Final answer:
To find the net force due to the nitrogen on one wall of the container, use the ideal gas law and the formula for pressure. The net force is greater than the weight of the sample.
so the correct answer is (a) Net force: 4.94 L.atm; Weight comparison: Net force is greater.
Step-by-step explanation:
To find the net force due to the nitrogen on one wall of the container, we can use the ideal gas law and the formula for pressure.
The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.
Rearranging the equation to solve for pressure, we get P = (nRT)/V. Plugging in the values given in the question, we have P = (0.500 mol)(0.0821 L.atm/mol.K)(298 K) / 2.00 L = 2.47 atm. Since force is equal to pressure times area, and the area of one wall of the container is V, the net force is 2.47 atm * 2.00 L = 4.94 L.atm.
To compare this force to the sample's weight, we need to calculate the weight of the nitrogen gas. The weight of an object is equal to its mass times the acceleration due to gravity.
The mass of the nitrogen gas can be calculated by multiplying the number of moles by the molar mass. The molar mass of nitrogen gas is 28.01 g/mol, so the mass of the nitrogen gas is (0.500 mol)(28.01 g/mol) = 14.01 g. Converting the mass to kilograms, we get 0.01401 kg.
The weight is then (0.01401 kg)(9.8 m/s^2) = 0.137 N. Comparing the net force (4.94 L.atm) to the weight (0.137 N), we can see that the net force is greater, so the correct answer is (a) Net force: 4.94 L.atm; Weight comparison: Net force is greater.