Hi, this question is a ccalculation based chemistry question with the use of Mathematica. If you’re experienced with mathematica I’d appreciate the help because I must program it to run on it. Here is the question:
It is claimed that for some temperature, the van der Waals isotherm has an inflection point. Calculus
says that if the isotherm has an inflection point (a point here means a specific value of v and T) then at that point (dp/dv) and d2p/dv2 (second derivative) at constant temperature. These expressions contain partial derivatives of pressure with the volume. The subscript T indicates that when the
partial derivative is taken the temperature is held constant. The temperature T at which the isotherm has an inflection
point is called the critical temperature and it is denoted by Tc. The molar volume v at which the isotherm has an
inflection point is called the critical molar volume and it is denoted by vc. The values of v and T that satisfy equations
(1) and (2) are vc and Tc. Solve these equations analytically and express Tc and vc in terms of the parameters a and
b. If you insert Tc and vc in the van der Waals equation of state, you get the critical pressure pc in terms of a and b.
Determine the equations that express Tc, vc, and pc in terms of the parameters a and b (do not use numerical values for
a and b for ethane; get equations valid for any gas).
Help please! I have attached my work below in an .txt file, although it should be a .nb file for the mathematica code!