Question

A sheet of polyethylene 1.5-mm thick is being used as an oxygen barrier at a temperature of 600K. If the flux is 2.48 x 10-5 kg/m2 s, what concentration of oxygen must be maintained on the high-pressure side to ensure that the concentration

Answer 1

Complete Question

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Answer:

The concentration of  high-pressure side is  $C_1 = 0.722 \ kg/m^3$

Explanation:

From the question we are told that

    The thickness of the polyethylene is  $d = 1.5 \ mm = 0.0015 \ m$

     The  temperature is  $T = 600 \ K$

      The flux is  $JA = 2.48 *10^{-5} \ kg/m^2\cdot s$

      The concentration on the low-pressure side is  $C_2 = 0.5 \ kg/m^3$

       The initial diffusivity  is  $D_o = 6.2 *10^{-4} \ m^2 /s$

       The activation energy for  diffusion is   $Q_d = 41 \ kJ /mol = 41*10^3 J /mol$

Generally the diffusivity  of the oxygen at 600 K can be  mathematically evaluated  as

        $D = D_o * e^{- \frac{Q_d}{R * T } }$  

substituting values  

         $D = 6.2*10^{-4} * e^{- \frac{41 *10^3}{8.314 * 600 } }$  

          $D = 1.671 *10^{-7} \ m^2 /s$  

Generally the flux is mathematically represented as

          $JA = D * \frac{C_1 -C_2}{d}$

Where $C_1$ is the concentration of oxygen at the higher side

       So  

             $C_1 = d * \frac{JA}{D} + C_2$

substituting values  

             $C_1 = 0.0015 * \frac{2.48*10^{-5}}{1.671*10^{-7}} + 0.5$

              $C_1 = 0.722 \ kg/m^3$