a . By differentiation, find an expression for the coefficient of thermal expansion of a gas obeying the van der Waals equation of state. b . Find the value of the coefficient of thermal expansion of nitrogen gas at 298.15 K and V = 24.4 L mol -1. 1.36 .* Write an expression for the isotherm al com pressibility of a nonideal gas obeying the Redlich- Kwong equation of state 1.37. The experimental value of the compression factor Z= PV /RT for hydrogen gas at T= 273.15 K and Vm = 0.1497 L/mol -i is 1.13 36. Find the values of Z predicted by the van der Waals, Dieterici, and Redlich - Kwong equations of state for these conditions. Calculate the percent error for each. 1.38 . The parameters for the van der Waals equation of state for a mixture of gases can be approximated by use of the mixing rules: a = alxi + a12x1x2 + azx2 b = bix, + b12*1-*2 + bzx? Where x, and x, are the mole fractions of the two substances and where a,,b , a,, and b, are the van der Waals parameters of the two substances . The quantities a 12 and b, 2 are defined by a12 = (a12)1/2 (bis + 6, 13 ) 3 b12 = a . Using these mixing rules and the van der Waals equation of state, find the pressure of a mixture of 0.79 molof N, and 0.21 mol of O, at 298.15 K and at a mean molar volume (defined as V/ .; ) of 0.00350 mamol -. Compare your answer with the pressure of an ideal gas under the same conditions. b . Using the van der Waals equation of state , find the pressure of pure N, at 298.15 K and at a molar volume of 0.00350 m 3 mol - 1. c. Using the van der Waals equation of state , find the pressure of pure O, at 298.15 K and at a molar volume of 0.00350 m 3mol-i