Comprehensive fitting exercise (200 points)

Your task is to calculate the fugacity coefficient φ of HCN at concentration c = 1/V_m = 8 mol/L from the concentration–pressure data given below.
Use the ideal gas constant value R = 8.31446 J/(mol K).
The temperature T is only slightly above the critical temperature which makes fitting difficult.

The formula is (details in Czech)

ln φ(c) = ∫₀^c ([ z(c') − 1 ] /c') dc' − ln z(c) + z(c) − 1,

z(c) = p(c)/cRT.

Hints:

• The simplest possibility for p(c) is the truncated virial expansion,
      p(c) = cRT(1 + Bc + Cc² + Dc³ + ... ),
  where B, C, D... are parameters.
• Do not forget to convert units appropriately.
• Fit the parameters, determine s = √S²/(n−p) and also the covariance matrix.
• Plot the data of p(c) along with their fit.
• Repeat the above points with a different number of parameters. Determine the best number of parameters.
• Integrate the formula for ln φ(c) analytically.
• Calculate φ(c) with the error estimate (standard deviation).