In his investigations of the relationship of the volume of a gas to its temperature at a fixed pressure, John Dalton reported that a volume of air expanded nearly by "equal parts" with a 77.5 degree F increase in temperature from 55 degree F to 132.5 degree F, and with another 77.5 degree F increase in temperature from 132.5 degree F to 210 degree F. a) Suppose that the gas is ideal. Then one mole occupies 23.463 L at 55.0 degree F and p = 1.000 atm. Find the increase in the volume of the gas when the temperature is raised to 132.5 degree F, while the pressure stays at 1.000 atm. b) Then find the increase in the volume of the gas when the temperature is raised further from 132.5 degree F to 210.0 degree F, while p = 1.000 atm. c) Did the volumes increase by "equal parts" with the two temperature increases? d) Suppose that Dalton was working with nitrogen gas. The van der Waals parameters for nitrogen are a = 1.3661 dm^6 bar mol^-2 = 1.3483 dm^6 atm/mol^-2 and b = 0.038577 dm^3 mol^-1. Assuming that the van der Waals equation provides a good description of nitrogen gas, find the volume of one mole of the gas at T = 55.0 degree F and p = 1.000 atm. You will need to solve for the volume numerically here and also in parts e) and f). e) Find the volume of one mole of nitrogen gas according to the van der Waals equation, when T = 132.5 degree F and p = 1.000 atm. f) Find the volume of one mole of nitrogen gas according to the van der Waals equation, when T = 210.0 degree F and p = 1.000 atm. g) According to Dalton, Col. Roi claimed that the volume increase in part f) should be smaller than the increase in part e), while de Morveau claimed that the volume increase in part f) should be greater than the increase in part e). Based on your results, who is right, Col. Roi or de Morveau?