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When temperature and pressure confitions are not too severe, equations of state me be integrated explicitly to determine the fugacity of a gas. Derive an expression for ln(f/p) for a van der Waal's gas. (HINT: Wrtie van der Waals equation in virial form.) Use your equation to calculate (a) the fugacities and (b) the fugacity coefficients for methane at the following pressures: 0, 10, 1000, and 500 atmospheres. At what pressures are the fugacity coefficients equal to unity? at what pressures is the fugacity equal to 1.0000 atm?