To determine the volume in cm³ of carbon dioxide (CO₂) discharged by the human body each day, we need to follow a series of steps involving the molar mass of CO₂ and the volume it occupies at standard temperature and pressure (STP).
1. Determine the molar mass of CO₂:
- Carbon dioxide (CO₂) is composed of one carbon (C) atom and two oxygen (O) atoms.
- The atomic mass of carbon (C) is 12 grams/mole.
- The atomic mass of oxygen (O) is 16 grams/mole.
- Therefore, the molar mass of CO₂ = 12 + 162 = 44 grams/mole.
2. Calculate the number of moles of CO₂ discharged each day:
- Given that the human body discharges 925 grams of CO₂ each day,
- Number of moles of CO₂ = mass (grams) / molar mass (grams/mole).
- Number of moles of CO₂ = 925 grams / 44 grams/mole ≈ 21.0227 moles.
3. Determine the volume occupied by one mole of CO₂ at STP:
- At standard temperature and pressure, one mole of any gas occupies 22.414 liters.
- 1 liter = 1000 cm³.
- Therefore, 22.414 liters = 22.414 1000 cm³ = 22414 cm³.
4. Calculate the total volume of CO₂ discharged in cm³:
- The volume of CO₂ = number of moles volume occupied per mole.
- Volume of CO₂ = 21.0227 moles 22414 cm³/mole ≈ 471203.4091 cm³.
Thus, the human body discharges approximately 471203.4091 cm³ of carbon dioxide each day at standard temperature and pressure.
