Answer:
[tex]D_{2} = 2.590\times 10^{-13}\,\frac{m^{2}}{s}[/tex]
Explanation:
The diffusion coefficient is computed by using this Arrhenius-type Model:
[tex]D = D_{o} \cdot e^{-\frac{E}{R_{u}\cdot T} }[/tex]
The following is constructed by dividing to two distinct diffusion coefficients:
[tex]\frac{D_{2}}{D_{1}} = \frac{e^{\frac{E}{R_{u}\cdot T_{1}} }}{e^{\frac{E}{R_{u}\cdot T_{2}}}}[/tex]
[tex]\frac{D_{2}}{D_{1}} = e^{\frac{E}{R_{u}}\cdot (\frac{1}{T_{1}}-\frac{1}{T_{2}} ) }[/tex]
Any diffusion coefficient at a different temperature can be found by using this formula:
[tex]D_{2} = D_{1}\cdot e^{\frac{E}{R_{u}}\cdot (\frac{1}{T_{1}}-\frac{1}{T_{2}} ) }[/tex]
[tex]D_{2} = (7.7\times 10^{-12}\,\frac{m^{2}}{s})\cdot e^{\frac{124000\,\frac{kJ}{kmol} }{8.314\frac{kPa\cdot m^{3}}{kmol\cdot K}}\cdot (\frac{1}{1423.15\,K}-\frac{1}{1075.15\,K} ) }[/tex]
[tex]D_{2} = 2.590\times 10^{-13}\,\frac{m^{2}}{s}[/tex]
