A solution of ethanol is in a cylindrical bottle, of radius 5 cm, with a head sp

Question

A solution of ethanol is in a cylindrical bottle, of radius 5 cm, with a head space of stagnant airextending 5 cm above the ethanol. The ethanol can evaporate into the air, and you are to consider the reduction in ethanol loss by placing a permeable cork (0.1 mm thick) at the top ofthe bottle. The bottle, with cork, is shown in the following figure:

a) If the price of ethanol is $39 per kmol, what is the cost of ethanol evaporated per year without the cork?

b) If the cork is added, what is the cost of ethanol lost per year?

0.0001 m The total pressure in the gas phase is 1 atm, with or without the cork. The vapor pressure of ethanol is 0.08 atm (8100 and the pressure of ethanol outside the bottle (above the cork) is 0. 0.05 m You may assume that: -the height of ethanol in the bottle remains constant (it is refilled periodically to account for any evaporation) pBM may be approximated at 0.96 atm, Necessary Data: temperature is 300 K. ethanol diffusion coefficient for ethanol in air at 300 Kis 7x10-4 m2/s. permeability of ethanol through the cork material at 300 K is PM- 12 m3 ethanol(STP) s m2 Pa/m area of a circle is Tr 0.05 m R 8314 J/kmol K.

Explanation / Answer

The formula for diffusion of A through non-diffusing B is

=D*Pt(Pa1 - Pa2) / (R*T*Z*PBM)

D = diffusivity = 7*10-4 m2/s

Pt = total pressure = 1 atm

Pa1 = 0.08 atm and Pa2 = 0

R =8314 J/molK

T = temperature = 300 K

part (a)

flux = 4.736*10-5 kmol/m2s

area = 3.14*0.052 = 7.854*10-3 m2

Hence, cost = 39*flux*area*365*24*3600

cost = 457.48

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