,\text{mol}$ of water vapor, $\mathrm{H_2O}$, and $0.500\,\text{mol}$ of helium gas, $\mathrm{He}$ (inert gas). The temperature is raised to $700\,\text{K}$ in the presence of a suitable catalyst so that the water–gas shift reaction takes place:

$$\mathrm{CO(g) + H_2O(g) \rightarrow CO_2(g) + H_2(g)}$$

When the final state of the reaction is reached at $700\,\text{K}$, the total pressure inside the reactor is $8.40\,\text{atm}$. An independent analysis indicates that the mole fraction of carbon dioxide is $0.200$. Assume ideal gases.

1. a) Show whether the total number of moles of gas changes during the reaction and explain why the total pressure alone would not allow the yield to be determined. Use the composition analysis to calculate it.
2. b) Calculate the mole fraction of each component in the resulting gas mixture and the partial pressure of $\mathrm{H_2}$ at $700\,\text{K}$.

Data: Universal gas constant $R = 0.082\,\text{atm}\times\text{L}/(\text{mol}\times\text{K})$.

A solid sample of $4,800\,\text{g}$ consisting exclusively of a homogeneous mixture of calcium carbonate, $\mathrm{CaCO_3}$, and magnesium carbonate, $\mathrm{MgCO_3}$, is subjected to exhaustive thermal calcination in a furnace until complete decomposition into the respective solid oxides and carbon dioxide:

$$\mathrm{CaCO_3(s) \rightarrow CaO(s) + CO_2(g)}$$ $$\mathrm{MgCO_3(s) \rightarrow MgO(s) + CO_2(g)}$$

All the $\mathrm{CO_2}$ gas released is confined in a sealed closed container of $2,500\,\text{L}$, into which $0.0200\,\text{mol}$ of neon gas, $\mathrm{Ne}$ (inert), had previously been introduced. After the container stabilizes at a temperature of $320\,^{\circ}\text{C}$, the total pressure of the system is measured.

1. a) If the mass of the solid residue formed by the oxides after calcination is $2,424\,\text{g}$, calculate the percentage by mass of each carbonate in the initial mixture.
2. b) Determine the total pressure and the partial pressure of $\mathrm{CO_2}$ in the container after the gas has been added at $320\,^{\circ}\text{C}$.

Data: Relative atomic masses: $\mathrm{C} = 12.01$; $\mathrm{O} = 16.00$; $\mathrm{Mg} = 24.31$; $\mathrm{Ca} = 40.08$. $R = 0.082\,\text{atm}\times\text{L}/(\text{mol}\times\text{K})$.

To determine the purity of a sample of commercial granulated metallic zinc containing inert impurities, $3,500\,\text{g}$ of this sample is reacted with an excess of aqueous hydrochloric acid solution according to:

$$\mathrm{Zn(s) + 2\,HCl(aq) \rightarrow ZnCl_2(aq) + H_2(g)}$$

The hydrogen gas produced is collected over water in an inverted graduated cylinder at a temperature of $25.0\,^{\circ}\text{C}$. The volume of gas measured is $1,240\,\text{L}$ and the external barometric pressure in the lab is $752.0\,\text{mmHg}$. The water levels inside and outside the cylinder are equal. The zinc reaction is complete, but only $95.0\,\%$ of the hydrogen generated is recovered in the cylinder. Assume ideal behavior.

1. a) Calculate the partial pressure due exclusively to the dry hydrogen gas inside the cylinder.
2. b) Determine the mass of pure zinc that reacted and the percentage purity of the sample analyzed.

Data: Relative atomic masses: $\mathrm{H} = 1,008$; $\mathrm{Zn} = 65.38$. Saturated vapor pressure of water at $25.0\,^{\circ}\text{C} = 23.8\,\text{mmHg}$; $1\,\text{atm} = 760\,\text{mmHg}$; $R = 0.082\,\text{atm}\times\text{L}/(\text{mol}\times\text{K})$.