You are analyzing the loss of co2 from a 12 fl. oz. straight-walled bottle filled with 95 vol% co2 at 25 °c and a pressure of 55 psig. the bottle is 9" tall and 2.5" in internal diameter. the hemispherical bottom is covered by a 2" tall base cap that serves as a permeation barrier. in its upper 3" section, the bottle has a very thick wall which provides significant barrier relative to the 0.27 mm sidewall. you decide to estimate the molar loss over a 24 hour period (to allow adoption of a pseudo-steady state assumption).
a. sketch the system.
b. set up the problem and show all steps of the process.
c. perform the calculation (determine the loss of co2 over a day's period).
additional assumptions:
the diffusion coefficient for co2 though the sidewall is 2.0x10-13 m²/s.
the solubility of the co2 into the sidewall is 1.1x104 g/m3/bar (where the pressure units refer to the partial pressure of co2).
ambient pressure is o psig. the atmospheric co2 concentration is 407 ppm.
because the co2 concentration in the sidewall is relatively small, the local molar concentration, c, can be deemed constant.