Final answer:
To assess if the scuba tank was filled to its 220 bar capacity at 20°C, the ideal gas law must be used to compare the moles of air at the tank's rated pressure and the supplied air at a diver's pressure of 2.37 atm. Calculations will show if the air provided is less than the tank's capacity, indicating it was not filled to the maximum.
Step-by-step explanation:
To determine if the scuba tank was filled to capacity at 20 °C, we can use the ideal gas law (PV=nRT) and compare the total amount of air supplied to the diver at a pressure of 2.37 atm (equivalent to 45 feet depth) against the tank's capacity at a pressure of 220 bar (or 220 times atmospheric pressure).
Assessment
- Convert the tank's rated pressure from bar to atm (1 bar = 0.98692 atm) to maintain consistency with the diver's pressure units.
- Convert the liter measurements into volumes relative to standard conditions (STP: 1 atm, 0 °C).
- Use the ideal gas law to calculate the number of moles (n) of air contained in the scuba tank at its rated pressure and temperature.
- Use the ideal gas law again to calculate the number of moles of air corresponding to the volume of 1860 L of air at 2.37 atm and 20 °C (the diver's conditions).
- Compare the two results to assess if the tank was filled to its capacity.
Placeholder Values:
- 1 bar = 0.98692 atm
- 220 bar = 220 x 0.98692 atm
- R (ideal gas constant) = 0.0821 L·atm/mol·K
- Temperature in Kelvin = 20 °C + 273.15
Upon calculation, if the moles of air calculated at the diver's condition (2.37 atm, 20 °C) are less than the moles of air the tank can hold at its rated condition (220 bar, 20°C), the scuba tank was not filled to capacity.