Final answer:
To produce an average pressure of 1 atm, approximately 1.952 × 10^24 oxygen molecules traveling at a certain speed would be necessary.
Step-by-step explanation:
The question asks about the number of oxygen molecules necessary to produce an average pressure of 1 atm. To answer this, we need to use the ideal gas law and the molar volume of gases at standard temperature and pressure (STP). At STP, 1 mole of any ideal gas occupies a volume of 22.4 liters.
Therefore, in order to determine the number of oxygen molecules necessary to produce an average pressure of 1 atm, we need to calculate the number of moles of oxygen gas required, and then convert that to molecules using Avogadro's number.
Given the volume of the aquarium is 40 L and the partial pressure of O₂ is 0.21 atm, we can use the ideal gas law to calculate the number of moles of O₂:
n = PV/RT = (0.21 atm)(40 L) / (0.0821 L·atm/mol·K)(298 K)
Solving for n, we find that n = 3.242 moles of O₂. To convert this to molecules, we can use Avogadro's number:
N = n * 6.02 × 10^23
Therefore, the number of oxygen molecules necessary to produce an average pressure of 1 atm is approximately 1.952 × 10^24 oxygen molecules.