Final answer:
The pressure of O₂ in the flask can be calculated using the ideal gas law and the van der Waals equation. The ideal gas law equation is P = (nRT) / V, and the van der Waals equation is (P + (an^2 / V^2)) * (V - nb) = nRT. The difference between these two equations arises from the consideration of the volume and attractions between gas molecules in the van der Waals equation.
Step-by-step explanation:
(a) According to the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant (0.0821 L.atm/mol.K), and T is the temperature in Kelvin. We can rearrange this equation to solve for pressure:
P = (nRT) / V
Plugging in the values from the question, we have:
P = (0.36 mol * 0.0821 L.atm/mol.K * 225 K) / 300 mL
P = 0.01378 atm
(b) The van der Waals equation corrects for the volume and attractions between gas molecules. It is given by:
(P + (an^2 / V^2)) * (V - nb) = nRT
Plugging in the values, we have:
(P + (0.138 J.m³/mol² * (0.36 mol)²) / ((300 mL / 1000) L)²) * ((300 mL / 1000) L - (3.18 x 10^-5 m³/mol * 0.36 mol)) = 0.36 mol * 8.314 J/(mol.K) * 225 K
After solving for P, we get:
P = 0.01369 atm
(c) The reason for the difference between the ideal gas law and the van der Waals equation is that the van der Waals equation takes into account the volume of gas molecules and the attractions between them, while the ideal gas law assumes that gas molecules have no volume or attractions. The difference is relatively small in this case because the pressure and temperature are not very high or low.