The build-up of excess carbon dioxide in the air of a...

The build-up of excess carbon dioxide in the air of a submerged submarine is prevented by reacting $\mathrm{CO}_{2}$ with sodium peroxide, $\mathrm{Na}_{2} \mathrm{O}_{2}$ $$2 \mathrm{Na}_{2} \mathrm{O}_{2}(\mathrm{~s})+2 \mathrm{CO}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{~s})+\mathrm{O}_{2}(\mathrm{~g})$$ Calculate the mass of $\mathrm{Na}_{2} \mathrm{O}_{2}$ needed in a $24.0-\mathrm{h}$ period per submariner if each exhales $240 \mathrm{~mL} \mathrm{CO}_{2}$ per minute at $21^{\circ} \mathrm{C}$ and $1.02 \mathrm{~atm} .$

The build-up of excess carbon dioxide in the air of a submerged submarine is prevented by reacting $\mathrm{CO}_{2}$ with sodium peroxide, $\mathrm{Na}_{2} \mathrm{O}_{2}$
$$2 \mathrm{Na}_{2} \mathrm{O}_{2}(\mathrm{~s})+2 \mathrm{CO}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{~s})+\mathrm{O}_{2}(\mathrm{~g})$$
Calculate the mass of $\mathrm{Na}_{2} \mathrm{O}_{2}$ needed in a $24.0-\mathrm{h}$ period per submariner if each exhales $240 \mathrm{~mL} \mathrm{CO}_{2}$ per minute
at $21^{\circ} \mathrm{C}$ and $1.02 \mathrm{~atm} .$

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Key Concepts

Stoichiometry

Stoichiometry involves using a balanced chemical equation to determine the ratios between reactants and products. This concept allows you to calculate the exact amount of a reactant needed or product formed by analyzing the molar proportions in the reaction.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) is a fundamental principle in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is essential for calculating the number of moles of a gas from its volume under specified conditions, thereby linking experimental measurements to theoretical predictions.

Mole Concept

The mole concept is a counting unit in chemistry that expresses amounts of a chemical substance. It provides a bridge between the mass of a substance and the number of individual molecules or atoms, allowing for conversions between grams and moles using the substance's molar mass.

Dimensional Analysis

Dimensional analysis is a systematic method for converting units and ensuring that calculations maintain consistent units across all terms. It is used to convert measurements such as volume, pressure, and time in order to apply them accurately within formulas like the Ideal Gas Law.

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