I'm given a container of gas that is kept at constant temperature, and whose volume is decreased by applying pressure, from A to E, as the graph shows. I am given the temperature, the total moles in the container, and the following data: At B the molar volume is 1.153, and the pressure is 17.76. At C the molar volume is .8167, and the pressure is 17.76. At D the molar volume is .032, and the pressure is 17.76.
Given this data, and I emphasize, only this data (no critical P, T, or Vmolar), find the van der Waals constants, a and b, for the gas.
I've been working on it for 3 hours and so far all I can come up with is a single equation in terms of a and b at point B: 17.76=RT/(Vmolar-b) - a/Vmolar^2 At point C, the equation would be the same as what I came up with for B, since the temperature and pressure remains the same as B, and we're in the region of co-existence, so Vmolar is at its maximum for the gaseous phase and therefore also is the same as in B (any further increase in Vmolar causes precipitation).
Any and all help is greatly appreciated.