Assume that a water/acetic acid solution can be considered as an ideal solution.

Question

Assume that a water/acetic acid solution can be considered as an ideal solution. For 25 degree C and 1bar, complete the following calculations and state all necessary assumptions. The specific volume of water at the given T, P is 1.003 times 10^-3m^3/kg. Assume that water is an incompressible liquid. Calculate the Ponyting correction factor for pure water. Is Raoult's law justified for this condition? The vapor pressure of water at the given T is 0.03166bar. Calculate the fugacity of water in the solution at xH_2O = 0.42.

Explanation / Answer

1.

Saturation pressure of water at 25 degree C, Psat = 0.03166 bar = 3166 Pa

Pressure, P = 1 bar = 100000 pa

Poynting correction factor = exp (VL ( P - Psat) / (RT))

Molar volume, VL = 1.003 x 10-3 / 1000 * 18 = 1.81 x 10-5 m3/mol

Temperature, T = 25 + 273.15 K = 298.15 K

Poynting correction factor, = exp (1.81 x 10-5 * ( 100000 - 3166) / (8.314 * 298.15)) = 1.0007

Raoult's Law is justified for this condition because:

a) Poynting correction factor is nearly equal to 1.

b) Saturated vapor of water is highly dilute or fugacity coefficient, = 1

2.

Mole fraction of water, X = 0.42

Fugacity of water, f = * Psat * * X

f = 1 * 0.03166 * 1.0007 * 0.42 = 0.0133 bar

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