Given the data from the question, the astronauts do not have enough sodium hydroxide in the cabin to cleanse the cabin air of the carbon dioxide.
<h3>How to determine the total CO₂</h3>
- CO₂ emitted per astronaut per day = 500 g
- CO₂ for 3 astronaut per day = 3 × 500 = 1500 g
- CO₂ for 3 astronaut for 2 days = 2 × 1500 = 3000 g
<h3>Balanced equation </h3>
2NaOH + CO₂ —>Na₂CO₃ + H₂O
Molar mass of NaOH = 40 g/mol
Mass of NaOH from the balanced equation = 2 × 40 = 80 g
Molar mass of CO₂ = 44 g/mol
Mass of CO₂ from the balanced equation = 1 × 44 = 44 g
SUMMARY
From the balanced equation above,
44 g of CO₂ required 80 g of NaOH
<h3>How to determine the mass of NaOH needed </h3>
From the balanced equation above,
44 g of CO₂ required 80 g of NaOH
Therefore,
3000 g of CO₂ will require = (3000 × 80) / 44 = 5454.55 g of NaOH
From the calculation made above, we can see that 5454.55 g of NaOH is needed by the astronaut to clean the cabin air but unfortunately, they only have 5000 g of NaOH.
Thus, we can conclude that the astronauts do not have enough NaOH to clean the air
Learn more about stoichiometry:
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