Problem 1 (Tosun): Modified Atmosphere Packaging (MAP) is the process of adjusting the gas composition in the headspace of food packages to prolong shelf life. The gas mixture usually consists of carbon dioxide, nitrogen, and oxygen. Meat packages, for example, contain high concentrations of carbon dioxide to prevent the growth of microor- ganisms by suppressing microbial activity. Consider one-dimensional diffusion of carbon dioxide through a new polymeric film 270 um thick under steady conditions. The partial pressure of carbon dioxide inside the package is 0.6 atm and outside it is 0.03 atm. If PM = 19 barrer, estimate the molar flux of carbon dioxide. A small note regarding units of solubility and permeability: Solubility SB/A (of gas B in solid A) has units of (mtp of B)/(m of A)/Pa (of partial pressure of gas m(STP) outside solid). Hence the solubility units can be written as The solubility m3 Pa of h20 in HDPE at 25 C would be 9 x 10-6 m(STP) (Basmadjian, Table 3.6). Since m3 Pa appending 10-6 (or an appropriately power) to each of the table entries, Basmadjian m(STP) multiplies each of the values by 106. That is the same as altering the units to m3MPa m(STP) m2 The product of SB/A and DBA is the permeability PB/A and is given by m3 Pa m(STP) In many of your problems, you may not want PB/A in units of but in mPa kilo moles (of B) units of m3 Pa To do this conversion, we simply divide PB/A in units m(STP) PBA kilomoles of B m2 by 22.4 m (STP)/kilomole. So, m3 Pa 22.4 m3 (of A)Pa m(STP) m2 permeability is more useful units if PB/A is in units of m3 Pa Basmadjian gives values of permability and solubility using cm rather than m for length scale. It does not make a difference for solubility becase the the length scales on the numerator and denominator cancel. They do not for permeability. The way to use Basmadian's permeability values is as follows: (1) convert the units to SI system - take X- S m2 X S m2 S m? of is a S cm2 the values in Basmadjian's table and multiply by 10-13 (as suggested by Basmadjian) and then by 10-4 to get to SI units. (2) Take this value and divide by 22.4 to get permeability kilomoles of B m in units of m3(of A)Pa Now we come to barrer! What is this barrer? It is defined as follows: cm(STP) 1 barrer = 10-10 cm(of solid)cmHg s 1 bar = 105 Pa = 75 cmHg 1 cmHg = 1333.22 Pa. Hence m(STP) m2 1 barrer = 10-14 m(STP) m2 75 x 10-19 m(of solid) 1333.22 Pa m(of solid) Pa Now you know how to convert 19 barrer. Irrespective of all these units, keep in mind that in m'p = - the permittivity has units of s, yes, just s. It is more useful to write it in the form kgm-25-1 Obviously, Pa.m-1 S 9 1 PB/A and are related to each other - they only differ in the units
