Question

Humans exhale carbon dioxide when they breathe. if the concentration of carbon dioxide in the air that people breathe gets too high, it can be fatal. therefore, in space shuttles, submarines, and other sealed environments, it is common to use "air scrubbers" to remove carbon dioxide from the air. the air scrubbers on the space shuttle remove carbon dioxide by using lithium hydroxide (lioh). the reaction in the air scrubbers is shown below: co2 2lioh li2co3 h2o each astronaut produces 8.8 × 102 g co2 per day that must be removed from the air on the shuttle. if a typical shuttle mission is 9 days, and the shuttle can carry 3.50 × 104 g lioh, what is the maximum number of people the shuttle can safely carry for one mission?

Answer 1

Answer: 4 people can carry safely for one mission.

Explanation: To calculate the number of moles of $CO_2$ produces by 1 astronaut, we use the formula:

$Moles=\frac{\text{Given mass}}{\text{Molar mass}}$    ....(1)

Molar mass of carbon dioxide = 44 g/mol

Given mass of carbon dioxide = $8.8\times 10^2g$

Putting values in equation 1, we get:

$Moles=\frac{8.8\times 10^2g}{44g/mol}=200moles$

We are given a chemical equation:

$CO_2+2LiOH\rightarrow Li_2CO_3+H_2O$

Moles of LiOH by using equation 1, we get:

Molar mass of LiOH = 24 g/mol

$Moles=\frac{3.40\times 10^4g}{24g/mol}=1458.3moles$

By stoichiometry of the reaction,

2 moles of LiOH produces 1 mole of $CO_2$

So. 1458.3 moles of LiOH will produce = $\frac{1}{2}\times 1458.3=729.15moles$ of $CO_2$

Applying Unitary method:

As, 200 moles of $CO_2$ are produced by 1 astronaut

So, 729.15 moles of $CO_2$ will be produced by = $\frac{1}{200}\times 729.15=3.64\approx 4$ astronauts.

Answer 2

The maximum number of people the shuttle can safely carry for one mission is 4.