The experimental critical constants for water are 647.126K, 217.66 atm, and 0.05

Question

The experimental critical constants for water are 647.126K, 217.66 atm, and 0.05595 L mol-1. Calculate the values for the Van der Waals constants a and b from these values. By substitution in the Van der Waals equation of state, obtain a value for the gas constant, R, and calculate the percentage by which it deviates from the accepted value of the Universal Gas Constant. Calculate the experimental critical compression factor for water and the percentage by which it deviates from the Van der Waals value. Predict the Boyle temperature for water based on the assumption that it obeys the Van der Waals equation of state.

Explanation / Answer

Pc = a/27b^2 = 217.66....(1) Tc = 8a / 27bR = 647.126 K....(2) Vc = 3b = 0.05595....(3) From (3), b = 0.01865 L/mol From (1), a = 217.66 * 27*b*b = 2.0441 L2 atm / mol2 Van der wall eqn: (Pc + a/Vc2) (Vc - b) = RTc 870.643 * 0.0373 = R * 647.126 R = 0.05018 R accepted = 0.0821 Deviation %age = 38.8% Compression factor varies inversely with R. so Experimental = K*12.18 Vanderwall = K*19.93 Deviation %age = 63 %

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