Explain how the van der waals equation of state, which interrelates pressure, p, molar volume, v, and absolute temperature, t, equation (1), takes account of departures from ideal-gas behaviour. what is the significance of the constants a and b in the equation and what are the units of a and b? (b) (p+(b) rt (1) [3 marks] for any equation of state used to describe the behaviour of a gas, what three mathematical cond itions must be satisfied at the critical point? (c) [2 marks] (d) if the van der waals equation is used, derive three equations which may be solved simultaneously to find values for the critical pressure, p, critical molar volume, ve, and critical temperature, te, in terms of the constants a, b and r note you are not being asked to sol ve the equations [3 marks] given that the critical compressibility factor = and a 30? pc and b = e rewrite the van der waals equation explicitly for reduced pressure, p, as a function of reduced temperature, tr, and reduced molar volume . [5 marks] (e) in terms of reduced variables, the thermal expansivity of a gas, a, is given by (f) equation (2) (2) pr starting from the equation you derived in part (e), derive an equation for a in terms of , and t