Question

One problem concerning space flight is the removal of carbon dioxide \(\left(\mathrm{CO}_{2}\right.\), molecular weight \(\left.=44.0 \mathrm{~g} / \mathrm{mole}\right)\) emitted by the human body (about \(924 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) per day). One solution is to react \(\mathrm{CO}_{2}\) with sodium hydroxide \((\mathrm{NaOH}\), molecular weight \(=40.0 \mathrm{~g} / \mathrm{mole}\) ) to form water and sodium carbonate \(\left(\mathrm{Na}_{2} \mathrm{CO}_{3}\right.\), molecular weight \(\left.=94 \mathrm{~g} / \mathrm{mole}\right)\) according to the following reation: \(2 \mathrm{NaOH}+\mathrm{CO}_{2} \rightarrow \mathrm{NaCO}_{3}+\mathrm{H}_{2} \mathrm{O}\) How much \(\mathrm{NaOH}\) must be carried on board a space capsule to remove the \(\mathrm{CO}_{2}\) produced by an astronaut on a 10 day flight?

Short answer

Therefore, \(16800 \: \text{g}\) of NaOH must be carried on board a space capsule to remove the CO₂ produced by an astronaut on a 10-day flight.

Step-by-step solution

Convert the mass of CO₂ produced per day to moles

To convert the mass of CO₂ produced to moles, we can use the following formula: \[number\:of\:moles=\frac{mass}{molecular\:weight}\] For CO₂, the mass produced per day is 924 g and the molecular weight is 44.0 g/mole. Thus, the number of moles of CO₂ produced per day is: \[moles\:of\:CO_{2}=\frac{924\:g}{44.0\:g/mole}\]

Determine the moles of NaOH required for the reaction

From the chemical equation, we know that 2 moles of NaOH react with 1 mole of CO₂. \[2\:NaOH + CO_{2}\rightarrow Na_{2}CO_{3} + H_{2}O\] So, to determine the moles of NaOH required for the reaction, we can multiply the moles of CO₂ produced by 2: \[moles\:of\:NaOH = 2\:moles\:CO_{2}\]

Convert the moles of NaOH to grams

To convert the moles of NaOH to grams, we can use the following formula: \[mass = number\:of\:moles \times molecular\:weight\] For NaOH, the molecular weight is 40.0 g/mole. Thus, the mass of NaOH required per day is: \[mass\:of\:NaOH = moles\:of\:NaOH \times 40.0\:g/mole\]

Calculate the total mass of NaOH needed for a 10-day flight

To find the total mass of NaOH needed for a 10-day flight, multiply the mass of NaOH required per day by the number of days (10): \[total\:mass\:of\:NaOH = 10\:days \times mass\:of\:NaOH\:per\:day\] Now, let's plug in the values and calculate the total mass of NaOH required for the flight: Moless of CO₂ produced per day: \[moles\:of\:CO_{2}=\frac{924\:g}{44.0\:g/mole} = 21\:moles\] Moles of NaOH required for the reaction: \[moles\:of\:NaOH = 2 \times 21\:moles\:CO_{2} = 42\:moles\] Mass of NaOH required per day: \[mass\:of\:NaOH = 42\:moles \times 40.0\:g/mole = 1680\:g\] Total mass of NaOH needed for a 10-day flight: \[total\:mass\:of\:NaOH = 10\:days \times 1680\:g/day = 16800\:g\] Therefore, 16800 g of NaOH must be carried on board a space capsule to remove the CO₂ produced by an astronaut on a 10-day flight.

Key concepts

Mole Concept

In chemistry, the mole concept is crucial for understanding the relationships between quantities of substances in reactions. A mole is a unit that measures the amount of substance. It corresponds to the number of atoms in 12 grams of carbon-12, which is approximately Avogadro’s number, \(6.022 \times 10^{23}\) particles.

In the exercise, we deal with carbon dioxide (\(\mathrm{CO}_{2}\)) and sodium hydroxide (\(\mathrm{NaOH}\)), and we need to convert grams into moles to understand how much \(\mathrm{NaOH}\) is required to react with \(\mathrm{CO}_{2}\). The formula \( \text{Number of moles} = \frac{\text{mass}}{\text{molecular weight}} \) is used here. This conversion is vital for stoichiometric calculations, ensuring the correct proportions of reactants and products in chemical reactions.

Understanding the mole concept allows us to convert real-world measurements into moles and back, which is necessary to perform any meaningful chemical calculation, such as determining the requirements for a space flight.

Chemical Reactions

Chemical reactions involve the transformation of substances, termed reactants, into new substances, called products. The stoichiometry of a reaction tells us the quantities of reactants needed and products formed, based on balanced chemical equations.

In the given problem, the reaction used to remove \(\mathrm{CO}_{2}\) in a spacecraft is: \[2 \ \mathrm{NaOH} + \mathrm{CO}_{2} \rightarrow \mathrm{Na}_{2}\mathrm{CO}_{3} + \mathrm{H}_{2}O\] This balanced equation informs us that two moles of \(\mathrm{NaOH}\) are required to react with one mole of \(\mathrm{CO}_{2}\) to produce water and sodium carbonate.

The stoichiometry here ensures that all produced \(\mathrm{CO}_{2}\) during the space flight is efficiently neutralized by the available \(\mathrm{NaOH}\). Careful calculations, based on stoichiometry principles, help prevent excess waste and ensure safety during missions.

Space Flight Chemistry

Space flight chemistry focuses on the chemical processes and safety protocols necessary for astronauts' wellbeing and the successful completion of missions. When humans are in space, they exhale \(\mathrm{CO}_{2}\), which must be removed for safe and breathable air.

In the practical context of a space flight mission, we must calculate the precise amounts of chemicals needed to maintain life-supporting conditions. The problem involves calculating how much \(\mathrm{NaOH}\) is essential to eliminate the daily production of \(\mathrm{CO}_{2}\) by an astronaut over 10 days.

• The use of \(\mathrm{NaOH}\) for \(\mathrm{CO}_{2}\) removal is an example of a crucial reaction in life support systems.
• Ensures that enclosed environments, like spacecraft, do not accumulate toxic levels of \(\mathrm{CO}_{2}\).
• Demands precise chemical management to avoid unnecessary cargo weight and to ensure the safety of all onboard.

Space flight chemistry is a vital and exciting field, integrating rigorous chemical calculations and safety measures to ensure successful human space exploration.