The Redlich-Kwong equation of state was perhaps the first predictive equation of state that moved beyond the 1873 equation developed by van der Waals. It relates pressure P, molar volume V, and temperature T as P=VbRTV(V+b)a/TZ=1+ZBBZ+BA The second form (in terms of ZPV/RT) is easier to use numerically for obtaining a solution when (T,P) are specified. This equation of state is capable of predicting a liquid phase (small V ) as well as a vapor phase (higher V ) for temperatures and pressures that are below the critical point. The parameters are determined as b=0.08664RTc/Pca=0.42747R2Tc2.5/PcB=bP/RTA=aP/R2T2.5 The parameters A and B combine a and b with the desired (T,P) in order to make the equation in Z easier to use. The labels Tc and Pc are the temperature and pressure of the critical point for the substance being considered. These are tabulated in many sources, including the books by Felder and Rousseau and by Dahm and Visco. The critical properties of isobutane are Tc=407.85K and Pc=36.40 bar. The gas constant in these units equals 83.14cm3bar/molK. 1. Use the Newton-Raphson method to solve for the molar volumes (in cm3/mol ) of isobutane vapor at the condition (T=350K,P=5 bar). NOTE: I encourage you to use the form of the equation of state in terms of Z, rather than P. You can use P, T, and the critical properties to determine A and B. Then solve for Z by root finding. Then determine V from V=ZRT/P. I know this seems like more work, but it is easier in the long run. Really. SUGGESTION: for an ideal gas, Z=1. This can be a useful first guess for determining the molar volume of a real gas