Balancing equations Original Scenario-Based Download PDF

Questions

1. 1.

   A geothermal filtration facility within the volcanic mantle of an ocean moon neutralizes corrosive chlorine gas by reacting it with hot aqueous potassium hydroxide. The scrubbing process proceeds according to the unbalanced chemical equation $a\text{Cl}_2\text{(g)} + b\text{KOH(aq)} \rightarrow c\text{KCl(aq)} + d\text{KClO}_3\text{(aq)} + e\text{H}_2\text{O(l)}$. When this chemical equation is balanced using the lowest whole-number coefficients, what is the ratio of the stoichiometric coefficient of potassium hydroxide to that of potassium chlorate ($b : d$)?

   • A) 6 : 1
   • B) 3 : 1
   • C) 2 : 1
   • D) 5 : 1
2. 2.

   Aboard an exploratory research vessel drifting through the upper atmosphere of a gas giant, an automated flare beacon ignites phosphine gas with collected atmospheric oxygen to signal its survey drone. The combustion proceeds according to the unbalanced chemical equation $a\text{PH}_3\text{(g)} + b\text{O}_2\text{(g)} \rightarrow c\text{P}_4\text{O}_{10}\text{(s)} + d\text{H}_2\text{O}\text{(g)}$. When this equation is balanced using the lowest whole-number coefficients, what is the value obtained by subtracting the sum of the product coefficients from the sum of the reactant coefficients, calculated as $(a + b) - (c + d)$?

   • A) 5
   • B) 1
   • C) 7
   • D) 12
3. 3.

   Deep beneath the ice crust of an extraterrestrial moon, an autonomous exploration probe generates methane propellant by reacting stored aluminum carbide with subglacial liquid water. The process follows the unbalanced chemical equation $a\text{Al}_4\text{C}_3\text{(s)} + b\text{H}_2\text{O}\text{(l)} \rightarrow c\text{Al(OH)}_3\text{(s)} + d\text{CH}_4\text{(g)}$. To program the reactant metering valves, which ordered set of the lowest whole-number coefficients $(a, b, c, d)$ correctly balances this reaction?

   • A) (1, 6, 2, 3)
   • B) (2, 12, 4, 3)
   • C) (1, 12, 4, 3)
   • D) (2, 24, 8, 6)
4. 4.

   Aboard an automated orbital smelting facility stationed above a sulfurous exoplanet, industrial processors roast pyrite ore to yield solid iron(III) oxide and gaseous sulfur dioxide according to the unbalanced reaction $a \text{FeS}_2\text{(s)} + b \text{O}_2\text{(g)} \rightarrow c \text{Fe}_2\text{O}_3\text{(s)} + d \text{SO}_2\text{(g)}$. To calibrate the gas injection valves, the station computer requires the coefficients to be balanced using the smallest possible whole numbers. What is the sum of the stoichiometric coefficients, calculated as $(a + b + c + d)$?

   • A) 21
   • B) 25
   • C) 27
   • D) 13
5. 5.

   Deep within the subterranean bio-dome of an uncharted volcanic moon, an automated atmospheric scrubber neutralizes toxic nitrogen dioxide by reacting it with gaseous ammonia according to the reaction $w\,\text{NH}_3\text{(g)} + x\,\text{NO}_2\text{(g)} \rightarrow y\,\text{N}_2\text{(g)} + z\,\text{H}_2\text{O}\text{(g)}$. To ensure optimal life-support performance, the habitat computer must calibrate its mass-flow sensors based on the exact stoichiometry. When this chemical equation is balanced using the lowest whole-number coefficients, what is the value of the stoichiometric coefficient $y$ for nitrogen gas ($\text{N}_2$)?

   • A) 7
   • B) 4
   • C) 6
   • D) 8