Mole ratios Transitional Reasoning Practice

Questions

1. 1.

   In the industrial Kroll process, titanium(IV) chloride vapor is reduced by molten magnesium inside a high-temperature batch reactor according to the equation $\text{TiCl}_4\text{(g)} + 2\text{Mg(l)} \rightarrow \text{Ti(s)} + 2\text{MgCl}_2\text{(l)}$. A metallurgical engineer prepares a reaction charge that must completely consume 48.0 moles of magnesium. Based on the stoichiometric mole ratios of the balanced reaction, what amount of $\text{TiCl}_4$ is required, and what is the mole ratio of $\text{MgCl}_2$ byproduct formed to elemental $\text{Ti}$ produced?

   • A) 96.0 mol of $\text{TiCl}_4$, with a mole ratio of 1 : 2
   • B) 48.0 mol of $\text{TiCl}_4$, with a mole ratio of 1 : 1
   • C) 24.0 mol of $\text{TiCl}_4$, with a mole ratio of 1 : 2
   • D) 24.0 mol of $\text{TiCl}_4$, with a mole ratio of 2 : 1
2. 2.

   An analytical chemist investigates the roasting of an unknown copper sulfide mineral, $\text{Cu}_x\text{S}_y$, in the presence of excess oxygen gas according to the general reaction $\text{Cu}_x\text{S}_y\text{(s)} + \left(\frac{x}{2} + y\right)\text{O}_2\text{(g)} \rightarrow x\,\text{CuO(s)} + y\,\text{SO}_2\text{(g)}$. In a laboratory trial, the complete reaction of 0.250 moles of $\text{Cu}_x\text{S}_y$ produces exactly 0.500 moles of solid copper(II) oxide, $\text{CuO}$, and 0.250 moles of sulfur dioxide gas, $\text{SO}_2$. Based on these quantitative mole ratios, what is the chemical formula of the mineral, and what is the stoichiometric mole ratio of $\text{O}_2$ consumed to $\text{CuO}$ produced in the balanced equation?

   • A) Formula: $\text{CuS}$; stoichiometric mole ratio of $\text{O}_2$ to $\text{CuO}$ is $3 : 2$
   • B) Formula: $\text{CuS}_2$; stoichiometric mole ratio of $\text{O}_2$ to $\text{CuO}$ is $2 : 1$
   • C) Formula: $\text{Cu}_2\text{S}$; stoichiometric mole ratio of $\text{O}_2$ to $\text{CuO}$ is $2 : 1$
   • D) Formula: $\text{Cu}_2\text{S}$; stoichiometric mole ratio of $\text{O}_2$ to $\text{CuO}$ is $1 : 1$
3. 3.

   In an industrial synthesis of silicon carbide, solid silicon dioxide reacts with carbon in an electric arc furnace according to the equation $\text{SiO}_2(\text{s}) + 3\text{C}(\text{s}) \rightarrow \text{SiC}(\text{s}) + 2\text{CO}(\text{g})$. A reaction mixture containing 12.0 moles of silicon dioxide and 30.0 moles of carbon is heated until the limiting reactant is completely consumed. Based on the stoichiometric mole ratios of the balanced equation, what amount of the excess reactant remains unreacted, and what amount of carbon monoxide gas is evolved?

   • A) 2.0 moles of carbon remaining and 20.0 moles of carbon monoxide evolved
   • B) 6.0 moles of silicon dioxide remaining and 10.0 moles of carbon monoxide evolved
   • C) 4.0 moles of silicon dioxide remaining and 15.0 moles of carbon monoxide evolved
   • D) 2.0 moles of silicon dioxide remaining and 20.0 moles of carbon monoxide evolved
4. 4.

   In an automotive airbag system, solid sodium azide decomposes rapidly upon impact according to the equation $2\text{NaN}_3\text{(s)} \rightarrow 2\text{Na(s)} + 3\text{N}_2\text{(g)}$. To neutralize the reactive sodium byproduct, potassium nitrate is incorporated to react according to the equation $10\text{Na(s)} + 2\text{KNO}_3\text{(s)} \rightarrow \text{K}_2\text{O(s)} + 5\text{Na}_2\text{O(s)} + \text{N}_2\text{(g)}$. If a deployment event produces 4.50 moles of nitrogen gas in the primary decomposition reaction, what amount of potassium nitrate is stoichiometrically required to completely consume all the sodium metal produced?

   • A) 3.00 mol
   • B) 1.50 mol
   • C) 0.90 mol
   • D) 0.60 mol
5. 5.

   A chemical technician monitors the complete combustion of propane gas according to the balanced equation $\text{C}_3\text{H}_8\text{(g)} + 5\text{O}_2\text{(g)} \rightarrow 3\text{CO}_2\text{(g)} + 4\text{H}_2\text{O(g)}$. During a trial run, the reaction goes to completion and yields exactly 2.40 moles of water vapor. Based on the stoichiometric mole ratios of this reaction, what amount of oxygen gas was consumed and what initial amount of propane was reacted?

   • A) 1.92 mol $\text{O}_2$ consumed and 0.48 mol $\text{C}_3\text{H}_8$ reacted
   • B) 2.00 mol $\text{O}_2$ consumed and 0.80 mol $\text{C}_3\text{H}_8$ reacted
   • C) 2.40 mol $\text{O}_2$ consumed and 0.60 mol $\text{C}_3\text{H}_8$ reacted
   • D) 3.00 mol $\text{O}_2$ consumed and 0.60 mol $\text{C}_3\text{H}_8$ reacted

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