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Rebreathing Devices In the first episode of George Lucas's Star Wars series, Qui-Gon Jinn and Obi-Wan Kenobi can visit the underwater world of the Gungans only by using A99 Aquata Breathers, which allow them to survive underwater for up to two hours. While the tiny devices may be from the farfetched world of science fiction, current technology exists for transforming carbon dioxide to oxygen. These self- contained rebreathers are used by a select group of underwater cave explorers and can act as self-rescue devices. The chemistry is based on the following chemical reactions, using either potassium superoxide or sodium peroxide:$$\begin{array}{l}4 \mathrm{KO}_{2}(s)+2 \mathrm{CO}_{2}(g) \rightarrow 2 \mathrm{K}_{2}\mathrm{CO}_{3}(s)+3 \mathrm{O}_{2}(g) \\\2 \mathrm{Na}_{2} \mathrm{O}_{2}(s)+2 \mathrm{CO}_{2}(g) \rightarrow 2 \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{O}_{2}(g)\end{array}$$.a. The respiratory rate at rest for an average, healthy adult is 12 breaths per minute. If the average breath takes in \(0.500 \mathrm{L}\) of \(\mathrm{O}_{2}(d=1.429 \mathrm{g} / \mathrm{L})\) into the lungs, how many grams of \(\mathrm{KO}_{2}\) are needed to produce enough oxygen for two hours underwater? b. Would you need more or less \(\mathrm{Na}_{2} \mathrm{O}_{2}\) to produce an equivalent amount of oxygen? c. Given the densities of \(\mathrm{KO}_{2}(2.14 \mathrm{g} / \mathrm{mL})\) and \(\mathrm{Na}_{2} \mathrm{O}_{2}\) \((2.805 \mathrm{g} / \mathrm{mL}),\) which solid material would occupy less volume in a rebreather device?

Step by step solution

01

Calculate the total amount of oxygen inhaled in 2 hours

First, let's find out how much oxygen is inhaled by a person over the course of 2 hours. We know that an average adult takes in 0.500 L of oxygen per breath and breathes 12 times per minute. So in 2 hours (120 minutes), the total oxygen inhaled is: 0.500 L/breath * 12 breaths/minute * 120 minutes = 7200 L of oxygen.

02

Convert L of oxygen to grams

Next, we need to convert the volume of oxygen to grams so that we can use it for stoichiometric calculations. We are given the density of oxygen as 1.429 g/L. To convert this to grams, we simply multiply the volume by the density: 7200 L * 1.429 g/L = 10,288.8 g of oxygen.

03

Calculate the required grams of KO2

To determine the amount of potassium peroxide (KO2) needed to generate this much oxygen, we use the stoichiometric ratio from the balanced chemical equation: 4 KO2 ---> 3 O2. We'll calculate the amount of KO2 required for 10,288.8 g of oxygen: (4 mol KO2 / 3 mol O2) * (10,288.8 g of O2 / 32 g/mol O2) * (71 g/mol KO2) = 10,146.67 g of KO2.

04

Comparing the amount of Na2O2 needed

We will now use the same calculations for sodium peroxide (Na2O2), using the balanced chemical equation: 2 Na2O2 ---> O2. (2 mol Na2O2 / 1 mol O2) * (10,288.8 g of O2 / 32 g/mol O2) * (78 g/mol Na2O2) = 20,103.3 g of Na2O2. Comparing the amounts of both compounds needed, we can see that less KO2 (10,146.67 g) is required compared to Na2O2 (20,103.3 g) to produce the same amount of oxygen.

05

Compare the volume occupied by each solid material

Lastly, we will compare the volumes of the two compounds given their densities: Volume of KO2 = (10,146.67 g) / (2.14 g/mL) = 4743.49 mL. Volume of Na2O2 = (20,103.3 g) / (2.805 g/mL) = 7168.93 mL. So, KO2 would occupy a smaller volume (4743.49 mL) in the rebreather device, as compared to Na2O2 (7168.93 mL).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Potassium Superoxide

Potassium superoxide, chemically represented as KOâ‚‚, plays a crucial role in oxygen regeneration in rebreather systems. These systems are valuable for divers who rely on converting carbon dioxide back into breathable oxygen. Potassium superoxide reacts with carbon dioxide to produce potassium carbonate and oxygen. The balanced chemical equation for this reaction is: \[ 4 \text{KO}_2(s) + 2 \text{CO}_2(g) \rightarrow 2 \text{K}_2\text{CO}_3(s) + 3 \text{O}_2(g) \] Here's how it works in simpler terms: - Potassium superoxide comes in contact with carbon dioxide, often found in exhaled breath. - The reaction results in the production of free oxygen and a byproduct known as potassium carbonate. In the reaction, every four moles of KOâ‚‚ generate three moles of oxygen. This characteristic makes KOâ‚‚ an efficient candidate for oxygen regeneration compared to other chemicals. Its efficacy is evidenced by the smaller mass required to produce a substantial amount of oxygen. While KOâ‚‚ takes less space and mass, handling it needs caution due to its highly reactive nature.

Sodium Peroxide

Sodium peroxide, abbreviated as Naâ‚‚Oâ‚‚, is another chemical used in rebreather devices for oxygen production. It is slightly less efficient than potassium superoxide, but still serves its purpose in certain conditions. When sodium peroxide reacts with carbon dioxide, it yields sodium carbonate and oxygen, as shown in the balanced equation: \[ 2 \text{Na}_2\text{O}_2(s) + 2 \text{CO}_2(g) \rightarrow 2 \text{Na}_2\text{CO}_3(s) + \text{O}_2(g) \] Important points about sodium peroxide: - In the case of Naâ‚‚Oâ‚‚, two moles of this compound are needed to produce just one mole of oxygen. - The requirement for more mass to generate similar oxygen quantities makes it less efficient than KOâ‚‚. Sodium peroxide's higher mass to oxygen generation ratio might result in bulkier and heavier equipment. However, certain situations, like availability or specific reaction conditions, may call for its use over KOâ‚‚. Despite needing more material, Naâ‚‚Oâ‚‚ can be a practical solution in rebreathers if KOâ‚‚ is not an option.

Chemical Stoichiometry

Chemical stoichiometry is a fundamental concept in chemistry that involves calculating the quantities of reactants and products in chemical reactions. It is crucial for understanding the amount of each substance involved in reactions such as those occurring within rebreather devices. Let's explore stoichiometry with these key ideas: - **Balanced Equations**: The balanced chemical equations for KOâ‚‚ and Naâ‚‚Oâ‚‚ reactions are the starting point. They provide the stoichiometric coefficients that indicate the proportions of reactants and products. - **Mole Ratio**: The mole ratio, derived from balanced equations, helps determine the relationship between reactants and products. For example, the ratio of KOâ‚‚ to Oâ‚‚ is 4:3, while it's 2:1 for Naâ‚‚Oâ‚‚ to Oâ‚‚. - **Mass Calculations**: Using the mole ratio and molar masses, it's possible to convert moles of a substance to grams, which is often needed in practical applications like creating rebreather devices. Understanding stoichiometry allows us to precisely calculate how much reactant is required to generate a specific amount of product, like oxygen in this context. This ensures that rebreather devices are efficient and function correctly, as the calculations dictate the right amounts of superoxides needed for adequate oxygen supply.