Answer: To determine the number of liters of oxygen needed to produce a given number of water molecules, we need to use the concept of stoichiometry and the Avogadro's number.
First, let's find the number of oxygen molecules required to produce 6.518 × 10^22 molecules of water. The balanced chemical equation for the production of water is:
2 H2 + O2 -> 2 H2O
From the equation, we can see that 2 molecules of H2O are produced for every 1 molecule of O2. Therefore, the number of O2 molecules needed is half the number of water molecules:
Number of O2 molecules = (6.518 × 10^22 molecules of water) / 2
Next, we'll use Avogadro's number, which states that 1 mole of any substance contains 6.022 × 10^23 particles (atoms, molecules, etc.). Since we have the number of oxygen molecules, we can calculate the number of moles of oxygen:
Number of moles of O2 = (Number of O2 molecules) / (Avogadro's number)
Finally, we'll convert the number of moles to liters using the ideal gas law, assuming standard temperature and pressure (STP), where 1 mole of any ideal gas occupies 22.4 liters:
Number of liters of O2 = (Number of moles of O2) * (22.4 liters/mole)
Let's calculate the number of liters of oxygen needed:
Number of O2 molecules = (6.518 × 10^22 molecules of water) / 2
Number of moles of O2 = (Number of O2 molecules) / (Avogadro's number)
Number of liters of O2 = (Number of moles of O2) * (22.4 liters/mole)
Plug in the values to calculate the number of liters of oxygen needed.