Set up a Mathematica notebook with Problem Set 6 as the Title Cell, and your name in the subtitle. Make a separate Section Cell for each problem below. 1) Solve the equations below, using Inverse[ ]. Display the result with MatrixForm[] for easier reading. 0.996V1+0.196V2=10.004V1+0.004V2=0.02V30.800V2=0.98V3 2) Ammonia can be described with the van der Waals equation of state: P=VbRTV2a where a=425.3kPaL2/mol2 and b=0.0374L/mol. a) With P in kPa,V and b in L/mol, and T in Kelvin, what is the value of R you should use? (Hint: consider the units in the ideal gas law.) b) Plot the isotherm (the right-hand side, i.e., "what P equals") versus V using Plot[ ]. It is helpful to also plot a horizontal line at 5000kPa to compare to the isotherm. Combine these two lines in one plot (this is a list of two functions). V should range from 0.055 to 1 , in order to get a good picture of what is going on. c) Evaluate the molar volumes of liquid and vapor phase ammonia at T=350K and P=5000kPa using i) FindRoot[ ] and ii) NSolve[ ]