(Solved): The permeability coefficient of a type of small gas molecule in a polymer is dependent on absolute t ...

The permeability coefficient of a type of small gas molecule in a polymer is dependent on absolute temperature according to the following equation:

where and PMo and Qp are constants for a given gas-polymer pair. Consider the diffusion of hydrogen through a poly(dimethyl siloxane) (PDMSO) sheet 15 mm thick. The hydrogen pressures at the two faces are 23 kPa and 1 kPa, which are maintained constant. Assume a condition of steady state diffusion and the following:

Compute the diffusion flux [in (cm³ STP)/cm² –s] at 308 K. for this diffusion system.

The permeability coefficient of a type of small gas molecule in a polymer is dependent on absolute temperature according to the following equation: \[ P_{M}=P_{M o} \exp \left(-\frac{Q_{p}}{R T}\right) \] where and and are constants for a given gas-polymer pair. Consider the diffusion of hydrogen through a poly(dimethyl siloxane) (PDMSO) sheet \( 15 \mathrm{~mm} \) thick. The hydrogen pressures at the two faces are \( 23 \mathrm{kPa} \) and \( 1 \mathrm{kPa} \), which are maintained constant. Assume a condition of steady state diffusion and the following: \[ \begin{array}{l} P_{M_{0}}=1.45 \times 10^{-8}\left(\mathrm{~cm}^{3} \mathrm{STP}\right)(\mathrm{cm}) / \mathrm{cm}^{2}-\mathrm{s}-\mathrm{Pa} \\ Q_{p}=13.7 \mathrm{~kJ} / \mathrm{mol} \end{array} \] Compute the diffusion flux \( \left[\right. \) in \( \left.\left(\mathrm{cm}^{3} \mathrm{STP}\right) / \mathrm{cm}^{2}-\mathrm{s}\right] \) at \( 308 \mathrm{~K} \). for this diffusion system. \[ J=0.00000563223(\mathrm{~cm} 3 \text { STP) } / \mathrm{cm} 2-\mathrm{s} \] \[ J=0.00000145433(\mathrm{~cm} 3 \text { STP) } / \mathrm{cm} 2-\mathrm{s} \] \[ J=0.000001007101 \mathrm{~cm} 3 \mathrm{STP} / \mathrm{cm} 2-\mathrm{s} \] \[ J=1.71 \mathrm{E}-7(\mathrm{~cm} 3 \mathrm{STP}) / \mathrm{cm} 2-\mathrm{s} \]