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Using the mechanical EOS given in your book, calculate the critical compressibility Zc = PcV c RTc for (a) the van der Waals equation, (b) the Soave equation, and (c) the Peng–Robinson equation. (d) Discuss the relative accuracy of each equation in relation to real fluids by comparing to the critical compressibilities for methane, n-butane, n-octane, methanol and water.