Question

The space shuttle environmental control system handled excess \(\mathrm{CO}_{2}\) (which the astronauts breathe out; it is 4.0\(\%\) by mass of exhaled air) by reacting it with lithium hydroxide, LiOH, pellets to form lithium carbonate, Li \(_{2} \mathrm{CO}_{3},\) and water. If there were seven astronauts on board the shuttle, and each exhales \(20 .\) L of air per minute, how long could clean air be generated if there were \(25,000\) g of LiOH pellets available for each shuttle mission? Assume the density of air is 0.0010 \(\mathrm{g} / \mathrm{mL}\) .

Short answer

Clean air could be generated for approximately 4103.09 minutes, or about 68 hours and 23 minutes, using 25,000 g of LiOH pellets for the given shuttle mission.

Step-by-step solution

Calculate the total mass of exhaled air by the astronauts per minute

Let's find the total mass of exhaled air per minute by all seven astronauts. As the density of air is 0.0010 g/mL and each astronaut exhales 20 L of air per minute, we can calculate the mass as follows: Total volume of exhaled air by 7 astronauts = 7 astronauts * 20 L/minute * 1000 mL/L = 140,000 mL/minute Mass of exhaled air = Volume * Density = 140,000 mL/minute * 0.0010 g/mL = 140 g/minute

Calculate the total mass of exhaled CO2 by the astronauts per minute

Given that the CO2 comprises 4% of the mass of exhaled air, we can calculate the mass of CO2 exhaled per minute as: Mass of CO2 = 4% of Mass of exhaled air per minute = (4/100) * 140 g/minute = 5.6 g/minute

Write the balanced chemical equation for the reaction

We are given that the CO2 reacts with LiOH to form Li2CO3 and water. Writing and balancing the chemical equation for the reaction: 2 LiOH + CO2 → Li2CO3 + H2O

Determine the mass of CO2 that reacts with the given mass of LiOH

First, we need to find the moles of LiOH, given that there are 25,000 g of LiOH pellets available. The molar mass of LiOH = 6.94 (Li) + 15.999 (O) + 1.007 (H) = 23.95 g/mol. Moles of LiOH = Mass / Molar mass = 25,000 g / 23.95 g/mol = 1043.84 mol Now, from the balanced equation, 2 moles of LiOH react with 1 mole of CO2. Therefore, the moles of CO2 that react with 1043.84 moles of LiOH = 1043.84/2 = 521.92 moles. The molar mass of CO2 = 12.01 (C) + 15.999 x 2 (O) = 44.009 g/mol. Mass of CO2 that can react with 25,000 g of LiOH: = 521.92 mol * 44.009 g/mol = 22,977.32 g

Calculate the duration for which the LiOH pellets can generate clean air

Now that we know the mass of CO2 that can react with the given mass of LiOH and the mass of CO2 exhaled by astronauts per minute, we can calculate the duration for which clean air can be generated as: Duration = (Mass of CO2 that can react with LiOH) / (Mass of CO2 exhaled per minute) = 22,977.32 g / 5.6 g/minute = 4103.09 minutes Therefore, clean air could be generated for approximately 4103.09 minutes, or about 68 hours and 23 minutes, using 25,000 g of LiOH pellets for the given shuttle mission.

Key concepts

Molar Mass Calculation

Molar mass is crucial in stoichiometry, which involves calculations during chemical reactions.
The molar mass of a compound is the mass of one mole of that substance.
It's calculated by adding the atomic masses of all atoms in the molecule. These atomic masses can be found on the periodic table. Let's consider lithium hydroxide (LiOH) as an example. Lithium has an atomic mass of 6.94 g/mol, oxygen is 15.999 g/mol, and hydrogen is 1.007 g/mol. By adding these together, we find the molar mass of LiOH:

• Li: 6.94 g/mol
• O: 15.999 g/mol
• H: 1.007 g/mol

Adding these: 6.94 + 15.999 + 1.007 = 23.95 g/mol.
Understanding molar mass is essential as it allows us to convert between grams of a substance and moles, an important step for stoichiometry.

Chemical Reaction

Chemical reactions describe how substances interact to form new products.
They involve breaking and forming bonds, changing the arrangement of atoms.
In our exercise, the chemical reaction between carbon dioxide (\(\mathrm{CO}_2\)) and lithium hydroxide (LiOH) produces lithium carbonate (\(\mathrm{Li}_2\mathrm{CO}_3\)) and water (\(\mathrm{H}_2\mathrm{O}\)).This specific reaction is vital for maintaining the environment inside a shuttle. When astronauts exhale, they produce \(\mathrm{CO}_2\).
Reacting with LiOH, \(\mathrm{CO}_2\) is converted into solid \(\mathrm{Li}_2\mathrm{CO}_3\), effectively removing it from the air.
This process is crucial for keeping the air breathable for astronauts during their mission.

Balanced Equation

Balancing chemical equations ensures that the same number of each type of atom exists on both sides of the equation. This reflects the law of conservation of mass.
In our case, we have:\[2 \mathrm{LiOH} + \mathrm{CO}_2 \rightarrow \mathrm{Li}_2\mathrm{CO}_3 + \mathrm{H}_2\mathrm{O}\]This balanced equation shows that two hydroxide ions are necessary to react with one carbon dioxide molecule.
This balance is important because it allows us to understand the exact ratios of reactants needed to fully complete the reaction without leftover elements.
In this example, two LiOH molecules react to form one \(\mathrm{Li}_2\mathrm{CO}_3\) molecule and one molecule of water. Balancing equations is a significant skill for anyone studying chemistry, as it facilitates accurate calculations and predictions in reactions.

Environmental Control System

In space missions, an environmental control system (ECS) is vital for maintaining a livable atmosphere in the spaceship or space station.
It involves complex systems that handle life-supporting tasks such as temperature regulation and air purification.For example, using LiOH pellets to absorb exhaled \(\mathrm{CO}_2\) is a crucial function of the ECS.
The system ensures that the amount of \(\mathrm{CO}_2\) does not reach harmful levels.
This is essential as too much \(\mathrm{CO}_2\) can lead to serious health issues.
By removing excess \(\mathrm{CO}_2\) and providing clean air, the ECS helps keep astronauts safe and comfortable during their mission. Understanding how these systems work is crucial, particularly in designing effective solutions that permit extended human presence in space.